valuation of foreign currency options some empirical tests this paper investigates the efficiency of the market for foreign currency options with the help of a modified version of the black scholes model the evidence in the ex post tests is inconsistent with this hypothesis since we find a large number of opportunities for abnormal profits a second set of tests is conducted on an ex ante basis to determine whether these profit opportunities exist even if the execution of the strategy is delayed by one day the evidence from these tests provides more support for the hypothesis of market efficiency

on the pricing of european and american foreign currency options a clarification abstract this paper amends misprints in adams watt 1987 of simulated american foreign currency call prices and for purposes of completeness provides simulation results for corresponding european calls and european and american puts on spot foreign exchange

the pricing of foreign currency options this study examines the assumption that the exchange rate follows a log normal probability distribution and it tests whether different stochastic specifications translate into important differences in implied option prices we investigate a class of processes which includes the log normal probability distribution as a limiting case none of the models performs particularly well the main problem appears to be that the volatility estimates from actual exchange rate data are significantly smaller than those implied by observed option prices la formation du prix des options sur des devises etrangeres cette etude examine le pos tulat que le taux de change suit une courbe de probabilite log normale et verifie si des specifications stochastiques differentes se traduisent en des diff6rences importantes dans les prix des options qui en decoulent les auteurs examinent une famille de processus dont le processus log normal est un cas limite aucun des modeles ne donne des resultats particu lierement bons le probleme principal semble etre que la volatilite des evaluations a partir des donnees sur les taux de change reel est plus faible et de maniere significative que celle des evaluations derivees des prix d options observes

realignment risk and currency option pricing in target zones abstract this paper extends the krugman target zone model by including a realignment mechanism various properties of that realignment mechanism are discussed the movement of the exchange rate is governed both by a wiener process on fundamental and by a poisson jump process with endogenous realignment size the realignment mechanism is such that except in cases where a speculative attack occurs no jump in fundamental is needed to accompany the jump in the exchange rate a risk neutral valuation of currency options is constructed some properties of option values under realignment risk are illustrated by numerical results

agents ability to manage information in centralized markets comparing two wholesale fish markets abstract in this paper we perform an empirical investigation to detect if and how agents behavior changes with the amount of available information they have to this aim we use data from two wholesale fish markets of different thicknesses we tackle the issue by investigating features such as the dynamics of the structure of attendance in auctions the varieties of fish presentations during the seller s turn and the presence of long term relationships between buyers and sellers we perform the investigation in this way instead of focusing on the dispersion and dynamics of prices to prevent unobserved quality differences of the traded fish varieties from biasing the results of the analysis the results of our investigation are consistent with a situation in which the magnitude of phenomena like buyers loyalty to sellers and agents following rules of thumb increases with the market thickness

assessing credit risk in a financial institution s off balance sheet commitments the first part of this paper presents a general approach to valuing a financial institution s contracts when there is credit risk the approach uses contingent claims pricing theory and is particularly appropriate for an off balance sheet contract such as a swap that can have either a positive or a negative value to the counterparty the second part of the paper extends the analysis by considering the problem faced by bank supervisory authorities of determining capital requirements for off balance sheet contracts

testing for imperfect competition at the fulton fish market in this article i report the results of a study of the prices paid by individual buyers at the fulton fish market in new york city in principle this is a highly competitive market in which there should be no predictable price differences across customers who are equally costly to service the results indicate that different buyers pay different prices for fish of identical quality for example asian buyers pay 7 less for whiting than do white buyers a result which is inconsistent with the model of perfect competition

pricing european average rate currency options abstract this paper develops a simple methodology that yields closed form analytical approximations for valuing european option claims involving the arithmetic average of future foreign exchange rates the main advantage of the approach is that it avoids the need to adopt time consuming numerical procedures the precision of the resulting formula and the distributional assumption that underlies it is examined by way of monte carlo simulations jel f31

efficiency tests of the foreign currency options market based on a new options transactions data base from the philadelphia stock exchange foreign currency options market this paper examines the importance of the effect of nonsynchronous prices and transaction costs on the usual option market efficiency tests the tests conducted are based on the transaction cost adjusted early exercise and put call parity pricing boundaries applicable to the american foreign currency options market the test results show that the put call parity boundary tests are sensitive to both nonsynchronous prices and transaction costs the early exercise boundary tests are sensitive to transaction costs but are not very sensitive to simultaneity of the option price and the underlying spot price under the no transaction costs scenario a large number of early exercise boundary violations is found even when simultaneous spot and option prices are used these violations disappear when actual transaction costs are taken into account

systematic jump risks in a small open economy simultaneous equilibrium valuation of options on the market portfolio and the exchange rate abstract the valuation of stock options and currency options has witnessed an explosion of new development in the past 20 years these models set up either in a partial equilibrium or a general equilibrium framework have certainly enriched our understanding of option valuation in one way or the other however the main drawback of these models is that stock options and currency options are analyzed in separate contexts the co movement of the stock market and the currency market is absent from the option valuation analysis such co movement is extremely important and is best illustrated by the southeast asian financial crisis to overcome this drawback this paper uses an equilibrium model to investigate the joint dynamics of the exchange rate and the market portfolio in a small open monetary economy with jump diffusion money supplies and aggregate dividends it is shown that the exchange rate and the market portfolio are strongly correlated since both are driven by the same economic fundamentals furthermore options on the exchange rate and the market portfolio are evaluated in the same equilibrium context the analysis shows that parameters describing the same economic fundamentals have very different effects on currency and stock options

corporate issues of foreign currency exchange warrants a case study of financial innovation and risk management abstract we argue that hedging and risk management activities of modern corporations arise as a direct consequence of attempts to create shareholder wealth through financial innovation we formalize this argument by examining in detail corporate issues of foreign currency exchange warrants we then focus on one multiple issuer to demonstrate how the foreign exchange risk created by the sale of the warrants can be eliminated the use of off balance sheet risk management techniques to lock in the benefits of selling overpriced securities raises questions about the information content of innovative corporate financing decisions

finite maturity caps and floors on continuous flows models of interest rate caps and floors are typically based on discrete rates over finite horizons while existing real option models describe perpetual claims on the maximum of two continuous flows in this paper we produce formulae for finite maturity caps and floors that are contingent on continuous flows we present hedge ratios and discuss applications where a lognormally distributed flow variable is suitable for other situations where practitioners use proprietary models the formula presented is useful as a quick tractable and universal means for mapping quoted implied to prices and vice versa

common factors and local factors implications for term structures and exchange rates this paper studies a multi factor two country term structure and exchange rate model when a diversification effect for an international bond portfolio is expected it shows that the diversification gain calls upon certain restrictions on the process of the stochastic discount factor in a factor structured economy existence of local factors is shown to be a necessary condition for the gains from investing in foreign bonds further the exchange rate risk premia are shown to be a function of the differentials of the risk premia of the factors in bond returns empirical results reveal the tendency for investors to respond sensitively to rare shocks which is shown to be a potential solution to the forward premium puzzle

options on the minimum or the maximum of two risky assets analysis and applications this paper provides analytical formulas for european put and call options on the minimum or the maximum of two risky assets the properties of these formulas are discussed in detail options on the minimum or the maximum of two risky assets are useful to price a wide variety of contingent claims of interest to financial economists applications discussed in this paper include the valuation of foreign currency debt option bonds compensation plans risk sharing contracts secured debt and growth opportunities involving mutually exclusive investments

hedging the risks from writing foreign currency options abstract this paper considers the ways in which banks and other financial institutions can hedge their risks when they write non exchange traded foreign currency options key factors affecting the performance of delta hedging are identified and hedging schemes involving the use of exchange traded options are analyzed the schemes are tested using both simulated data and data from trades on the philadelphia exchange between february 1983 and september 1984

arbitrage tests of the efficiency of the foreign currency options market in this paper the lower boundary excercise price and put call parity conditions for foreign currency options are subjected to empirical testing the tests are directed towards the examination of the hypothesis that the foreign currency option market is efficient the evidence in the ex post tests is inconsistent with this hypothesis since a large number of violations of theoretical conditions are found in the data

changes of numeraire for pricing futures forwards and options a change of numeraire argument is used to derive a general option parity or equivalence result relating american call and put prices and to obtain new expressions for futures and forward prices the general parity result unifies and extends a number of existing results the new futures and forward pricing formulas are often simpler to compute in multifactor models than existing alternatives we also extend previous work by deriving a general formula relating exchange options to ordinary call options a number of applications to diffusion models including stochastic volatility stochastic interest rate and stochastic dividend rate models and jump diffusion models are examined a self financing portfolio is called a numeraire if security prices measured in units of this portfolio admit an equivalent martingale measure the most commonly used numeraire is the reinvested short rate process the corresponding equivalent martingale measure is the risk neutral measure geman el karoui and rochet 1995 show that other numeraires can simplify many asset pricing problems in this article we build on their results and using the reinvested asset price as the numeraire unify and extend the literature on option parity or equivalence results relating american call and put prices for asset and futures options the same numeraire change is used to obtain new pricing formulas for futures and forwards that are often simpler to compute in multifactor models finally we use a numeraire change to simplify exchange option pricing extending a similar result in geman el karoui and rochet to dividend paying assets the change of numeraire method is most intuitive in the context of foreign currency derivative securities as discussed by grabbe 1983 an american call option to buy 1 dm with dollar price process s for k dollars is equivalent to an american put option to sell k dollars with dm price process k s for a strike price of 1 dm the dollar price of the call must therefore equal the product of the current exchange rate s0 and the dm price of the put the call price is computed using the dollar value of a u s i am grateful to kerry back the editor and costis skiadas for their many helpful suggestions thanks also to peter demarzo matt jackson naveen khanna david marshall robert mcdonald jim moser phyllis payette and an anonymous referee for their comments this article subsumes schroder 1992

international money and stock market contingent claims abstract we develop a unified approach with closed form solutions for pricing bonds stocks currencies and their derivatives the specification assumes a fundamental risk factor represented by a stochastic positive definite matrix following a wishart autoregressive war process by assuming a volatility in mean specification for the domestic stock returns and the relative changes of exchange rates and a domestic stochastic discount factor exponential affine with respect to the fundamental risk it is possible to derive closed form solutions for the term structures of interest rates and for the risk neutral probabilities while keeping the flexibility of the model in particular i the domestic and foreign term structures are jointly affine and correspond to wishart quadratic term structures which can ensure the positivity of interest rates ii in this framework where the stock price follows a model with stochastic volatility we obtain explicit or quasi explicit formulas for futures and forward contracts swaps and options this extends results by heston 1993 and ball and roma 1994

a moving boundary approach to american option pricing this paper describes a method to solve the free boundary problem that arises in the pricing of american options most numerical methods for american option pricing exploit the representation of the option price as the expected pay off under the risk neutral measure and calculate the price for a given time to expiration and stock price they do not solve the related free boundary problem explicitly the advantage of solving the free boundary problem is that it provides the entire price function as well as the optimal exercise boundary explicitly our approach which we term the moving boundary approach is based on using a boundary guess and the value associated with the guess to construct an improved boundary it is also shown that on iteration the sequence of boundaries converge monotonically to the optimal exercise boundary examples illustrating the convergence behavior as well as discussions providing insight into the method are also presented finally we compare runtimes and speeds with other methods that solve the free boundary problem and compute the optimal boundaries explicitly like the front fixing method penalty method method based on the integral representations and the method by brennan and schwartz 1977 the valuation of american put options journal of finance 32 2 449 462

the pricing of dollar denominated yen dm warrants abstract this paper investigates the pricing of dollar denominated cross currency warrants options traded in us markets in a black scholes setting we obtain closed form option pricing formulas for european warrants we describe the intuition behind the differences in the properties of these securities versus standard foreign currency options concentrating on parameter sensitivity as well as hedging aspects we show that us cross currency warrants can be hedged using three underlying assets although the fundamental pde involves only one asset this analytical framework is applied to observed prices for at t s nyse traded us yen dm cross currency warrant we examine and attempt to explain the deviations between model and observed prices uncovered by the empirical work we find evidence of misspecification in standard currency option pricing models jel f31

exchange rate intervention with options abstract we consider the problem of a central bank that has exchange rate goals in a partial equilibrium setting we compare direct intervention through sale purchase of reserves in the currency market with an alternative strategy of intervention with options the investment bank the central bank deals with will have to hedge its position and therefore buy or sell the underlying security the foreign currency and bonds intervention through options seems to perform better but the value of the cross elasticity exchange rate interest rate is crucial we provide some grounds for the construction of a full equilibrium model

pricing foreign currency options under stochastic interest rates abstract in this paper we build a general framework to price contingent claims on foreign currencies using the heath et al 1987 model of the term structure closed form solutions are obtained for european options on currencies and currency futures assuming that the volatility functions determining the term structure are deterministic as such this paper provides an example of a bond price process for both the domestic and foreign economies consistent with grabbe s 1983 formulation of the same problem

equilibrium valuation of foreign exchange claims this article studies the equilibrium valuation of foreign exchange contingent claims within a continuous time lucas 1982 two country model exchange rates interest rates and in particular factor risk prices are all endogenously and jointly determined this guarantees the internal consistency of these price processes with a general equilibrium in the same model closed form valuation formulas are presented for currency options and currency futures options common to these formulas is that stochastic volatility and stochastic interest rates are admitted hedge ratios and other comparative statics are also provided analytically it is shown that most existing currency option models are included as special cases this article studies the equilibrium valuation and hedging of foreign exchange contingent claims the framework for analysis is the continuous time counterpart of the well known two country monetary model of lucas 1982 1 that is we use the modeling structure of lucas 1982 and adopt his representativeagent perfect pooling equilibrium notion rather than extending the lucas setup to a cox ingersoll and ross 1985a henceforth cir production economy as is done in nielsen and saa requejo 1993 for our purpose the lucas framework offers the desired simplicity and tractability we assume a stochastic structure for the international economy such that the resulting nominal interest rates and exchange rate dynamics exhibit similar empirically plausible features as the corresponding ones in nielsen and saa requejo 1993 for example the endogenous interest rates are positively correlated across national borders campbell and clarida 1987 and ilmanen 1995 as a predictor of future spot exchange rates the equilibrium forward exchange rate is biased in a direction consistent with the forward premium puzzle

green economy and related concepts an overview for the last ten years the notion of a green economy has become increasingly attractive to policy makers however green economy covers a lot of diverse concepts and its links with sustainability are not always clear in this article we focus on definitions of green economy and related concepts and an evaluation of these concepts against the criterion of strong and weak sustainability the article serves three purposes firstly we identify and describe diverse theories concepts approaches and tools related to a green economy among these are the theories of environmental economics and ecological economics the concepts and approaches of cleaner production waste hierarchy bio economy industrial ecology circular economy nature based solutions and dematerialization through product servicizing and tools like life cycle assessment and cost benefit analysis secondly we develop a framework that shows the capacity of the green economy concepts approaches and tools to support the transition towards sustainability such a framework can serve as a heuristic to embed diverse concepts and approaches into a green economy framework thirdly we briefly discuss green economy concepts with respect to their impact on strong and weak sustainability depending on the different concepts approaches and tools identified in the green economy framework different degrees of substitutability and trade offs between environmental and economic benefits are allowed and more or less structural changes of our modes of living are required by discussing the notion of green economy and related concepts approaches and tools we seek to make a contribution to their definitions and relationships as a prerequisite for operationalizing green economy

valuation of libor contingent fx options abstract a libor contingent fx option represents a currency option whose payoff occurs only if a prespecified interest rate at maturity is either above or below a prespecified level the product permits investors to express an exchange rate view that is based on or coupled with an interest rate view and is less expensive than a plain vanilla fx option this paper provides analytic solutions for pricing several types of libor contingent fx options under certain specifications of the initial domestic forward curve foreign forward curve and the exchange rate simulations are conducted to illustrate certain properties of these products

learning to bid in sequential dutch auctions abstract we propose an agent based computational model to investigate sequential dutch auctions with particular emphasis on markets for perishable goods and we take as an example wholesale fish markets buyers in these markets sell the fish they purchase on a retail market the paper provides an original model of boundedly rational behavior for wholesale buyers behavior incorporating learning to improve profits conjectures as to the bids that will be made and fictitious learning we analyze the dynamics of the aggregate price under different market conditions in order to explain the emergence of market price patterns such as the well known declining price paradox and the empirically observed fact that the very last transactions in the day may be at a higher price the proposed behavioral model provides alternative explanations for market price dynamics to those which depend on standard hypotheses such as diminishing marginal profits furthermore agents learn the option value of having the possibility of bidding in later rounds when confronted with random buyers such as occasional participants or new entrants they learn to bid in the optimal way without being conscious of the strategies of the other buyers when faced with other buyers who are also learning their behavior still displays some of the characteristics learned in the simpler case even though the problem is not analytically tractable

trade and market thickness effects on organizations globalization by raising the number of buyers available to each seller and the number of sellers available to each buyer raises the thickness or the effective number of participants of every market market thickness can have subtle effects on incentives and organizations alleviating hold up problems resulting in less vertical integration more informal contracting and more cooperative and innovative relationships with subcontractors however it can also weaken long run relationships distorting relationship specific investments and risk sharing this paper surveys the theory and empirical evidence indicating when market thickness helps and when it hurts jel f15 l14 l22

valuation of american options on foreign currency abstract pricing models for american call and put options on foreign currency are derived herein these models are used to investigate the efficiency of the market for foreign currency options the evidence presented here indicates that market prices for these options deviate substantially from their corresponding model prices in addition it is shown that a hedging strategy executed at transaction prices can be used to translate an observed deviation of market from model prices into positive excess profits however these profits are eliminated if the strategy is executed at bid and offer prices

the performance of alternative valuation models in the otc currency options market abstract we compare option valuation models based on regime switching garch and jump diffusion processes to a standard smile model in which black and scholes 1973 implied volatilities are allowed to vary across strike prices the regime switching garch and jump diffusion models provide significant improvement over a fixed smile model in fitting gbp and jpy option prices both in sample and out of sample the jump diffusion model achieves the tightest fit a time varying smile model however provides hedging performance that is comparable to the other models for the gbp options this result suggests that standard option valuation techniques may provide a reasonable basis for trading and hedging strategies

currency option pricing with mean reversion and uncovered interest parity a revision of the garman kohlhagen model abstract we consider a model for the pricing of currency options where the logarithm of the exchange rate exhibits mean reversion i e follows the omstein uhlenbeck process we mention reasons why exchange rates could exhibit mean reversion the domestic and foreign short interest rates are related to the logarithm of the exchange rate through uncovered interest parity under these assumptions we derive formulas for the value of a european currency option from the point of view of both domestic and foreign investors we also derive formulas for options on forward and futures contracts we compare option values computed by means of the garman kohlhagen model with corresponding results from our model it appears that our model cannot explain all instances of mispricing of currency options by the garman kohlhagen model which have been reported by previous authors the main virtue of our paper however is that we derive a simple model which incorporates clear theoretical relationship between the exchange rate and the domestic and foreign interest rates

misspecification and the pricing and hedging of long term foreign currency options abstract this study examines the effects of stochastic volatility upon the pricing and hedging of long term foreign currency options the traditional method of pricing such options uses a constant volatility option model with an implicit volatility derived from a short term traded option we show that the traditional method leads to small pricing errors for short and medium term options but does a poor job in pricing long term options the traditional method also does a poor job for all maturities in determining the derivatives of the option s value with respect to the exchange rate delta and the volatility vega the errors in calculating these derivatives which are used in forming the replicating portfolio lead to large and costly errors in error hedging

an expository note on the valuation of foreign exchange options abstract this note describes the application of the binomial model to the valuation of foreign exchange options and reports simulated pricesof american as well as europen call and put options we find significant deviations of simulated call prices from those reported elsewhere this casts some doubt on empirical findings that american calls have significant pricing errors

tests of an american option pricing model on the foreign currency options market this paper tests the ability of the american option pricing model proposed by parkinson 18 or mason 14 to explain the pricing of the foreign currency options traded on the philadelphia stock exchange from february 28 1983 to march 26 1985 we find that the model underprices out of the money options relative to at the money and in the money options this relative underpricing is driven by an underpricing of out of the money call options of short maturity in addition the degree of relative mispricing for most categories of options is shown to be a decreasing function of the time to maturity of the options longer maturity options appear to trade at similar levels of implied volatility whether they are in at or out of the money most of these biases appear consistent with the fact that the underlying spot currency rate follows a mixed jump diffusion process as described in 17

the pricing of call and put options on foreign exchange this paper derives pricing equations for european puts and calls on foreign exchange the call and put pricing formulas are unlike the black scholes equations for stock options in that there are two relevant interest rates interest rates are stochastic and boundary constraints differ in addition it is shown that both american call and put options have values larger than their european counterparts

transactions that did not happen and their influence on prices abstract this paper studies data from the wholesale fruit and vegetables market in marseille we have details of counteroffers to the prices that were proposed by the seller even when no transaction took place we analyse the evolution of prices and the relation between the final price struck and the proposals of the two parties periods with no buyer refusals of offers or bargaining with no transaction will lead to a revision of the seller s first price more importantly the sharing of the surplus moves in the buyer s favour during the day these theoretical predictions are confirmed by our data set

pricing contingent claims under interest rate and asset price risk this paper presents a general framework for pricing contingent claims under interest rate and asset price uncertainty the framework extends ho and lee s 1986 valuation framework by allowing not only future interest rates but also future asset prices to depend on the current term structure of interest rates the approach is shown to provide risk neutral valuation relationships that are consistent with the initial term structure of interest rates and can be applied to valuation of a broad class of assets including stock options convertible bonds and junk bonds

valuation and martingale properties of shadow prices an exposition abstract concepts of asset valuation based on the martingale properties of shadow or marginal utility prices in continuous time infinite horizon stochastic models of optimal saving and portfolio choice are reviewed and compared with their antecedents in static or deterministic economic theory applications of shadow pricing to valuation are described including a new derivation of the black scholes formula and a generalised net present value formula for valuing an indivisible project yielding a random income some new results are presented concerning i the characterisation of an optimum in a model of saving with an exogenous random income and ii the use of random time transforms to replace local by true martingales in the martingale and transversality conditions for optimal saving and portfolio choice

the ubiquity of habits and rules under what circumstances is it necessary or convenient for an agent to rely on habits or rules this paper focuses on the types of decision situations giving rise to their use even optimization requires the deployment of rules and for this reason mainstream economics cannot legitimately ignore these questions the argument is that habits and rules are ubiquitous in human activity in a new taxonomy seven types of decision situations are considered classified according to the type of information problem involved neither neoclassical nor behavioral economics can provide a complete account of the bases of habits or rules in these cases copyright 1997 by oxford university press

the effects of domestic and foreign yield curves on the value of currency american call options this paper examines the sensitivity of the values of foreign currency american call options to the domestic and foreign term structures of interest rates pricing performances of currency option models are compared with and without the term structure effects it is shown that there exist significant pricing biases if flat yield curves are assumed and that different shapes of domestic and foreign yield curves can have major impacts on currency option prices

dollar jump fears 1984 1992 distributional abnormalities implicit in currency futures options abstract deutsche mark and yen futures options over 1984 1992 and 1986 1992 respectively are examined for deviations from the lognormal assumption underlying standard option pricing models two methods are used an atheoretic skewness premium and daily estimates of moments using a model for pricing american foreign currency futures options under systematic exchange rate jump risk substantial variation over time is found in all moments including implicit skewness and kurtosis the implicit abnormalities predict future abnormalities in log differenced dm futures prices but not yen the peso problem implications do not explain standard rejections of uncovered interest parity

on the pricing of european and american foreign currency call options abstract this study uses cox ross analysis and dynamic programming techniques to price foreign currency call options we show that under certain conditions the american call price will exceed its european counterpart while under other conditions the two prices will be identical we find that the american premium is a complex function of the degree to which an option is in or out of the money and that this premium is greatest when an option is near in or out we present empirical evidence which shows that the american model significantly improves upon a european model however significant pricing errors associated with the american model remain

siegel s paradox and the pricing of currency options abstract it is an important property of a currency option that its value does not depend on whose point of view is taken that of the domestic or foreign investor option values obtained from the garman kohlhagen model do satisfy this property the merton jump diffusion model has been proposed as a more realistic currency option model to eliminate pricing biases inherent in the garman kohlhagen model the jump diffusion model assumes that the jump risk is non priced ie can be diversified away if both the domestic and foreign investor make that assumption then the jump diffusion model produces option values which are different for the two investors thus violating the law of one price this is an instance of the siegel paradox the extent to which computed option values may differ between the two investors is indicated through numerical examples

discrete time valuation of american options with stochastic interest rates we develop an arbitrage free discrete time model to price american style claims for which domestic term structure risk foreign term structure risk and currency risk are important this model combines a discrete version of the heath jarrow and morton 1992 term structure model with the binomial model of cox ross and rubinstein 1979 it converges weakly to the continuous time models in amin and jarrow 1991 1992 the general model is path dependent and can be implemented with arbitrary volatility functions to value claims with maturity up to five years the model is illustrated with applications to long dated american currency warrants and a cross rate swap from the quanto class article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

producing derivative assets with forward contracts this paper shows how a derivative security can be duplicated by a forward strategy and hence priced by arbitrage in terms ofthe forward price