Apparatus and process for calculating an option

The present invention introduces an apparatus and process which may be implemented on a vast variety of computer systems. The apparatus and process of the present invention use a computer system to receive and store data representative of a particular asset, a type of option (call or put), requested exercise price and a multitude of other variables related to the asset. The apparatus and process then generate data representative of an option premium. The data representative of the option may then be used for transacting an option, as the basis for determining a correlated expiring option premium, or to determine the premium of an asset relatable to a corresponding option.

TECHNICAL FIELD
 The present invention relates generally to an apparatus and process for
 automatically calculating options for use in a variety of markets, such as
 commodities or securities markets.
 BACKGROUND
 An "option" is generally used to hedge risk by providing the right to
 purchase or sell a commodity or other asset at a later time at a set price
 with only limited obligations. An option is similar to an insurance policy
 in that it insures that an asset may be purchased or sold at a later time
 at a set price in return for a premium, often referred to as an option
 premium, which is generally a relatively small percentage of the current
 value of the asset. One type of option is a "call option." A "call" option
 gives the purchaser of the option the right, but not the obligation, to
 buy a particular asset at a later time at a guaranteed price, often
 referred to as the "exercise price." Another type of option is a "put
 option". A "put" option gives the purchaser of the option the right, but
 not the obligation, to sell a particular asset at a later time at the
 exercise price. (The "put" option may be thought of as giving the owner
 the right to "put" the security into another's name at the exercise
 price.) In either instance, the seller of the call or put option is
 obligated to perform the associated transactions if the purchaser chooses
 to exercise its option.
 Options are utilized in a variety of asset-based transactions. For example,
 in the commodities market, commodity producers (e.g., farmers) often enter
 into option relationships with commodity users (e.g., manufacturers) and
 speculators; in the real estate market, real estate owners often enter
 into option relationships with real estate purchasers; and in the
 securities market, security holders often enter into option relationships
 with security purchasers.
 COMMODITY MARKET EXAMPLES
 A commodity user such as a cereal manufacturer may need a certain amount of
 corn and wheat at a future date. The Cereal manufacturer, rather than
 purchasing the corn and wheat, may purchase a "call" option from a
 speculator by rendering an option premium. The call option guarantees an
 exercise price for a set amount of corn and wheat at a future date. The
 speculator, in return for receiving the option premium, agrees to obtain
 the set amount of corn and wheat and sell it to the cereal manufacturer at
 the exercise price at the future date.
 If the price of the desired commodities increases, then the cereal
 manufacturer will likely exercise the "call" option and obtain the set
 amount of commodities from the seller at the guaranteed exercise price.
 Therefore, by paying the option premium in advance of knowing the future
 value of the commodities, the cereal manufacturer may save itself a
 substantial amount of money. If the price of the desired commodities does
 not reach the exercise price then the cereal manufacturer will not
 exercise the call option and will purchase the commodities on the open
 market at the going price.
 A commodity producer, such as a farmer, may plant his fields many months in
 advance of having a commodity ready for delivery. To guarantee a set
 future price for his commodity, the farmer may purchase a "put" option
 from a speculator. Here, if the price of the farmer's commodities goes
 down over the set period of time the farmer is guaranteed to receive a set
 amount of minimum income for his efforts from the speculator.
 Prior art systems are only capable of transacting options which expire
 after a certain period of "time". The purchaser of a call or put option
 using the prior art systems only has the right to exercise the option
 before it expires or on the expiration date.
 As shown in FIGS. 8-11, for a set period of time, an option transacted
 using a prior art system has some value associated with it depending on
 the type of option, the current value of the asset relative to the
 exercise price and other variables. However, the moment after the option
 expires, a purchased option, as shown in FIGS. 8 and 9, is worthless
 causing an option purchaser who may have owned a valuable option one day
 to own a worthless option the next day. Furthermore, not only is the
 option worthless, but the purchaser of the call or put option is no longer
 protected against future price fluctuations associated with the asset. On
 the other hand, as shown in FIGS. 10 and 11, a sold option, which might be
 falling in value, automatically rises to the value of the option premium
 and removes all future risks to the option seller the moment after the
 option expires.
 Turning to FIG. 8, a call option on shares of Company A is shown with an
 option premium of $5 per share and an exercise price of $55 per share.
 Ignoring the effect of "time" and other nominal costs associated with
 transacting options, the value of the options on the shares of Company A
 may increase or decrease based on the current price of the shares. For
 example, if the current share price rose from $50 to $56, then the value
 of the purchased call option would increase because it would be more
 likely to be exercised at the $55 per share exercise price. Further, if
 the current share price rose to $60, then the value of the purchased call
 option would increase even more because the owner of the purchased call
 option could now purchase shares of Company A at the exercise price of $55
 and sell them for $60 on the open market resulting in a $5 per share
 profit. Moreover, the value of the purchased call option would continue to
 increase if the current share price of the shares of Company A continued
 to rise higher and higher. Accordingly, as long as the current price of
 the asset (the shares of Company A) continues to increase, the profits
 associated with the return on investment for a purchaser of a call option
 are unlimited. However, as might be expected, the exact opposite results
 for the seller of the call option (see FIG. 10) in that the losses
 attributed to the seller of a call option are unlimited.
 On the other hand, continuing to ignore the effect of "time," if the
 current share price dropped from $50 to $45, then the value of the
 purchased call option would decrease because it would be less likely to be
 exercised at the $55 per share exercise price. Moreover, as the current
 share price dropped further, the purchased call option would be even less
 likely to be exercised. However, unlike the situation above where the
 value of the purchased call option continued to increase as the current
 share price increased, for a purchased call option associated with an
 asset which decreases in value, the maximum loss associated with the
 return on investment is limited to the option premium (for this example,
 $5 per share). Again, the exact opposite results for the seller of the
 call option in that the profits realized by the seller of a call option
 are capped at the option premium.
 Referring to FIGS. 9 and 11, similar yet opposite results may be realized
 by the purchaser and seller of a put option, respectively, using a prior
 art system for transacting options. Here, assume that investor P purchases
 a put option from investors who sells the put option on the shares of
 Company A with an exercise price of $45 in six months in return for an
 option premium of $5 per share.
 Here, again ignoring the effect of "time or other nominal costs," if the
 value of the shares of Company A fell to $44, then the value of the
 purchased put option (FIG. 9) would increase because it would be more
 likely to be exercised. Moreover, if the value of the shares continued to
 fall to $40, then the value of the purchased put option would increase
 even more because the owner of the purchased put option would be able to
 obtain shares of Company A at a price of $40 per share and sell these same
 shares at $45 per share by exercising its put option resulting in a $5 per
 share profit. Accordingly, as long as the current price of the asset (the
 shares of Company A) continue to decrease, the profits associated with the
 return on investment for a purchaser of a put option are limited to the
 exercise price (less the option premium paid) if the asset price fell to
 zero. However, the seller of the put option (See FIG. 12) realizes
 potential losses equal to the exercise price (less the option premium
 received) if the asset price fell to zero.
 On the other hand, if the current share price increases, then the value of
 the purchased put option would decrease because it would be less likely to
 be exercised. However, regardless of how much the share price increased,
 the maximum loss associated with the return on investment that the
 purchaser of a put option would realize is limited to the option premium.
 In contrast, the seller of the put option realizes a maximum profit of the
 option premium.
 Based on the above examples, it should be readily apparent that, ignoring
 "time," the purchaser of a call or a put option may essentially realize an
 unlimited gain while limiting his or her potential loss to the amount of
 the option premium. On the other hand, the seller of a call or a put
 option acts as an insurer by collecting the option premium in return for
 insuring that the purchaser of the option will be able to buy or sell the
 underlying asset at the exercise price. Thus, the Seller assumes all of
 the risks. To reallocate the risks, the element of time is used in option
 trading. The purchaser of an option is only allowed to exercise the option
 over a preset increment of "time".
 Referring again to FIGS. 8 and 9, even though a purchased call option may
 increase in value as the current price of the asset increases, the value
 of the call option whose current price has yet to reach the exercise price
 must always battle "time." In other words, the closer that the call option
 gets to its expiration date, the more "time" will have a negative effect
 on the value of the purchased call option because "time" will be running
 out for the current price of the asset to reach the exercise price. If the
 current price of the asset on the expiration date is below the exercise
 price for the purchased call option the option holder will (1) be left
 holding an option worth absolutely nothing and (2) be left unprotected in
 its efforts to buy a particular asset at a later "time." Thus, the
 purchaser assumes much more of the risk when options are limited to set
 times.
 Therefore, there exists a need in the art for a technique to limit the risk
 that an option purchaser must assume, which at the same time, is not
 unfair to the option Seller. More specifically, there exists a need in the
 art for an apparatus and process for calculating an option which is not
 dependent on "time" and is a fair value for the option Seller. The
 applicant refers to such an option as an "expirationless option."
 Current techniques for calculating options are based on finite times such
 as 3 months, 6 months, 9 months, and at the most 3 years. In these
 techniques, the maximum price of an expiring option is considered to be
 the underlying security price. However, in actuality, the maximum price
 for any expiring option is its expirationless counter-part which is always
 less than the security price. For this reason, the probability space of
 expiring options has been incorrectly determined in the current art. This
 error helps explain inconsistencies in efficient markets such as
 "volatility smiles," where the theoretical price for an out-of-the-money
 option is higher than the actual price sellers are willing to receive.
 This error in pricing is because the probability distribution that is
 assumed in the current art is the value S, rather than the smaller value
 for an expirationless option. Therefore, there exists a need in the art
 for an apparatus and process to calculate option prices that are not based
 on the maximum price of the underlying security, but rather are based on
 the price of an expirationless option that is counter part to the expiring
 option.
 A margin position is a means for an investor to purchase the right to
 acquire a particular asset (e.g., security) for an indefinite
 (expirationless) amount of time without having to pay the entire value of
 the asset at the time of purchase. An investor purchases the right to
 acquire the particular asset by opening a "long" margin position or a
 "short" margin position. A long margin position (also referred to as a
 conditional purchase) is opened when the investor expects the value of the
 asset to increase, and a short margin position (also referred to as a
 conditional sale) is opened when the investor expects the value of the
 asset to decrease.
 As shown in FIG. 12, a long margin position investor realizes a Return On
 Investment ("ROI") equal to the current value of an asset when the
 investor closes the margin position less the value of the asset when he
 opened the margin positioned. Therefore, if the value of an asset
 increases from $20 to $30, then the long margin position investor realizes
 a $10 profit when it closes the margin position. However, if the value of
 the asset decreases to $5, then the same investor realizes a $15 loss.
 On the other hand, as shown in FIG. 13, a short margin position investor
 realizes a ROI equal to the value of the asset when the investor opened
 the margin position less the value of the asset when it closes the margin
 position. Therefore, if the value of an asset decreases from $20 to $5,
 then the short margin position investor realizes a $15 profit when it
 closes the margin position. However, if the value of the asset increases
 to $30, then the same investor realizes a $10 loss. These margin
 positions, both long and short, may or may not have an interest cost
 calculated on the value of the conditional sale or purchase.
 A margin price in the securities market for an expirationless option on a
 particular asset is usually much higher than an option premium for an
 expiring option on the same asset. One reason for the substantial
 difference between the margin requirement and the option premium for an
 expiring option is that the entity (e.g., exchange or broker) offering the
 margin position essentially assumes more risk because, unlike the expiring
 option, the margin position does not automatically expire after a preset
 period of "time," (unless, of course, the underlying asset expires, such
 as a futures or commodity contract). Additionally, while an option
 purchaser has the right but not the obligation to execute the contract,
 each party in a margin position is obligated to perform.
 Since any expiring asset must be a derivative of or represent a contingent
 claim on a non-expiring asset, the margin position is assumed to be on the
 base of a non-expiring asset. In the case of a futures contract on corn,
 though the margin position is actually for the futures contract which will
 expire, this margin requirement can be demonstrated to actually represent
 the margin requirement for the corn, or base asset, as well. Using current
 techniques, a change in the futures contract is accomplished by "rolling
 over", or exchanging one contract for another to maintain the maximum
 future date of delivery or sale. The present invention will make this
 unnecessary.
 Unlike an option premium, the margin requirement is essentially refundable
 to the investor of a margin position. This refund is realized in that the
 margin requirement is applied to the purchase price (current value) at the
 time the investor of a margin position closes the margin position.
 Entities responsible for regulating margin positions (unscientifically)
 select a margin requirement balancing the demand of investors, speculators
 and hedgers with the protection of the respective market from default
 risk. These entities typically present margin requirements either as a
 fixed dollar amount (margin amount) associated with a particular asset or
 a fixed percentage (margin percentage) of the current price (value) of the
 particular asset.
 A swap is a type of security transaction that is typically based on large
 amounts of money or securities wherein the parties to the swap exchange
 risks based on a notional amount. For instance, a swap may include Party A
 agreeing to pay a fixed interest rate on a certain amount of money (i.e.,
 100,000,000) to Party B, in exchange for Party B agreeing to pay a
 floating interest rate based on the same amount of money to Party A.
 Generally, the floating interest rate is based on an index, such as the
 T-bill rate, plus a fixed offset. As the underlying index fluctuates, the
 amount of money exchanged between Party A and Party B also fluctuates.
 However, the underlying amount of money, the $100,000,000, does not
 exchange hands.
 Expirationless put and call option prices, because they have to be equal at
 the money, or where the current security price equals the exercise price,
 are arbitrized results. This is because the value of American options must
 equal the value of a replicating portfolio to avoid arbitrage
 opportunities and be consistent with economic equilibrium. Expirationless
 options are equivalent to a "swap" on the upside potential on the
 underlying security for the down side potential on the underlying
 security, or vise versa. Expirationless options can be considered a
 financial swap where the notional value is the underlying security price.
 Thus, there exists a need in the art for an apparatus and a process for
 calculating the price of an expirationless option that can be used as the
 basis of a swap agreement.
 Experts in the securities market and other markets dealing with options
 have concluded for many years that any system for transacting an option
 can only generate an option premium, which is fair to both the purchaser
 and seller of the option, if data representing the "time" in which the
 option expires is input into the system. More specifically, all algorithms
 that have been derived for generating fair option premiums include a
 variable for "time". Such algorithms include the Black-Scholes and
 Binomial Pricing. While some professionals in the securities markets have
 discussed the pricing of expirationless options, they have ignored the
 arbitrized requirements that the put and call be equal at the money and
 have only focused on when and under what conditions exercise would be
 optimal. They have further ignored the equality of volatility and interest
 rate costs between expirationless options and the underlying security.
 This is a critical omission since, under the assumptions in the current
 art concerning rational expectations and the absence of economic
 dominance, the interest rate and volatility assumptions in an option
 position equivalent to the underlying security demands equality of
 volatility and interest rates between the expirationless option and the
 underlying security.
 Moreover, not only is there a need for a system capable of transacting a
 fairly calculated premium for an option not dependent on "time," but there
 is a further need for such a system to automatically transact purchases
 and sales of expirationless options instantaneously while handling (1) the
 constantly changing current asset prices and other variables associated
 with the option premium pricing and (2) the high volume (millions) of
 daily options transacted in the securities market and other markets.
 The above-referenced shortcomings, and other shortcoming of the prior art
 systems for calculating and transacting options that expire are
 effectively overcome by the present invention, as described in further
 detail below.
 SUMMARY
 The present invention includes an apparatus and a process for calculating
 and transacting options. In addition, the present apparatus and process
 for calculating option prices may be used in calculating and transacting
 any asset which can be constructed as an individual or series of options,
 regardless of their expiration date. The present invention may be applied
 for calculating expirationless options and option prices in the securities
 market, as well as a variety of other asset-based markets.
 The present invention takes advantage of the inefficiency associated with
 the unscientifically selected margin requirements. More specifically, the
 present invention is able to combine the expirationless feature of the
 margin position and the limited risk of the expiring option by recognizing
 that, because the margin requirement is unscientifically selected, a price
 (an option premium) exists that would cause many dealing in margin
 positions and expiring options to find great benefits in transacting
 expirationless options.
 The present invention takes advantage of the unscientifically selected
 margin requirements by recognizing a particular relationship between
 margin positions and options. As shown in FIG. 14, a long margin position
 is equivalent to a purchased expiring call option and a sold expiring put
 option when the effect of "time" is discounted. Additionally, as shown in
 FIG. 15, a short margin position is equivalent to a sold expiring call
 option and a purchased expiring put option. In sum, if the effect of
 "time" is discounted, an entity allowing an investor to open a margin
 position (e.g., a long margin position), is in the same position that it
 would be if it simply allowed an investor to purchase an expiring option
 (e.g., a call) and sell an expiring option (e.g., a put).
 A significant feature of the present invention is that it is able to
 discount the effect of "time" to allow a margin position to be equivalent
 to a purchased and sold option, as described above. Specifically, the
 present invention is able to utilize any one of the multitude of expiring
 option algorithms for determining fair expiring option premiums, as
 mentioned in the Background of the Invention, to discount the effect of
 "time."
 All expiring option premium algorithms, in addition to including a "time"
 variable, include readily observable variables, such as the current value
 (price) of the asset, the historic price volatility of the asset (the
 standard deviation of the asset's historic price movement) and the current
 risk-free interest rate (the rate of return without default risk, such as
 a U.S. government T-Bill rate). Further, all expiring option premium
 algorithms include variables for the exercise price. Accordingly, the
 present invention uses the expiring option premium algorithms to discount
 the effect of "time" according to the following process: (1) the exercise
 price is set equal to the current price of the asset and (2) the option
 premium is set equal to the margin requirement for the asset. The present
 invention then uses the expiring option premium algorithm to generate the
 anticipated point in "time" (implied time) in which an expiring option
 would expire if the purchaser paid an option premium equal to the
 unscientifically set margin requirement of the asset and if the exercise
 price was equal to the current asset price (as it is for a margin position
 at the moment it is opened).
 The present invention utilizes the above process because the exercise price
 is always equal to the current asset price at the moment when the margin
 position is opened, and this is the point in time when an investor of a
 margin position would gladly pay an inflated option premium equal to the
 margin position requirement to limit his risk. Accordingly, the present
 invention is able to discount "time" to price a purchased and sold option
 such that they are equivalent to a margin position at the point where the
 asset price is assumed equal to the exercise price.
 After the implied time value is generated, the present invention sets the
 time value in the expiring option premium algorithm equal to the implied
 time value. The present invention then generates an expirationless option
 premium based on the particular exercise price selected by the investor.
 The present invention may be implemented on a vast variety of computer
 systems. More particularly, the present invention employs a computer
 system to receive and store data representative of the particular asset, a
 type of option (call or put), a requested exercise price and the multitude
 of other variables related to transacting an expirationless option on the
 asset. Then, responsive to the data received, the present invention uses
 the computer system to generate data representative of an expirationless
 option premium, and to transact the expirationless option using the
 expirationless option premium.
 In use, when a user wishes to purchase or sell an expirationless option,
 the user is prompted to input data representative of the asset, the type
 of option and the requested exercise price for the asset, into a keyboard
 or other means of the computer system. The apparatus and process of the
 present invention then prompt the user to enter certain other data related
 to transacting an expirationless option on the asset. The certain other
 data includes the current price for the asset on the open market, the
 historic price volatility of the asset, the current risk-free interest
 rate and the margin requirement associated with the asset. Because this
 data typically changes frequently, the present invention may alternatively
 receive this data from one or more data source (e.g., a database or
 real-time quote service such as S&P ComStock), connected to the computer
 system of the present invention. After all of the data is received, it is
 stored on a storage medium of the computer system.
 The present invention then uses one of the expiring option premium
 algorithms to generate the data representative of the expirationless
 option premium. More specifically, the present invention temporarily sets
 the option premium variable of these algorithms to the margin requirement
 data, temporarily sets the exercise price variable of these algorithms to
 the current asset price data and generates data for the implied time of
 these algorithms. The present invention then uses the implied time data
 and the exercise price data input by the user to generate the data for the
 option premium variable of these algorithms.
 The option premium data generated is the expirationless option premium used
 to transact the expirationless option for the particular asset.
 Accordingly, the option premium data is output for use in completing the
 expirationless option transaction.
 The present invention is particularly important to those who wish to
 protect themselves against price swings for indefinite periods of "time."
 In other words, individuals and entities may now concern themselves solely
 with the future price of an asset, and cease concerning themselves with
 the seemingly impossible task of predicting the "time" in which the asset
 may hit that price.
 For example, a cereal manufacturer whose cereal prices to its customers
 depend significantly on the price in which they are able to purchase
 wheat, can now better assure their customers of steady cereal prices by
 purchasing an expirationless call option using the present invention. More
 specifically, the cereal manufacturer can now ensure itself that it may
 continue to purchase wheat at or below a certain price (the exercise
 price), regardless of the "time" in the future when the price of wheat
 rises above the exercise price. Referring to FIG. 16, by utilizing the
 present invention, in return for the option premium, the cereal
 manufacturer is able to purchase an expirationless call option which has
 unlimited upside potential, limited downside potential (the option
 premium) and never becomes worthless.
 On the other hand, a farmer whose family depends on being able to sell his
 entire crop of wheat for a set minimum price would benefit significantly.
 Specifically, the farmer who was unable to predict whether wheat prices
 might drop next year or in five years may purchase an expirationless put
 option using the present invention to ensure that his wheat will be
 purchased at a certain price (the exercise price) regardless of the "time"
 in the future when the price of wheat drops below the exercise price.
 Referring to FIG. 17, by utilizing the present invention, in return for an
 option premium, the farmer is able to purchase an expirationless put
 option which has unlimited upside potential, limited downside potential
 (the option premium) and never becomes worthless.
 Another aspect of the present invention is that it is capable of handling
 constantly changing current asset prices and other variables associated
 with generating the option premium price and transacting the
 expirationless option. As described above, by using one or more data
 source, data from a variety of places, regardless of location, may be
 constantly updated and stored for use in generating the option premium
 price at any given moment in time.
 A further aspect of the present invention is that it is capable of
 automatically and essentially instantaneously transacting an
 expirationless option in the securities market and other markets
 throughout the world. This is especially important in the securities
 market because millions of option contracts are typically transacted
 daily. This feature is also important because of the volatility of the
 variables used to generate the option premium price. This makes the
 essentially instantaneous transaction capability imperative, especially in
 the securities market.
 A yet further aspect of the present invention is that it is capable of
 handling extinction bands. An extinction band is a price higher than the
 exercise price for a put option and lower than the exercise price for a
 call option. The extinction band price is selected because a particular
 entity responsible for exchange management may wish to implement
 expirationless options without significantly increasing record-keeping
 requirements for the respective exchange. By introducing extinction bands,
 or forced closure of an expirationless option based not on time, but on
 the distance of the exercise price from the current asset price, an
 exchange may retain the aforementioned benefits of expirationless options
 for their members without significantly increasing record keeping
 requirements. The pricing algorithm for this variant of the expirationless
 option assumes that both the band, the maximum distance of the exercise
 price from the asset price and the extinction date (or the effective date
 of measurement of the exercise price from the current asset price) for
 these options is known. If these variables are not known, then the
 expirationless option with extinction bands is priced exactly as the
 expirationless option without extinction bands.
 A yet further aspect of the present invention is that it is capable of
 facilitating the determination of conventional expiring option premiums
 utilizing the expirationless option price as the maximum price for the
 expiring option. This allows for more accurate determination of the option
 price than is possible using the underlying security price as the maximum
 price of an expiring option.
 Yet another aspect of the present invention is that it is capable of
 facilitating the accurate determination of premiums for any financial
 instrument which can be expressed in terms of an option or combination of
 options. In order to determine a premium for a financial instrument, the
 premiums for corresponding option or options are first determined
 utilizing the corresponding expirationless option price. The expiring
 option premiums are then relatable to the premiums of the related
 financial instrument as appropriate for the instrument type. Examples of
 financial instruments which may be determined utilizing the present
 invention include, but are not limited to equity, bonds, futures, forwards
 and swaps.
 The aforementioned and other aspects of the present invention are described
 in the detailed description and attached illustrations which follow.

DETAILED DESCRIPTION
 The various aspects of the present invention may be implemented on numerous
 types of computer systems, but is preferably implemented on a
 client/server network 100 as shown in FIG. 1. The client/server network
 100 includes a server 110 connected to a plurality of clients 120, also
 known as end-user workstations, and a data source 130 running on a token
 ring environment.
 As shown in FIG. 2, each end user workstation 120 may includes a
 microprocessor 210, a display 220, a keyboard 230, a mouse 240, a printer
 260, and a storage medium 250 (e.g., a disk array, tape, optical drive,
 tape drive or floppy drive).
 As shown in FIG. 3, each server 110 may include a microprocessor 310 and a
 storage medium 350. The server may use Microsoft NT or peer-to-peer with
 one peer dedicated as a server or their equivalent.
 Data sources 130 may be a Quotron system or its equivalent, which may
 regularly receive data via satellite communications 135, land line
 connections (e.g., a modem) 137 or the like. However, any other source
 capable of receiving and providing data relevant to transacting the
 expirationless option may be used in the present invention.
 An exemplary client/server network suitable for implementing aspects of the
 present invention is a Windows NT PC LAN. These clients, servers, and
 client/server networks are mentioned for illustrative purposes only and,
 as may be appreciated by one of ordinary skill in the art, suitable
 equivalents may be substituted.
 In an exemplary embodiment, when a user wishes to purchase or sell an
 expirationless option related to a particular asset, the user may view the
 display 220 of the end user workstation 120 to obtain instructions on how
 to transact the expirationless option contract.
 Referring to FIG. 4, at step 410 of the Main Module, the display 220
 displays a prompt requesting the user to indicate when the user is ready
 to transact the expirationless option. By pressing the ENTER key on the
 keyboard 230 or clicking on a START box on the display 220 with the mouse
 240, the present invention starts its operation of transacting the
 expirationless option by proceeding to step 420. For simplicity purposes,
 it may be assumed that the microprocessor 210 of the end-user workstation
 120 and the microprocessor 310 of the server 110 coordinate all tasks of
 the end-user workstation 120 and server 110 of the computer system,
 respectively, and all tasks between the two.
 At step 415, the user is prompted to input data representative of a
 particular asset. Upon receiving the data representative of a particular
 asset, the present invention proceeds to step 420.
 At step 420, the user is prompted to select which option pricing algorithm
 he or she wishes to use to transact the expirationless option. Such
 algorithms include, but are not limited to, the Black-Scholes, the
 Binomial Pricing, the Finite Difference and the Analytic Approximation
 algorithms. These algorithms are widely used in connection with
 determining expiring option premiums and are available in both proprietary
 and shareware software from Montgomery Investment Technology. The option
 prices provided in this detailed description were determined using this
 free Internet service, and demonstrate that any option pricing algorithm
 may be used to determine expirationless option prices. For example, the
 Black-Scholes algorithm is:
 ##EQU1##
 Where:
 c=OPT_PREM=the option premium
 S=ASSET_PRICE=the current price for a particular asset
 X=X_PRICE=the exercise price
 r=T_BILL=the current risk-free interest rate
 s=VOLATLTY=the standard deviation of the historic asset price movement
 commonly referred to as the asset's volatility
 T=the time until expiration (for an expiring option)
 In another example, the Binomial Pricing algorithm is:
 ##EQU2##
 Where:
 c=OPT_PREM=the option premium
 S=ASSET_PRICE=the current price for a particular asset
 K=X_PRICE=the exercise price
 r=T_BILL=the current risk-free interest rate
 n=the number of periods (the time) until expiration (for an expiring
 option)
 ##EQU3##
 u=minimum value of an upward movement in the price of the underlying asset
 (e.g., $1/8.sup.th in most stocks), and
 d=minimum value of a downward movement in the price of the underlying asset
 ($0.0001 in most futures or commodities) Note: u and d are generally
 established by the exchange and may be stored in a storage medium for
 access or simply input into the system on an as needed basis.
 Further, as one of ordinary skill in the art would readily appreciate,
 other related expiring options algorithms may be used to transact an
 expirationless option. Upon receiving a number related to the user's
 selected algorithm processing continues at step 430. In an alternative
 embodiment step 420 may be removed entirely by only using a single option
 algorithm.
 At step 430, the user is prompted to input whether or not it wishes to
 include extinction bands in the expirationless option transaction. If the
 user selects no, then processing continues at step 500, otherwise
 processing continues at step 700.
 Referring to FIG. 5, at step 500 the CALC Module is executed. The CALC
 Module is used to calculate the expirationless option premium ignoring
 extinction bands. Of course, if used exclusively in markets or on
 exchanges without extinction bands, step 430 may be removed entirely.
 Processing then continues at step 600 where the DATA_ENTRY Module is
 executed. The DATA_ENTRY Module, as shown in FIG. 6, is used to prompt the
 user to input data and to accept the data input by the user.
 At step 601, the user is prompted to input the current price for the
 particular asset. The user may obtain the current price for the particular
 asset from a variety of sources, such as the data source 130. At step 602,
 it is determined whether the current price of the asset has been received.
 If not, then processing returns to step 601, otherwise the current price
 of the asset received is stored in the ASSET_PRICE variable in the storage
 medium 250 and processing continues at step 603.
 In another embodiment, steps 601 and 602 may be replaced by a step which
 automatically accesses the current price for the particular asset from the
 data source 130. In yet another embodiment, steps 601 and 602 may be
 replaced by a step which automatically accesses the current price for the
 particular asset from the storage medium 350 of the server 110 which may
 be updated automatically by the data source 130 or manually by an
 administrator of the network.
 At step 603, the user is prompted to input the current risk-free interest
 rate. The user may obtain the current risk-free interest rate from a
 variety of sources, such as the data source 130. At step 604, a
 determination is made as to whether the current risk-free interest rate
 has been received. If not, then the processing continues at step 603,
 otherwise the current risk-free interest rate received is stored in the
 T_BILL variable in the storage medium 250 and processing continues at step
 605.
 In another embodiment, steps 603 and 604 may be replaced by a step which
 automatically accesses the current risk-free interest rate from the data
 source 130. In yet another embodiment, steps 603 and 604 may be replaced
 by a step which automatically accesses the current risk-free interest rate
 from the storage medium 350 of the server 110 which may be updated
 automatically by the data source 130 or manually by an administrator of
 the network.
 At step 605, the user is prompted to input the standard deviation of the
 price movement related to the asset known as the "historic price
 volatility of the asset." The user may obtain the historic price
 volatility of the asset from a variety of sources, such as the data source
 130. At step 606, a determination is made as to whether the historic price
 volatility of the asset has been received. If not, then the processing
 continues at step 605, otherwise the historic price volatility of the
 asset received is stored in the VOLATLTY variable in the storage medium
 250 and processing continues at step 607.
 In another embodiment, steps 605 and 606 may be replaced by a step which
 automatically accesses the historic price volatility of the asset from the
 data source 130. In yet another embodiment, steps 605 and 606 may be
 replaced by a step which automatically accesses the historic price
 volatility of the asset from the storage medium 350 of the server 110
 which may be updated automatically by the data source 130 or manually by
 an administrator of the network.
 At step 607, the user is prompted to input the exercise price for the
 particular asset. At step 608, a determination is made as to whether the
 exercise price of the asset has been received. If not, then processing
 continues at step 607, otherwise the exercise price of the asset received
 is stored in the X_PRICE variable in the storage medium 250 and processing
 continues at step 609.
 At step 609, the user is prompted to input the option type (either a call
 option or a put option). At step 610, the present invention then verifies
 whether the option type has been received. If not, then the processing
 returns to step 609, otherwise the processing stores the option type under
 the OPT_TYPE variable in the storage medium 250 and proceeds to step 611.
 At step 611, the user is prompted to input the margin requirement (margin
 amount or margin percentage) related to the particular asset. The user may
 obtain the margin requirement from a variety of sources, such as the data
 source 130. At step 612, a determination is made as to whether the margin
 requirement for the asset has been received. If not, then processing
 returns to step 611, otherwise the margin requirement for the asset
 received is stored in the MARGIN variable in the storage medium 250 and
 processing continues at step 699, and then to step 510 of the CALC Module
 at FIG. 5.
 In another embodiment, steps 611 and 612 may be replaced by a step which
 automatically accesses the margin requirement from the data source 130. In
 yet another embodiment, steps 611 and 612 may be replaced by a step which
 automatically accesses the margin requirement from the storage medium 350
 of the server 10 which may be updated automatically by the data source 130
 or manually by an administrator of the network.
 At step 510, the temporary option premium is equated to the value of the
 margin requirement (MARGIN) and stored in the TEMP_OPT_PREM variable in
 the storage medium 250. Processing then continues at step 520, where a
 temporary exercise price is set equal to the current price of the asset
 (ASSET_PRICE) and the temporary exercise price is stored under the
 TX_PRICE variable in the storage medium 250. Processing then continues at
 step 530.
 At step 530, the implied time for the expirationless option is determined
 using the option pricing algorithm selected at step 420. The implied time
 is then stored in the IMPLD_T variable in the storage medium 250.
 Processing then continues at step 540.
 At step 540, the actual option premium for the expirationless option is
 determined by again using the option pricing algorithm selected at step
 420, the X_PRICE selected at step 607, and the implied time value
 (IMPLD_T). Processing then continues at step 440 of the Main Module at
 FIG. 4.
 Referring back to step 430, if the user selects to include extinction bands
 in the expirationless option transaction, processing continues at step 700
 of the CALC_E module. Referring to FIG. 7 at step 700 the CALC_E module
 calculates the expirationless option premium taking into account
 extinction bands.
 Processing then continues at step 600 at the DATA_ENTRY Module. Again, the
 DATA_ENTRY Module, as shown in FIG. 6, is used to prompt the user to input
 data and to accept the data input by the user.
 At step 601, the user is prompted to input the current price for the
 particular asset. The user may obtain the current price for the particular
 asset from a variety of sources, such as the data source 130. At step 602,
 a determination is made as to whether the current price of the asset has
 been received. If not, then processing returns to step 601, otherwise the
 current price of the asset received is stored in the ASSET_PRICE variable
 in the storage medium 250 and processing continues at step 603.
 In another embodiment, steps 601 and 602 may be replaced by a step which
 automatically accesses the current price from the data source 130. In yet
 another embodiment, steps 601 and 602 may be replaced by a step which
 automatically accesses the current price from the storage medium 350 of
 the server 110 which may be updated automatically by the data source 130
 or manually by an administrator of the network.
 At step 603, the user is prompted to input the current risk-free interest
 rate. The user may obtain the current risk-free interest rate from a
 variety of sources, such as the data source 130. At step 604, a
 determination is made as to whether the current risk-free interest rate
 has been received. If not, then processing returns to step 603, otherwise
 the current risk-free interest rate received is stored in the T_BILL
 variable in the storage medium 250 and processing continues at step 605.
 In another embodiment, steps 603 and 604 may be replaced by a step which
 automatically accesses the current risk-free interest rate from the data
 source 130. In yet another embodiment, steps 603 and 604 may be replaced
 by a step which automatically accesses the current risk-free interest rate
 from the storage medium 350 of the server 110 which may be updated
 automatically by the data source 130 or manually by an administrator of
 the network.
 At step 605, the user is prompted to input the standard deviation of the
 price movement related to the asset known as the "historic price
 volatility of the asset." The user may obtain the historic price
 volatility of the asset from a variety of sources, such as the data source
 130. At step 606, a determination is made as to whether the historic price
 volatility of the asset has been received. If not, processing returns to
 step 605, otherwise the historic price volatility of the asset received is
 stored in the VOLATLTY variable in the storage medium 250 and processing
 continues at step 607.
 In another embodiment, steps 605 and 606 may be replaced by a step which
 automatically accesses the historic price volatility of the asset from the
 data source 130. In yet another embodiment, steps 605 and 606 may be
 replaced by a step which automatically accesses the historic price
 volatility of the asset from the storage medium 350 of the server 110
 which may be updated automatically by the data source 130 or manually by
 an administrator of the network.
 At step 607, the user is prompted to input the exercise price for the
 particular asset. At step 608, the processing then verifies whether the
 exercise price of the asset has been received. If not, then the processing
 returns to step 607, otherwise the processing stores the exercise price of
 the asset received under the X_PRICE variable in the storage medium 250
 and proceeds to step 609.
 At step 609, the user is prompted to input the option type (either a call
 option or a put option). At step 610, a determination is made as to
 whether the option type has been received. If not, then processing returns
 to step 609, otherwise the option type is stored in the OPT_TYPE variable
 in the storage medium 250 and processing continues at step 611.
 At step 611, the user is prompted to input the margin requirement (margin
 amount or margin percentage) related to the particular asset. The user may
 obtain the margin requirement from a variety of sources, such as the data
 source 130. At step 612, a determination is made as to whether the margin
 requirement for the asset has been received. If not, then processing
 returns to step 611, otherwise the margin requirement for the asset
 received is stored in the MARGIN variable in the storage medium 250 and
 processing continues at step 699, and then to step 510 of the CALC_E
 Module at FIG. 7.
 In another embodiment, steps 611 and 612 may be replaced by a step which
 automatically accesses the margin requirement from the data source 130. In
 yet another embodiment, steps 611 and 612 may be replaced by a step which
 automatically accesses the margin requirement from the storage medium 350
 of the server 110 which may be updated automatically by the data source
 130 or manually by an administrator of the network.
 At step 710, the user is prompted to input whether or not it wishes to
 determine the extinction band in percentages or in dollars. If the user
 selects percentages, then processing continues at step 720, otherwise
 processing continues at step 750.
 At step 720, the user is prompted to input the percentage price movement to
 be used to determine the extinction band and the percentage is stored in
 the PERCENT variable in the storage medium 250. Processing then continues
 at step 725, where it determines whether the expirationless option type
 (OPTION_TYPE) is a "call" or a "put". If the expirationless option is a
 "call," then processing continues at step 730, otherwise processing
 continues at step 735.
 At step 730, the current asset price (ASSET_PRICE) for the "call" option is
 set to the current asset price (ASSET_PRICE) multiplied by the value
 composed of the percentage price movement (PERCENT) plus one. On the other
 hand, at step 735, the current asset price (ASSET_PRICE) for the "put"
 option is set to the current asset price (ASSET_PRICE) multiplied by the
 value composed of the percentage price movement (PERCENT) minus one.
 Processing then proceeds from step 730 or step 735 to step 775. Processing,
 at step 775, accesses and receives the extinction date for the particular
 asset (EXT_DATE) which has been set by the exchange and stored by the
 system administrator from the storage medium 250 or 350. Of course, the
 extinction date could also be manually input by the user of the present
 invention, who could manually input the extinction date set by the
 exchange each time the system is used. Processing then continues step 780.
 At step 780, processing then determines the option premium for the
 expirationless option taking into account the extinction band by again
 using the option pricing algorithm selected at step 420 and setting the
 value of time until expiration in the algorithm to EXT_DATE. Processing
 then continues at step 799.
 Referring back to step 710, if the user selects to use dollars to determine
 the extinction band, then the invention proceeds to step 750. At step 750,
 the user is prompted to input the minimum dollar amount price movement to
 be used to determine the extinction band, and the dollar amount price
 movement is stored in the TICK variable in the storage medium 250. At step
 755, processing then sets the BAND variable to dollars.
 Processing then continues at step 760, where a determination is made as to
 whether the expirationless option type (OPTION_TYPE) is a "call" or a
 "put" option. If the expirationless option is a "call," then processing
 continues at step 765, otherwise processing continues at step 770.
 At step 765, the current asset price (ASSET_PRICE) for the "call" option is
 set to the current asset price (ASSET_PRICE) plus the BAND divided by the
 dollar amount price movement (TICK). On the other hand, at step 770, the
 current asset price (ASSET_PRICE) for the "put" option is set to the
 current price (ASSET_PRICE) minus the BAND divided by the dollar amount
 price movement (TICK).
 Processing then continues at step 765 or step 770 to step 775. Processing
 continues at step 775, accesses and receives the extinction date for the
 particular asset (EXT_DATE) which has been set by the exchange and stored
 by the system administrator from the storage medium 250 or 350. Of course,
 the extinction date could also be manually input by the user, who could
 manually input the extinction date set by the exchange each time the
 system is used. Processing then continues at step 780.
 At step 780, processing then determines the option premium for the
 expirationless option taking into account the extinction band by again
 using the option pricing algorithm selected at step 420 and setting the
 value of time until expiration in the algorithm to EXT_DATE. The present
 invention then processing continues at step 799.
 At step 799, the present invention proceeds to step 440 of the Main Module
 at FIG. 4, where it stores the expirationless option premium under the
 variable OPT_PREM at the storage medium 250. At step 450, the processing
 may optionally complete the current financial transaction by issuing a buy
 or sell hard copy (ticket) to the user which includes the asset premium
 and other pertinent information related to the transaction.
 In another embodiment, rather than issuing a buy or sell hard copy to the
 user, the hard copy may be issued by printing a hard copy to a
 buyer/seller located in the "trading pit" at the Chicago Exchange, the
 "desk" at the New York Exchange, or at any other similar destination of
 other exchanges throughout the world. Once received by a buyer/seller at
 an exchange, the buyer/seller may then enter the confirmation order and
 other information to effect the transfer of any necessary funds upon the
 closing of the market, as is customary. In yet another embodiment, rather
 than issuing a buy or sell hard copy to the user, executing the
 transaction may include electronically placing or transferring the
 transaction information into a queue of a transaction server along with
 other transactions. When the queued transaction is removed from M the
 queue (i.e., by an operator or by a software program), a search for a
 matching order is performed (e.g., if the executed transaction is a buy,
 the operator or software program searches for a matching sell
 transaction). Thus, executing an expirationless option transaction
 includes, but is not limited to, issuing a hard copy to the user, issuing
 a hard copy to a buyer/seller at the exchange, or initiating an automatic
 electronic transaction. The present invention anticipates the use of these
 and other similar methods for executing the transaction and should not be
 limited to any particular method.
 The processing then proceeds to step 470, where the user is prompted to
 determine whether it wishes to transact another expirationless option. If
 yes, then the present invention proceeds to step 420, where the user is
 again prompted by the video display 220 to select an option pricing
 algorithm. If no, then the present invention proceeds to step 499, where
 it ends the expirationless option transactions for the current user.
 Of note, the exemplary embodiment of the present invention assumes that,
 even though they may not be in actuality, the interest rates and dividend
 yield associated with each particular asset (e.g., a stock, bond, etc.)
 are zero. The reason for the assumption is that algorithms used in
 connection with pricing the underlying asset already factor the interest
 rate and dividend yield into the asset price. These algorithms may be
 either mathematical, inductive or both. Accordingly, the present invention
 for transacting an expirationless options using the same algorithms used
 for expiring options factors the interest rate and dividend yield into the
 option premium, but at a value of zero to ensure both the call and the put
 option at S=X have a price equal to the margin requirement.
 The following examples illustrate the time/cost relationship between
 expiring options, premiums, expirationless options and margin
 requirements. Both examples assume a margin requirement of 25%, a current
 asset price of 150, a historic price volatility of 35%, and a current
 risk-free interest rate of 6%. Thus, using Black-Scholes algorithm, an
 implied time of 1210.09 days is derived.
 The first example assumes a call option with an exercise price of $60 is
 requested by the investor.

Expiring Expirationless
 Time to Option Option Margin
 Expiration Premium Premium Requirement
 Six Months $2.15 $9.29 $12.5
 One Year 4.59 9.29 12.5
 Eighteen 6.65 9.29 12.5
 Months
 Two Years 8.56 9.29 12.5
 Three Years 11.87 9.29 12.5
 Five Years 16.63 9.29 12.5
 Ten Years $27.04 $9.29 $12.5
 The second example assumes a put option with an exercise price of $40 is
 requested by the investor.

Expiring Expirationless
 Time to Option Option Margin
 Expiration Premium Premium Requirement
 Six Months 0.85 6.91 12.5
 One Year 1.78 6.91 12.5
 Eighteen 2.45 6.91 12.5
 Months
 Two Years 2.96 6.91 12.5
 Three Years 3.66 6.91 12.5
 Five Years 4.29 6.91 12.5
 Ten Years 4.45 6.91 12.5
 In another embodiment, the method of the current invention may be utilized
 to calculate an expirationless option premium using a simplified form of
 an expiring option algorithm. Typical option pricing calculations require
 not just a life expectancy of an expirationless option, but a volatility
 assumption over the life of the option as well. This would seem to be
 impossible over the undetermined time frame of the expirationless option.
 However, if the security price already contains an interest rate
 assumption, we can express the volatility portion of the Black-Scholes
 algorithm in terms of the current price. If we know the expirationless put
 and call must be equal in price, then we can solve for an implied time to
 expiration at S=X; and use this implied time to solve for option prices at
 exercise prices other than the current security price.
 For an expirationless option, the Black-Scholes formula takes the form:
EQU C=e.sup.-dt S N(d1)-E e.sup.-rt N(d2)
 Where
 C=Option Premium
 S=Current stock price
 E=Option exercise price
 T=Time to expiration
 d=Dividend yield
 r=Riskfree interest rate
 v=Stock volatility
 d1=[ln(S/E)+(r-d+0.5v.sup.2)T]/v SQRT(T)
 d2=d1-vSQRT(T)
 The expirationless call option price can be calculated by setting dividends
 and the risk-free rate to zero, and setting the exercise price equal to
 the stock price. An expirationless option can be calculated under any set
 of assumptions concerning the distribution of prices of the underlying
 security. This method assumes a log normal price distribution. It is then
 possible to calculate the time for which the call price=the put pice=0.5S.
 It should be clear that S is the lowest price to buy the security in the
 open market. In effect this will be the lower of the actual price or the
 margin requirement.
 The Black-Scholes formula reduces to the following. Note that N is the
 cumulative normal distribution while NINV is the inverse cumulative normal
 distribution. Also, the call price=the put price=0.5 S, and is referred to
 as the variable Margin.
EQU C=0.5S=S N(d1)-S N(d2)
EQU 0.5=N(d1)-N(d2)
 ##EQU4##
 Since:
EQU Margin=N(0.5V SQRT(T))-N(-0.5V SQRT(T))
 And N(0.5v SQRT(T) and N(-0.5v SQRT(T)) are opposing numbers around zero,
 then
EQU Margin/2=N(0.5v SQRT(T))
EQU NINV(Margin/2)=0.5V SQRT(T)
EQU NINV(Margin/2)/0.5v=SQRT(T)
EQU (NINV(Margin/2)0.5v)).sup.2 =T
 Now that time is purely a function of volatility it can be applied back to
 the Black-Scholes formula as follows:
EQU Allowing x=2 NJNV (Margin/2) and T=(x/v).sup.2 =x.sup.2 /v.sup.2
 ##EQU5##
 From the equation above for the expirationless option we apply d1 and d2.
EQU EPO=C=SN(In(S/E)/x+0.5x)-EN(In(S/E)/x-0.5x)
 Therefore, the expirationless option premium can be calculated purely as a
 function of the stock price and the exercise price and x, where x=2 NINV
 (Margin/2).
 In yet another embodiment, the method of the present invention may be
 utilized to calculate an expirationless option premium which may then, in
 turn, be utilized as a basis to determine a premium for a conventional
 expiring option. Previous methods for pricing expiring options have
 considered the maximum price of an expiring option to be the price of the
 underlying security. However, the maximum price of an expiring option is
 actually not the price of the underlying security, but is instead the
 price of an otherwise identical expirationless option. Accordingly, by
 utilizing the value for an expirationless option as determined under the
 present invention, the price of a traditional expiring option can be more
 accurately calculated. The method for determining an expiring option price
 utilizing an expirationless option premium determined according to the
 method of the present invention proceeds generally as follows. First, data
 representative of the particular asset underlying the expiring option, the
 option type (call or put), an exercise price for the option, the current
 price of the particular asset underlying the option, the historic price
 volatility of the particular asset and the margin requirement for the
 particular asset are input at step. Then, the current price of the
 underlying security is used as the expiration price to solve an expiring
 option equation (such as the Black-Scholes, the Binomial Pricing, the
 Finite Difference and the Analytic Approximation algorithms) for an
 implied time to expiration. Next, the implied time to expiration is used
 as the basis for calculating the price for the corresponding
 expirationless option. The expirationless option price is then used as the
 maximum price of the corresponding expiring option in determining the
 premium for the expiring option.
 In regards to an expirationless option, the present invention includes any
 contingent claim upon the assets, promise of payment, equity, production
 units or currency of any group, organization, body, institution or
 collective over any measure of time and any measure of value, regardless
 of whether the claim has an artificial minimum (floor) or maximum (cap),
 regardless of whether the claim is contingent upon unforeseeable or
 controllable action, regardless of whether the claim is called by an other
 name, or is characterized as any product, issue or promise which can be
 demonstrated to be an individual or series of options, regardless of their
 life span
 The art has and continues to maintain that the maximum value of any
 expiring option is the underlying product, and that such maximum value is
 a determinant in pricing said option, when such statements are clearly
 false given that expirationless options exist, since the maximum value of
 any expiring option is an otherwise identical nonexpiring option. Given
 that we have a priority claim on nonexpiring options, whose value or price
 is an integral component of correctly pricing expiring options, our claim
 is expanded to cover not only expiring options, but any financial product
 which can be demonstrated to be an individual or series of options.
 Expirationless options calculated according to the method of the present
 invention may also be used in constructing any combination or permutation
 of expiring options currently used. For example, these options may include
 but are not limited to:
 Asian options: average price/rate and strike options.
 Barrier options: including knock-out or knock-in, with and without rebate.
 Binary options: including binary barrier, all-or-none and gap.
 Chooser options: which are options to choose a put or call in the future.
 Compound options: which are options where the underlying security is an
 option.
 Crack/Spread options: which are options on the distance between prices of
 two assets.
 Currency Translated options: which are foreign exchange options translated
 into another currency.
 Jump options: which are options priced using a jump-diffusion process.
 Lookback options: which are options based on minimum or maximum price
 within a certain period.
 Rainbow options: which are options on the minimum or maximum of two assets.
 Other miscellaneous options: such as options on U.S. or foreign "stripped"
 government securities divided into two or more instruments of principal
 and interest or price and dividend, likewise options on stripped
 corporate, agency, and municipal securities, notes, bills and Certificates
 of Deposit; options on Callables, which are securities callable at premium
 or discount; options on Odd-First, -Last, -Middle, or securities with
 varying coupon/dividend periods; and Options on Futures, Forwards,
 Currencies, Commodities, Swaps, Debt, Metals, Indices or any other
 financial instrument not detailed here.
 Even though the present invention has been described substantially in terms
 of utilizing the margin requirement of a margin position in the securities
 market, equivalents to the margin requirement in other markets (e.g.,
 earnest money in the real estate market) may be utilized. Further, even
 though an exemplary embodiment of the present invention is described
 assuming that the margin requirement on the underlying security is equal
 for both the long and short positions, this need not be the case.
 Specifically, even in cases where the margin position requirements are
 different, it should be obvious to one of the ordinary skill in the art
 that the present invention can be used to determine the expirationless
 option premiums comprising each respective position by using the long
 position margin requirement for purchasing expirationless call options and
 selling expirationless put options, while using the short position margin
 requirement for purchasing expirationless put options and selling
 expirationless call options.
 Furthermore, a variety of other financial instruments have been shown to be
 equivalent or relatable to options. Therefore, the premiums of each of
 these financial instruments may be determined utilizing an expiring or
 expirationless option premium determined according to the method of the
 present invention. Examples of these option relatable financial
 instruments, provided for example and not limitation, include:
 Equity: Ownership of a corporation is actually a contingent claim on the
 assets of the corporation that does not expire and only occurs at a zero
 strike price. Thus, equity can be considered to be an option.
 Bonds, Loans, Private Placements: These fixed-income instruments are
 identical to an individual or series of cash-settled, "capped" call
 options--a call option with a maximum benefit. These options are purchased
 with the expectation that the issuer will remain a viable, profitable
 entity. However, the maximum return on the call is "capped" at some amount
 (the coupon payment and principal payment at the end of the period). One
 capped option represents each coupon payment as well as the principal or
 notional value repaid. Fixed income instruments may take one of the
 following forms:
 Zero Coupon: One payment of principal at end of term.
 Floating Rate Coupon: One principal payment at end of term and coupon
 payments calculated based on an interest rate calculated from some
 external benchmark (90-day Treasury, 90-day LIBOR, etc.)
 Level Coupon: One principal payment at end of term and coupon payments
 based on an interest rate agreed at the start of the term.
 Amortizing: No principal payment is made during the term of the loan; the
 principal is repaid over the term as part of the coupon payments.
 Forward Contracts: A forward contract obligates its owner to buy a given
 asset on a specified date at a price (also known as the exercise price)
 specified at the origination of the contract This is identical to a
 combination of a long call option combined with a short put option or vice
 versa.
 Futures Contracts: Identical to forward, but typically traded on an
 exchange where default risk is eliminated by the exchange's guarantee of
 performance.
 Swaps: Two parties exchange ("swap") specified cash flows at specified
 intervals, typically "fixed for floating" or vice versa. A swap contract
 is really nothing more than a series of forward contracts.
 Forward Swap/Delayed Start Swap: A combination of a forward contract and a
 swap.
 Break Forwards: A forward contract with a floor (or a cap) in which the
 contract terminates early if prices fall (rise) to a certain level.
 StraddleslStrangles/Butterflies: Option combinations that provide differing
 payoffs based on price movements, typically combinations of puts and calls
 either both long or both short.
 Reverse Floating Rate Loan/Bull Floating Rate Notes: If the floating rate
 rises, the net coupon payment falls.
 Dual Currency Bond: Combination of a standard credit extension with a
 forward currency contract.
 Callable/Puttable Bonds: Standard bond and option on interest rates.
 Extendible Notes: Long a standard bond and short a call option (issuer).
 Puttable Stock: Stock issued with puts for investors to acquire more if the
 price falls.
 Bond w/Warrant: Level coupon bond and an option on shares of the issuing
 firm.
 Convertible Bond: Bond convertible into shares of the issuing firm.
 LYON (Liquid Yield Option Notes): Puttable, callable, convertible, zero
 coupon bonds.
 Commodity-Linked Bonds: A bond with interest payments linked to some
 commodity. Examples include:
 Oil-Indexed Notes: Standard note and options on crude oil.
 Copper Interest-Indexed Senior Subordinated Notes: Note with quarterly
 interest payments determined by the prevailing price of copper.
 Auction Rate Notes/Debentures: Interest rate reset by Dutch auction at the
 end of each interest period.
 Collaterallized Mortgage Obligations (CMOs)/Real Estate Mortgage Investment
 Conduits (REMICs): Mortgage payment stream divided into classes
 prioritized by rights to receive principal payments.
 Commercial Real-Estate Backed Bonds: Nonrecourse bonds serviced and backed
 by a specified piece of real estate.
 Credit Enhanced Debt Securities: Issuer's obligation to pay is backed by an
 irrevocable letter of credit or a surety bond.
 Dollar BILS: Floating zero coupon notes with interest rates figured
 retrospectively on an index of long-term high-grade corporate bonds.
 Foreign Exchange Paper: Commercial paper on foreign companies, usually
 those operating under a single currency.
 Floating/Bate Sensitive Notes: Coupon rate resets on spread over T-Bill,
 LIBOR, etc.
 Floating Rate Tax-Exempt Revenue Bonds: Coupon rate floats with index
 (commercial paper, etc.).
 Increasing Rate Notes: Coupon rate note increases by specified amount at
 specified intervals.
 Indexed Currency Option Notes or Principal Exchange Rate Linked Securities:
 Issuer pays reduced/increased principal based on appreciation/depreciation
 of foreign currency.
 Caps/Floors/Collars: Investor who writes a cap (floor/collar) agrees to
 make payments when the underlying exceeds the cap (falls below the
 floor/outside the collar) or vice versa.
 Interest Rate Reset Notes: Rate is reset after issuance to initial rate or
 some preset rate.
 Mortgage Pass-Through Certificates: Undivided interest in a pool of
 mortgages.
 Negotiable Certificates of Deposit: Registered CDs sold on an agency basis.
 Adjustable Tender Securities: issuer can periodically reset Terms.
 Puttable/Extendable Notes: At each period, issuer can redeem notes at par
 or extend maturity, notes can be put back to issuer at option of
 purchaser.
 Real Yield Securities: Coupon rate resets quarterly, typically to the Real
 Yield Spread plus some fixed amount.
 Receivable Pay-Through Securities: Undivided interest in a pool of
 receivables.
 Remarketed Reset Notes: Interest rate resets at end of each period to a
 rate remarketing agent determines will make the notes worth par.
 Stripped Mortgage Backed Securities: Coupon payments divided into interest
 only and principal only payments to investors.
 Stripped Treasuries/Municipals: Divided into coupon & principal (creates
 zero coupon bonds).
 Variable Coupon Renewable Notes: Coupon rate varies based on T-Bill, renews
 every 90 days unless terminated.
 Variable Rate Renewable Notes: Coupon rate varies monthly until investor
 terminates.
 Yield Curve/Maximum Rate Notes: Rate is specified at level minus LIBOR (or
 other standard index/yield).
 Adjustable Rate Preferred Stock: Dividend rate resets based on index/yield.
 Auction Rate Preferred Stock: Dividend rate resets by Dutch auction at
 regular intervals.
 Convertible Adjustable Preferred Stock: Convertible into common stock at
 certain dates under certain conditions.
 Remarketed Preferred Stock (SABRES): Dividend rate resets at the regular
 intervals to a rate set by the marketing agent to make the preferred stock
 worth par.
 Single Point Adjustable Rate Stock: Dividend rate reset regularly as a
 fixed percentage of some index/yield.
 State Rate Auction Preferred Stock: Fixed initial dividend period followed
 by the issuer's option to convert to a reset by Dutch auction at periodic
 intervals.
 Variable Cumulative Preferred Stock: Dividend rate reset at issuer's option
 to either auction or remarketing method.
 Adjustable Rate Convertible Debt: Interest rate varies directly with the
 underlying common stock dividend rate.
 Convertible Exchangeable Preferred Stock: Convertible preferred stock
 exchangeable at issuer's option for debt with identical rate and
 conversion terms.
 Convertible Reset Debentures: Convertible bond with interest rate reset at
 a predetermined time to an amount sufficient to give debentures a market
 value equal to their face amount.
 Debt with Mandatory Common Stock Purchase Contracts: Notes that obligate
 purchasers to buy sufficient stock from the issuer to retire the issue in
 full by the scheduled maturity date.
 Exchangeable Preferred Stock: Auction rate preferred stock exchanged for
 auction rate notes.
 Synthetic Convertible Debt: Debt and warrants replicating convertible debt.
 Zero Coupon Convertible Debt: Non-interest bearing convertible debt.
 Puttable Common Stock: Issue of common stock with the right to put the
 stock back to the issuer on a specified date at specified price.
 Although the present invention has been described in various embodiments
 and the various embodiments have been provided as examples of
 implementations of the present invention. It should be understood that the
 present invention is not limited to any particular shape, size, embodiment
 or configuration. On the contrary, the aspects of the present invention
 can be embodied in various manners within the scope and spirit of the
 invention as described herein.