jump diffusion processes and the term structure of interest rates the authors investigate the term structure of interest rates when the underlying state variables and production technologies follow the jump diffusion processes even in some cases where the traditional expectations theory about the term structure is consistent with general equilibrium under diffusion processes the traditional theory is not consistent under jump diffusion processes it is shown that bond prices are strictly higher under jump risks than otherwise and that consumers with logarithmic utility functions will develop hedge portfolios in the presence of jump diffusion a number of continuous time asset pricing models have been derived under stochastic diffusion processes with continuous sample paths see e g black and scholes 2 merton 21 breeden 3 and cox ingersoll and ross 8 however recent empirical studies see e g brown and dybvig 4 feinstone 10 and jarrow and rosenfeld 17 suggest that the underlying processes may follow

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

pricing european currency options a comparison of the modified black scholes model and a random variance model we use the modified black scholes model and a random variance option pricing model to study prices of european currency options traded in geneva the options which cannot be exercised early include calls and puts on the dollar swiss franc exchange rate in the empirical analysis we examine the model fit and the biases with respect to the strike price time to maturity and volatility there is some evidence of mispricing and there are small gains available by trading with the random variance model

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

currency option pricing with stochastic domestic and foreign interest rates this study develops a currency option pricing model under stochastic interest rates when interest rate parity holds and it is assumed that domestic and foreign bond prices have local variances that depend only on time we demonstrate how existing currency option models are simply derived from one framework empirical tests employing transactions option data reveal that a particularly simple form of the stochastic rate model is uniformly more accurate than a constant rate model for all boundaries and maturities tested

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

changing beliefs and systematic rational forecast errors with evidence from foreign exchange this paper addresses a new interpretation to the appearance in the early 1980s of systematic errors in forecasting the dollar exchange rate following a change in the process of a fundamental variable market participants revise their beliefs about the process using bayes rule since the market does not immediately recognize the change forecast errors are on average wrong during a period when the market is rationally learning for conservative parameter values the learning behavior of the dollar exchange rate in the early 1980s appears consistent with about half of the dollar s underprediction implied by the forward market copyright 1989 by american economic association

anomalies foreign exchange most all behavior can be explained by assuming that agents have stable well defined preferences and make rational choices consistent with those preferences in markets that eventually clear an empirical result qualifies as an anomaly if it is difficult to rationalize or if implausible assumptions are necessary to explain it within the paradigm this column will present a series of such anomalies readers are invited to suggest topics for future columns by sending a note with some reference to or better yet copies of the relevant research comments on anomalies printed here are also welcome the address

preference for the workplace investment in human capital and gender we use a hypothetical choice methodology to estimate preferences for workplace attributes from a sample of high ability undergraduates attending a highly selective university we estimate that women on average have a higher willingness to pay wtp for jobs with greater work flexibility and job stability and men have a higher wtp for jobs with higher earnings growth these job preferences relate to college major choices and to actual job choices reported in a follow up survey four years after graduation the gender differences in preferences explain at least a quarter of the early career gender wage gap

mixed diffusion jump process modeling of exchange rate movements this study demonstrates that the mixed diffusion jump process is superior to the stable laws or a mixture of normals as a model of exchange rate changes for the british pound french franc and the we st german mark relative to the united states dollar the parameter value s for the mixed diffusion jump process are dependent on the monetary policy regime in force in the united states with the estimates for the franc and mark being intertemporally similar but different from the pound copyright 1988 by mit press

on jump processes in the foreign exchange and stock markets exchange rates exhibit systematic discontinuities even after allowingfor conditional heteroskedasticity in the diffusion process the results are much more significant in theforeign exchange market than in the stock market which suggests differences in the structure of these markets finally this jump component is shown to explain some of the empirically observed mispricings in the currency options market the objective of this article is to analyze and compare the empirical distribution of returns in the stock market and in the foreign exchange market there are a number of reasons why a better understanding of the stochastic processes driving prices in these markets would be useful many financial models rely heavily on the assumption of a particular stochastic process while relatively little attention is paid to the empirical fit of the postulated distribution as a result models like option pricing models are applied indiscriminately to various markets such as the stock market and the foreign exchange market when the underlying processes may be fundamentally different the foreign exchange market for instance is characterized by active exchange rate man

are foreign exchange forecasts rational new evidence from survey data abstract tests of rationality in foreign exchange markets have been inconclusive because of disagreement over the relevant asset pricing model this paper uses a newly available set of data on foreign exchange expectations to directly test the rationality of four foreign currency markets overall the results reject the rational expectations hypothesis

a test for speculative bubbles in the sterling dollar exchange rate 1981 84 the u s dollar price of the u k pound sterling is tested for a speculative bubble defined as a period with a nonzero median in excessreturns a nonparametric procedure is developed which controls for data mining over the period of flexible exchange rates and finds a negative bubble in the excess return to holding sterling rather than dollar assets during the period 1981 84 possible interpretations arebootstrap equilibria rational bubbles nonsym metric fundamentals and nonrational expectations copyright 1986 by american economic association

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

reversal of asymmetries of allocation mechanisms under manipulation abstract consider a two person economy in which resources are allocated so as to maximize agent 1 s utility subject to the condition that agent 2 remains at least as well off as he was initially we show that agent 1 who is explicitly favored by the mechanism gains nothing by manipulation while agent 2 can reverse the asymmetry of the mechanism in his favor we give two other examples of mechanisms for which an analogous reversal of asymmetries takes place

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

sequential markets and the suboptimality of the friedman rule a cash in advance model with sequential markets is constructed where unanticipated monetary injections are nonneutral and can potentially produce large liquidity effects however if the monetary authority adheres to an optimal money rule money should not respond to unanticipated shocks so that a friedman rule is suboptimal and the monetary authority does not exploit the liquidity effect quantitatively the model can generate variability in money and nominal interest rates close to what is observed and can produce data with no obvious evidence of the existence of liquidity effects

general equilibrium pricing of options on the market portfolio with discontinuous returns when the price process for a long lived asset is of a mixed jump diffusion type pricing of options on that asset by arbitrage is not possible if trading is allowed only in the underlaying asset and a risk less bond using a general equilibrium framework we derive and analyze option prices when the underlying asset is the market portfolio with discontinuous returns the premium for the risk of jumps and the diffusion risks forms a significant part of the prices of the options in this economy an attempted replication of call and put options by the black scholes type of trading strategies may require substantial infusion of funds when jumps occur we study the cost and risk implications of such dynamic hedging plans article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

the valuation of options on futures contracts rational restrictions are derived for the values of american options on futures contracts for these options the optimal policy in general involves premature exercise a model is developed for valuing options on futures contracts in a constant interest rate setting despite the fact that premature exercise may be optimal the value of this american feature appears to be small and a european formula due to black serves as a useful approximation finally a model is developed to value these options in a world with stochastic interest rates it is shown that the pricing errors caused by ignoring the location of the interest rate relative to its long run mean range from 5 to 7 when the current rate is 200 basis points from its long run value the role of interest rate expectations is therefore crucial to the valuation optimal exercise policies are found from numerical methods for both models in recent years there has been a steady growth in the number of financial assets which one might properly call derivative assets that are available for trading on the organized exchanges among these the most recent and notable are options contracts written on available futures contracts options are now traded on the futures contracts on stock market indexes on the futures contracts on treasury instruments on the futures contracts on foreign exchange rates and on the futures contracts on some metals in design these options contracts do not differ substantially from the well known options contracts on common stock except that the underlying asset is a futures contract the received theory of the valuation of these options suggests that such contracts provide a direct vehicle for investors to alter the terminal payoffs on their portfolios to a desired distribution in the absence of these contracts investors would be forced to pursue a dynamic portfolio policy at the expense of considerable transactions in order to achieve a similar distribution indeed the availability of put options on the futures contracts on stock market indexes now enables well diversified investors to purchase portfolio insurance in his seminal work black 1 provided a complete description of forward and futures contracts as well as the description and valuation of european options on forward contracts and on spot commodities breeden 3 has examined the use of commodity options in a theoretical framework and courtadon 6 has studied the valuation of options on treasury bond futures french 13 cox