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312
A closedform solution for options with stochastic volatility with applications to bond and currency options
 Review of Financial Studies
, 1993
"... I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond option ..."
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Cited by 699 (4 self)
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I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strikeprice biases in the BlackScholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems. Many plaudits have been aptly used to describe Black and Scholes ’ (1973) contribution to option pricing theory. Despite subsequent development of option theory, the original BlackScholes formula for a European call option remains the most successful and widely used application. This formula is particularly useful because it relates the distribution of spot returns I thank Hans Knoch for computational assistance. I am grateful for the suggestions of Hyeng Keun (the referee) and for comments by participants
Option Pricing: A Simplified Approach
 Journal of Financial Economics
, 1979
"... This paper presents a simple discretetime model for valumg optlons. The fundamental econonuc principles of option pricing by arbitrage methods are particularly clear In this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Blac ..."
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Cited by 562 (8 self)
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This paper presents a simple discretetime model for valumg optlons. The fundamental econonuc principles of option pricing by arbitrage methods are particularly clear In this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Black&holes model, which has previously been derived only by much more difficult methods. The basic model readily lends itself to generalization in many ways. Moreover, by its very constructlon, it gives rise to a simple and efficient numerical procedure for valumg optlons for which premature exercise may be optimal. 1.
An empirical comparison of alternative models of the shortterm interest rate
 Journal of Finance
, 1992
"... prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtai ..."
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Cited by 307 (2 self)
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prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
The Determinants of Credit Spread Changes
, 2001
"... Using dealer’s quotes and transactions prices on straight industrial bonds, we investigate the determinants of credit spread changes. Variables that should in theory determine credit spread changes have rather limited explanatory power. Further, the residuals from this regression are highly crossco ..."
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Cited by 223 (2 self)
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Using dealer’s quotes and transactions prices on straight industrial bonds, we investigate the determinants of credit spread changes. Variables that should in theory determine credit spread changes have rather limited explanatory power. Further, the residuals from this regression are highly crosscorrelated, and principal components analysis implies they are mostly driven by a single common factor. Although we consider several macroeconomic and financial variables as candidate proxies, we cannot explain this common systematic component. Our results suggest that monthly credit spread changes are principally driven by local supply0 demand shocks that are independent of both creditrisk factors and standard proxies for liquidity.
The Variance Gamma Process and Option Pricing.
 European Finance Review
, 1998
"... : A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional par ..."
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Cited by 196 (26 self)
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: A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options. The statistical and risk neutral densities are estimated for data on the S&P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black Scholes model that is a parametric special case of the option pricing model d...
Nonparametric Estimation of StatePrice Densities Implicit In Financial Asset Prices
 JOURNAL OF FINANCE
, 1997
"... Implicit in the prices of traded financial assets are ArrowDebreu prices or, with continuous states, the stateprice density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and derive its asymptotic sampling theory. This estimator provides an arbitragefree metho ..."
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Cited by 190 (3 self)
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Implicit in the prices of traded financial assets are ArrowDebreu prices or, with continuous states, the stateprice density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and derive its asymptotic sampling theory. This estimator provides an arbitragefree method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an assetpricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility "smiles" for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.
Asset pricing at the millennium
 Journal of Finance
"... This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior ..."
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Cited by 123 (3 self)
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This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and crosssectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work. Theorists develop models with testable predictions; empirical researchers document “puzzles”—stylized facts that fail to fit established theories—and this stimulates the development of new theories. Such a process is part of the normal development of any science. Asset pricing, like the rest of economics, faces the special challenge that data are generated naturally rather than experimentally, and so researchers cannot control the quantity of data or the random shocks that affect the data. A particularly interesting characteristic of the asset pricing field is that these random shocks are also the subject matter of the theory. As Campbell, Lo, and MacKinlay ~1997, Chap. 1, p. 3! put it: What distinguishes financial economics is the central role that uncertainty plays in both financial theory and its empirical implementation. The starting point for every financial model is the uncertainty facing investors, and the substance of every financial model involves the impact of uncertainty on the behavior of investors and, ultimately, on mar* Department of Economics, Harvard University, Cambridge, Massachusetts
A JumpDiffusion Model for Option Pricing
 Management Science
, 2002
"... Brownian motion and normal distribution have been widely used in the Black–Scholes optionpricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (as ..."
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Cited by 113 (3 self)
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Brownian motion and normal distribution have been widely used in the Black–Scholes optionpricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called “volatility smile ” in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jumpdiffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of optionpricing problems, including call and put options, interest rate derivatives, and pathdependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.