black scholes approximations of call option prices with stochastic volatilities a note a piecewise linear weighting function for black scholes implied volatilities is used in conjunction with the black scholes call pricing model to approximate stochastic volatility european call prices a sensitivity analysis is conducted to compare simulated stochastic volatility call prices to the black scholes prices calculated with the weighted implied vo latilities the analysis indicates that a simple model can provide close approximations to the simulated prices with far less computational effort i introduction the volatility of the underlying asset is one of the more difficult parameters to estimate in any option pricing model the stochastic nature of the volatility of most financial assets is responsible for much of the difficulty while the early tests of the black scholes 1973 option pricing model rely upon historical prices for volatility estimates latane and rendleman s 1976 implied volatility technique has become the standard method of estimation unfortunately as beckers 1981 stresses although implied volatilities calculated from a stationary vari ance model may be of practical use it is inconsistent to use the black scholes model with a constant variance to obtain estimates of nonstationary variances l recent work conducted by hull and white 1987 and johnson and shanno 1987 has been directed at solving the problem of pricing european calls on assets with stochastic volatilities while hull and white provide a series solution for the case in which the variance and stock price are uncorrelated convergence is slow unless the variance of the assets volatility is relatively small for more general cases both hull and white and johnson and shanno rely upon monte carlo simulations to estimate option prices although the application of simulation techniques to option pricing first explored by boyle 1977 is often a useful method of estimating option prices the monte carlo method tends to be expensive and is often too time consuming for real time applications this study examines a simple method of approximat

position auctions with consumer search this paper examines a model in which advertisers bid for sponsored link positions on a search engine the value advertisers derive from each position is endogenized as coming from sales to a population of consumers who make rational inferences about rm qualities and search optimally consumer search strategies equilibrium bidding and the welfare benets of position auctions are analyzed implications for reserve prices and a number of other auction design questions are discussed

analytical upper bounds for american option prices american options require numerical methods namely lattice models to provide accurate price estimates the computations can become expensive when more than one state variable is involved analytical upper bounds can therefore provide a useful guideline for how high american values can reach in this paper we derive analytical closed form upper bounds for american option prices under stochastic interest rates stochastic volatility and jumps where american option prices are difficult to compute with accuracy in a stochastic volatility model heston 1993 and scott 1997 that has two random factors we demonstrate that the upper bound only takes a very small fraction of the time that the american option needs to compute

option pricing when the variance changes randomly theory estimation and an application in this paper we examine the pricing of european call options on stocks that have vari ance rates that change randomly we study continuous time diffusion processes for the stock return and the standard deviation parameter and we find that one must use the stock and two options to form a riskless hedge the riskless hedge does not lead to a unique option pricing function because the random standard deviation is not a traded security one must appeal to an equilibrium asset pricing model to derive a unique option pricing function in general the option price depends on the risk premium associated with the random standard deviation we find that the problem can be simplified by assuming that volatility risk can be diversified away and that changes in volatility are uncorrelated with the stock return the resulting solution is an integral ofthe black scholes formula and the distribution function for the variance of the stock price we show that accurate option prices can be computed via monte carlo simulations and we apply the model to a set of actual prices

the pricing of options on assets with stochastic volatilities one option pricing problem that has hitherto been unsolved is the pricing of a european call on an asset that has a stochastic volatility this paper examines this problem the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price numerical solutions are also produced for the case in which the volatility is correlated with the stock price it is found that the black scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity one option pricing problem that has hitherto remained unsolved is the pricing of a european call on a stock that has a stochastic volatility from the work of merton 12 garman 6 and cox ingersoll and ross 3 the differential equation that the option must satisfy is known the solution of this differential equation is independent of risk preferences if a the volatility is a traded asset or b the volatility is uncorrelated with aggregate consumption if either of these conditions holds the risk neutral valuation arguments of cox and ross 4 can be used in a straightfoward way this paper produces a solution in series form for the situation in which the stock price is instantaneously uncorrelated with the volatility we do not assume that the volatility is a traded asset also a constant correlation between the instantaneous rate of change of the volatility and the rate of change of aggregate consumption can be accommodated the option price is lower than the blackscholes b s 1 price when the option is close to being at the money and higher when it is deep in or deep out of the money the exercise prices for which overpricing by b s takes place are within about ten percent of the security price this is the range of exercise prices over which most option trading takes place so we may in general expect the b s price to overprice options this effect is exaggerated as the time to maturity increases one of the most surprising implications of this is that if the b s equation is used to determine the implied volatility of a near the money option the longer the time to maturity the lower the implied volatility numerical solutions for the case in which the volatility is correlated with the stock price are also examined the stochastic volatility problem has been examined by merton 13 geske 7 johnson 10 johnson and shanno 11 eisenberg 5 wiggins 16 and

interest rate volatility and the term structure a two factor general equilibrium model we develop a two factor general equilibrium model of the term structure the factors are the short term interest rate and the volatility of the short term interest rate we derive closed form expressions for discount bonds and study the properties of the term structure implied by the model the dependence of yields on volatility allows the model to capture many observed properties of the term structure we also derive closed form expressions for discount bond options we use hansen s generalized method of moments framework to test the cross sectional restrictions imposed by the model the tests support the two factor model there are essentially two approaches to the modeling of the term structure of interest rates in continuous time the equilibrium approach pioneered by

transaction data tests of s p 100 call option pricing this paper examines the pricing of s p 100 calls using 14 months of transactions data we find that market prices of s p 100 calls differ systematically from black scholes values the biases in black scholes model prices are both statistically and economically significant and correspond to biases that arise if market prices incorporate a stochastically changing volatility of the index

interest rate changes and borrower search behavior abstract borrower search behavior regarding an outside lender is correlated with interest rate changes the results of a survey among german households reveal that surprisingly few mortgage borrowers switch to an outside lender when refinancing in a period of declining interest rates although non switching borrowers face significantly higher interest rates a laboratory experiment which adds the case of rising interest rates reveals that borrowers efforts to screen offers by outside lenders are significantly higher when interest rates rise than when they fall this behavior cannot be reconciled with alternative explanations overall several billion p a are transferred to lenders

internet advertising and the generalized second price auction selling billions of dollars worth of keywords we investigate the generalized second price gsp auction a new mechanism used by search engines to sell online advertising although gsp looks similar to the vickrey clarke groves vcg mechanism its properties are very different unlike the vcg mechanism gsp generally does not have an equilibrium in dominant strategies and truth telling is not an equilibrium of gsp to analyze the properties of gsp we describe the generalized english auction that corresponds to gsp and show that it has a unique equilibrium this is an ex post equilibrium with the same payoffs to all players as the dominant strategy equilibrium of vcg

financial literacy and mortgage equity withdrawals abstract mortgage equity withdrawals mew are correlated with covariates consistent with a permanent income framework augmented for credit constraints we assess linkages between mew and financial literacy education using the health and retirement study hrs and panel study of income dynamics psid we find that the financially literate are 3 5 percentage points less likely to withdraw housing equity via non home equity loan mortgages using the hrs while college graduates are 5 percentage points less likely than those without a high school degree in the psid among those withdrawing housing equity in the psid college graduates extract significantly less equity and are less likely to have high levels of housing leverage after doing so

displaced diffusion option pricing this paper develops a new option pricing formula that pushes the underlying source of risk back to the risk of individual assets of the firm the formula simultaneously encompasses differential riskiness of the assets of the firm their relative weights in determining the value of the firm the effects of firm debt and the effects of a dividend policy with both constant and random components although this setting considerably generalizes the black scholes 1 analysis it nonetheless produces a formula via riskless arbitrage arguments that given estimated inputs is as easy to use as the black scholes formula

monte carlo methods for security pricing the monte carlo approach has proved to be a valuable and flexible computational tool in modern finance this paper discusses some of the recent applications of the monte carlo method to security pricing problems with emphasis on improvements in efficiency we first review some variance reduction methods that have proved useful in finance then we describe the use of deterministic low discrepancy sequences also known as quasi monte carlo methods for the valuation of complex derivative securities we summarize some recent applications of the monte carlo method to the estimation of partial derivatives or risk sensitivities and to the valuation of american options we conclude by mentioning other applications

pricing stock and bond options when the default free rate is stochastic we derive formulas for the valuation of call options on stocks and bonds when the defaultfree rate is stochastic the formulas highlight the role of the correlation between the unanticipated returns on the underlying security and the changes in the short term rate in determining the options value our numerical analysis indicates that option prices predicted by the proposed formula differ from those predicted by the black and scholes formula when this correlation is relatively large and the short term rate s instantaneous variance is relatively large as well moreover the proposed formula predicts higher lower stock option prices than those predicted by the black and scholes formula for correlation values that are lower higher than some positive critical value

the use of the control variate technique in option pricing this paper presents a generalized version of the lattice approach to pricing options it shows how the control variate technique can produce significant improvements in the effi ciency ofthe approach the control variate technique is illustrated using american puts on dividend and nondividend paying stocks

the term structure of implied forward volatility recovery and informational content in the corn options market using a flexible method we develop the term structure of volatility implied by corn futures options with differing maturities and evaluate its ability to predict subsequent realized price volatility the implied forward volatilities anticipate realized volatility well for the nearby interval the implied forward volatilities provide unbiased forecasts and are superior to forecasts based on historical volatilities for more distant intervals early year options predict the direction and magnitude of future volatility changes about as well as a three year moving average and better than a naive forecast however later year options display less forecast power in part due to reduced trading activity

stochastic volatility option pricing this paper examines alternative methods for pricing options when the underlying security volatility is stochastic we show that when there is no correlation between innovations in security price and volatility the characteristic function of the average variance of the price process plays a pivotal role it may be used to simplify fourier option pricing techniques and to implement simple power series methods we compare these methods for the alternative mean reverting stochastic volatility models introduced by stein and stein 1991 and heston 1993 we also examine the biases in the black scholes model that are eliminated by allowing for stochastic volatility and we correct some errors in the stein and stein 1991 analysis of this issue empirical evidence on underlying asset prices and on their derivatives strongly suggests that asset price volatility is stochastic the pricing of options under this condition is therefore an important problem in this paper we study alternative option pricing methods that account for stochastic volatility we are particularly concerned with power series methods which we show to be quite accurate and easy to implement for alternative volatility specifications we point out their relation with recently proposed exact methods this permits a precise assessment of the approximation involved in the simple power series approach and of the impact of stochastic volatility on option prices following garman 1976 stochastic volatility option prices must satisfy a bivariate fundamental partial differential equation pde in the two state variables security price and volatility since volatility is not spanned by assets in the econ omy the volatility risk may not be eliminated by arbitrage methods therefore its market price explicitly enters into the pde the associated risk premium is owen graduate school of management vanderbilt university nashville tn 37203 and universita di siena facolta di scienza economiche e bancarie 53100 siena italy respectively part of this research was supported from a grant from the dean s fund and the financial markets research center at the owen school of management vanderbilt university some of this research was completed while roma was visiting the anderson graduate school of management ofthe university of california at los angeles we thank participants of the finance accounting and economics workshop at the owen school of management vanderbilt university for useful comments we appreciate the suggestions of roger huang craig lewis ron masulis and walter torous we thank joanne ball for editorial

stock price distributions with stochastic volatility an analytic approach we study the stock price distributions that arise when prices follow a diffusion process with a stochastically varying volatility parameter we use analytic techniques to derive an explicit closed form solution for the case where volatility is driven by an arithmetic ornstein ublenbeck or ar1 process we then apply our results to two related problems in the finance literature 1 options pricing in a world of stochastic volatility and 2 the relationship between stochastic volatility and the nature of fat tailes in stock price distributions article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

a continuous time arbitrage pricing model with stochastic volatility and jumps we formulate and test a continuous time asset pricing model using u s equity market data we assume that stock returns are driven by common factors including random jump size poisson processes and brownian motions with stochastic volatility the model places overidentifying restrictions on the mean returns allowing one to identify risk neutral probability distributions useful in pricing derivative securities we test for the restrictions and decompose moments of the asset returns into the contributions made by different factors our econometric methods take full account of time aggregation

the pricing of stock index options in a general equilibrium model this paper analyzes the pricing of stock index options in a simple general equilibrium model in this model the volatility of the stock index and the spot rate of interest are functions of a stochastic variable the paper investigates the biases that arise when using the black scholes model with the assumed volatility and interest rate dynamics it is shown that the model can in principle explain the biases observed in empirical work on stock index options

how important is the correlation between returns and volatility in a stochastic volatility model empirical evidence from pricing and hedging in the s p 500 index options market abstract this paper examines the importance of allowing for correlation between returns and volatility in a continuous time stochastic volatility option pricing model specifically it tests the closed form stochastic volatility model of heston review of financial studies 6 1993 327 343 that allows for non zero correlation in terms of pricing and hedging options on the s p 500 index it is found that non zero correlation in the stochastic volatility model leads to significant improvements in mispricing of out of the money options and overall pricing performance compared to if correlation is constrained to be zero in terms of hedging non zero correlation results in significantly lower hedging errors for out of the money options

price competition with consumer confusion this paper proposes a model in which identical sellers of a homogenous product compete in both prices and price frames i e ways to present price information we model price framing by assuming that firms frame choices affect the comparability of their price offers consumers may fail to compare prices due to frame differentiation and due to frame complexity in the symmetric equilibrium the firms randomize over both price frames and prices and make positive profits this result is consistent with the observed coexistence of price and price frame dispersion in the market we also show that i the nature of equilibrium depends on which source of consumer confusion dominates and ii an increase in the number of firms can increase industry profits and harm consumers

consumer confusion in the mortgage market evidence of less than a perfectly transparent and competitive market consumers often shop with incomplete infor mation about prices even when prices have a take it or leave it character as at the grocery store most shoppers don t know the price of milk at all nearby stores in markets where prices are dickered finding the best deal is more challenging the car shopper paying cash has to make offers and counteroffers to get an idea of the lowest price acceptable to a dealer and work one dealer against another in the mortgage market the shopper s task is even more difficult not only are prices dickered but price has two dimensions the interest rate on the loan and

predicting currency return volatility abstract standard deviations and elasticity of variance coefficients implied in currency option prices are employed to predict subsequent currency return volatility despite documented variance non stationarity strong predictive relationships are found the predictive accuracies of standard deviations and elasticity coefficients are statistically indistinguishable finally predictive accuracy is invariant to the weighting techniques employed

forecasting stock return variance toward an understanding of stochastic implied volatilities we examine the behavior of measured variances from the options market and the underlying stock market under the joint hypotheses that markets are informationally efficient and that option prices are explained by a particular asset pricing model forecasts from time series models of the stockreturn process should not have predictive content given the market forecast as embodied in option prices both in sample and out of sample tests suggest that this hypothesis can be rejected using simulations we show that biases inherent in the procedure we use to imply variances cannot explain this result thus we provide evidence inconsistent with the orthogonality restrictions of option pricing models that assume that variance risk is unpriced these results also have implicationsfor optimal variance forecast rules

bayes nash equilibria of the generalized second price auction abstract we develop a bayes nash analysis of the generalized second price gsp auction the multi unit auction used by search engines to sell sponsored advertising positions our main result characterizes the efficient bayes nash equilibrium of the gsp and provides a necessary and sufficient condition that guarantees existence of such an equilibrium with only two positions this condition requires that the click through rate of the second position is sufficiently smaller than that of the first when an efficient equilibrium exists we provide a necessary and sufficient condition for the auction revenue to decrease as click through rates increase interestingly under optimal reserve prices revenue increases with the click through rates of all positions further we prove that no inefficient equilibrium of the gsp can be symmetric our results are in sharp contrast with the previous literature that studied the gsp under complete information

analysis of the term structure of implied volatilities from various empirical work it is well known that the volatility of asset returns changes over time this might be one of the reasons that implied volatilities differ for options that only differ in time to maturity we construct models for the relation between short and long term implied volatilities based on three different assumptions of stock return volatility behavior i e mean reverting garch and egarch models we test these relations on option price data and conclude that egarch gives the best description of asset prices and the term structure of options implied volatilities

option pricing when the variance is changing the monte carlo method is used to solve for the price of a call when the variance is changing stochastically

computational analysis of perfect information position auctions abstract after experimentation with other designs major search engines converged on weighted generalized second price auctions wgsps for selling keyword advertisements theoretical analysis is still not able to settle the question of why they found this design preferable to other alternatives we approach this question in a new way adopting an analytical paradigm we dub computational mechanism analysis specifically we sample position auction games from a given distribution encode them in a computationally efficient representation language compute their nash equilibria and calculate economic quantities of interest we considered seven widely studied valuation models from the literature and three position auction variants we found that wgsp consistently showed the best ads of any position auction measured both by social welfare and expected number of clicks in contrast we found that revenue was extremely variable across auction mechanisms and was highly sensitive to equilibrium selection the preference model and the valuation distribution

inferior products and profitable deception we analyse conditions facilitating profitable deception in a simple model of a competitive retail market firms selling homogenous products set anticipated prices that consumers understand and additional prices that naive consumers ignore unless revealed to them by a firm where we assume that there is a binding floor on the anticipated prices our main results establish that bad products those with lower social surplus than an alternative tend to be more reliably profitable than good products specifically 1 in a market with a single socially valuable product and sufficiently many firms a deceptive equilibrium in which firms hide additional prices does not exist and firms make zero profits but perversely 2 if the product is socially wasteful then a profitable deceptive equilibrium always exists furthermore 3 in a market with multiple products since a superior product both diverts sophisticated consumers and renders an inferior product socially wasteful in comparison it guarantees that firms can profitably sell the inferior product by deceiving consumers we apply our framework to the mutual fund and credit card markets arguing that it explains a number of empirical findings regarding these industries

stock price volatility mean reverting diffusion and noise abstract using weekly call option prices on twenty five stocks over a ten year period 1975 1985 and calls on the s p 500 stock index futures we find that ex ante market volatility follows a mixed mean reverting diffusion with noise process changes in volatility are correlated across stocks and a marketwide volatility effect is found strong forces pull the volatility back to its long term value the findings suggest the development of new option pricing models

nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active cboe option classes from august 23 1976 through august 31 1978

teaching teenagers in finance does it work abstract many initiatives worldwide aim at improving financial literacy through targeted education programs yet there is little evidence regarding their effectiveness we examine the impact of a short financial education program on teenagers in german high schools our findings reveal that the training program significantly increases teenagers interest in financial matters and their financial knowledge especially their ability to properly assess the riskiness of assets behaviorally we observe a decrease in the prevalence of self reported impulse purchases but at the same time find no evidence of a significant increase in savings

a nonparametric kernel regression approach for pricing options on stock market index abstractprevious options studies typically assume that the dynamics of the underlying asset price follow a geometric brownian motion gbm when pricing options on stocks stock indices currencies or futures however there is mounting empirical evidence that the volatility of asset price or return is far from constant this article in contrast to studies that use parametric approach for option pricing employs nonparametric kernel regression to deal with changing volatility and accordingly prices options on stock index specifically we first estimate nonparametrically the volatility of asset return in the gbm based on the nadaraya watson n w kernel estimator then based on the n w estimates for the volatility we use monte carlo simulation to compute option prices under different settings finally we compare the index option prices under our nonparametric model with those under the black scholes model and the stein stein model

houses as atms mortgage refinancing and macroeconomic uncertainty we estimate a structural model of household liquidity management in the presence of long term mortgages households face counter cyclical idiosyncratic labor income uncertainty and borrowing constraints which aect optimal choices of leverage precautionary saving in liquid assets and illiquid home equity debt repayment mortgage renancing and default taking the observed historical path of house prices aggregate

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 empirical comparison of continuous time models of implied volatility indices abstract we explore the ability of alternative popular continuous time diffusion and jump diffusion processes to capture the dynamics of implied volatility indices over time the performance of the various models is assessed under both econometric and financial metrics to this end data are employed from major european and american implied volatility indices and the rapidly growing cboe volatility futures market we find that the addition of jumps is necessary to capture the evolution of implied volatility indices under both metrics mean reversion is of second order importance though the results are consistent across the various metrics markets and construction methodologies

approximating volatility diffusions with cev arch models abstract this article develops a new model of the arch class which allows volatility to react nonlinearly to past shocks as a function of the past volatility level we show that this model approximates any cev diffusion model for stochastic volatility and we judge its empirical performance as a diffusion approximation to models of the short term rate with stochastic volatility and as a filter of the unobserved volatility we show that the estimation of the continuous time scheme to which the discrete time arch model converges can be safely based on simple moment conditions linking the discrete time to the continuous time parameters a natural substitute of a global specification test for just identified problems based on indirect inference shows in fact that this approximation to diffusions gives rise to a negligible disaggregation bias a monte carlo study reveals that the filtering performances of this model are remarkably good even in the presence of serious misspecification

optimal timing of transmission line investments in the face of uncertain demand an option valuation approach abstract grid based electrification programmes involve irreversible transmission line investments that can be delayed by temporarily resorting to decentralized powet supply technologies in this context decision makers face the difficulty that the future evolution of demand and thus the returns from postponing the transmission line investment are uncertain this imposes an opportunity cost resembling the value of a financial call option therefore standard option valuation techniques can be applied to solve the problem of timing transmission line investments in the presence of stochastic demand it is shown analytically and in terms of numerical examples that demand uncertainty may provide a strong incentive to defer the extension of the grid beyond the date that would be optimal under deterministic conditions

diagnosing consumer confusion and sub optimal shopping effort theory and mortgage market evidence mortgage loans are leading examples of transactions where experts on one side of the market take advantage of consumers lack of knowledge and experience we study the compensation that borrowers pay to mortgage brokers for assistance from application to closing two findings support the conclusion that confused borrowers overpay for brokers services i a model of effective shopping shows that bor rowers sacrifice at least 1 000 by shopping from too few brokers ii borrowers who compensate their brokers with both cash and a commission from the lender pay twice as much as similar borrowers who pay no cash jel d12 d14 g21 we study a large and financially complex expenditure that the majority of consumers make only a few times in their lives the payment for mortgage origination services in these transactions information is not only imperfect but traditional market practices have likely contributed to consumer confusion these payments range from 0 to 30 000 for mortgages of normal size mortgage brokers receive payments from both borrowers and from wholesale lenders on most loans broker fees paid in cash by the borrower are usually broken down into more than a dozen individual items such as origination fee discount points funding fee and doc prep in addition to these cash payments about half of the value that the bor rower transfers to the broker takes the form of a payment from the wholesale lender to the mortgage broker the borrower bears the burden of this part of the payment in the form of a higher interest rate on the loan these payments compensate mortgage brokers for arranging mortgage loans we stress that this paper is about how and how much borrowers pay their brokers for origination services the broker is an administrator of the process of loan origination the broker bears none of the risk of default on the mortgage so that risk is not a determinant of the broker s compensation under standard theories of pricing because consumers enter the mortgage market infrequently and because features of the market make it difficult to learn the best price mortgage origination pricing

quadratic variation based dynamic strategies the paper analyzes a family of dynamic trading strategies which do not rely on any stochastic process assumptions aside from continuity and positivity and in particular do not require predicting future volatilities derivative payoffs can still be replicated except that this occurs at the stopping time at which the realized cumulative squared volatility hits a predetermined level the application of these results to portfolio insurance is emphasized and hedging strategies studied by black and jones and by brennan and schwartz are generalized classical results on european style options arise as special cases for example the initial cost of replicating a call or a put under the new method is given by a generalized black scholes formula which yields the ordinary black scholes formula when the volatility is derterministic

option values under stochastic volatility theory and empirical estimates abstract this paper numerically solves the call option valuation problem given a fairly general continuous stochastic process for return volatility statistical estimators for volatility process parameters are derived and parameter estimates are calculated for several individual stocks and indices the resulting estimated option values do not differ dramatically from black scholes values in most cases although there is some evidence that for longer maturity index options black scholes overvalues out of the money calls in relation to in the money calls

valuing futures and options on volatility abstract this paper presents simple closed form expressions for volatility futures and option prices and examines their implications for the characteristics of these securities we show that the properties of these volatility derivatives are fundamentally different from those of conventional option and futures contracts this analysis also provides insights into the role that volatility derivatives may play in managing and hedging volatility risk in financial markets

option arbitrage and strategy with large price changes abstract arbitrage pricing theorems are derived for options on stocks with jumps as a well as local movements the resulting valuation formulas depend on observable variables only closed form valuation expressions are obtained in the case of large positive and negative jumps these results translate into a simple algebra for characterizing the risk of arbitrage and investment portfolios a continuous time formulation of the infinite variance hypothesis leads to isomorphic pricing expressions

on valuing american call options with the black scholes european formula empirical papers on option pricing have uncovered systematic differences between market prices and values produced by the black scholes european formula such biases have been found related to the exercise price the time to maturity and the variance we argue here that the american option variant of the black scholes formula has the potential to explain the first two biases and may partly explain the third it can also be used to understand the empirical finding that the striking price bias reverses itself in different sample periods the expected form of the striking price bias is explained in detail and is shown to be closely related to past empirical findings the black scholes european option pricing model tends to exhibit systematic empirical biases when used to value american call options the reported biases

the e v stationarity of secure returns some empirical evidence abstract the joint hypothesis that the expected return vector and the variance covariance matrix of returns are intertemporally stationary is rejected for the monthly return data for securities included on the crsp file this finding is robust in that it is invariant to the type of sampling procedure used and to whether nominal or real security returns are used in contrast the hypothesis that the correlation matrix of returns is intertemporally stationary could not be rejected for the same samples of securities

option pricing and implicit volatilities abstract this paper demonstrates that black scholes implied volatilities can be used to value options in many situations where the assumptions of the black scholes model are violated including i alternative stock processes ii stochastic interest rates and iii market frictions given its computational simplicity this procedure provides an attractive alternative to the more complex models with a direct estimation procedure

modelling implied volatility with ols and panel data models abstract the paper performs an empirical estimation of time varying volatility using ols regression error components and dummy variable models by regressing the implied volatility on time to maturity the strike price and a dummy both the daily ols equations and the panel data model provide more accurate estimates of black and scholes option prices than the bench mark standard deviation of log returns ft se 100 index european options are used for empirical analysis

valuing target price support programs with average option pricing the u s government deficiency payment program supplements farm income by transferring income from taxpayers to farmers when revenue lost due to the acreage restriction exceeds revenue gained from participating in the program farmers lose money by participating therefore measuring expected revenue from the government program is important so that farmers can decide whether to participate in the program this study uses a garch average option pricing model and the black average option pricing model to predict the implicit premium of the u s government deficiency payment program the average option pricing model considers the average price of the underlying asset over a fixed period a regression model based on the simulation results is provided so that the average option models can be easily used to project deficiency payments the results can be used by extension economists to help producers decide whether to participate in the program

a bayesian approach to modeling stock return volatility for option valuation new measures of stock return volatility are developed to increase the precision of stock option price estimates with bayesian statistical methods volatility estimates for a given stock are developed using prior information on the cross sectional patterns in return volatil ities for groups of stocks sorted on size financial leverage and trading volume call option values computed with the bayesian procedure generally improve prediction accuracy for market prices of call options relative to those computed using implied volatility standard historical volatility or even the actual ex post volatility that occurred during each option s life although the bayesian methods produce biased call price estimators they do reduce the systematic tendency of standard pricing approaches to overprice underprice options on high low volatility stocks little bias improvement is observed with respect to the time to maturity and moneyness of the call options

market valuation of bank assets and deposit insurance in canada we examine a sample of canadian banks and use option pricing theory to infer the market value of a bank s assets from the observed market value and volatility of its equity we find that market value estimates are significantly different from corresponding book values these differences vary significantly across banks suggesting that market values provide bank specific information not found in book values we also derive that risk adjusted deposit insurance premia for these banks our results suggest that the current fixed rate deposit insurance premium system has resulted in significant

hedging derivative securities and incomplete markets an e arbitrage approach given a european derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based we solve the optimal replication problem find a self financing dynamic portfolio strategy involving only the underlying securities that most closely approximates the payoff function at maturity by applying stochastic dynamic programming to the minimization of a mean squared error loss function under markov state dynamics we derive recursive expressions for the optimal replication strategy that are readily implemented in practice the approximation error or e of the optimal replication strategy is also given recursively and may be used to quantify the degree of market incompleteness to investigate the practical significance of these e arbitrage strategies we consider several numerical examples including path dependent options and options on assets with stochastic volatility and jumps