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138
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 149 (5 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.
Recovering Risk Aversion from Option Prices and Realized Returns. Manuscript
, 1998
"... A relationship exists between aggregate riskneutral and subjective probability distributions and risk aversion functions. Using a variation of the method developed by Jackwerth and Rubinstein (1996), we estimate riskneutral probabilities reliably from option prices. Subjective probabilities are es ..."
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Cited by 140 (7 self)
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A relationship exists between aggregate riskneutral and subjective probability distributions and risk aversion functions. Using a variation of the method developed by Jackwerth and Rubinstein (1996), we estimate riskneutral probabilities reliably from option prices. Subjective probabilities are estimated from realized returns. This paper then introduces a technique to empirically derive risk aversion functions implied by option prices and realized returns simultaneously. These risk aversion functions dramatically change shapes around the 1987 crash: Precrash, they are positive and decreasing in wealth and thus consistent with standard economic theory. Postcrash, they are partially negative and increasing and irreconcilable with the theory. Overpricing of outofthemoney puts is the most likely cause. A simulated trading strategy exploiting this overpricing shows excess returns even after accounting for the possibility of further crashes and transaction costs. * Jens Carsten Jackwerth is a visiting assistant professor at the London Business School. For helpful discussions I
Optionimplied Riskneutral Distributions and Implied Binomial Trees: A Literature Review
 JOURNAL OF DERIVATIVES
, 1999
"... In this partial and selective literature review of option implied riskneutral distributions and of implied binomial trees, we start by observing that in efficient markets, there is information contained in option prices, which might help us to design option pricing models. To this end, we review ..."
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Cited by 54 (3 self)
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In this partial and selective literature review of option implied riskneutral distributions and of implied binomial trees, we start by observing that in efficient markets, there is information contained in option prices, which might help us to design option pricing models. To this end, we review the numerous methods of recovering riskneutral probability distributions from option prices at one particular timetoexpiration and their applications. Next, we extend our attention beyond one timetoexpiration to the construction of implied binomial trees, which model the stochastic process of the underlying asset. Finally, we describe extensions of implied binomial trees, which incorporate stochastic volatility, as well as other nonparametric methods.
Calibrating Volatility Surfaces Via RelativeEntropy Minimization
 Applied Mathematical Finance
, 1997
"... We present a framework for calibrating a pricing model to a prescribed set of option prices quoted... ..."
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Cited by 50 (2 self)
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We present a framework for calibrating a pricing model to a prescribed set of option prices quoted...
Derivative asset analysis in models with leveldependent and stochastic volatility
 CWI QUARTERLY
, 1996
"... In this survey we discuss models with leveldependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical BlackScholes model; they have been developed in an effort to build models that are flexible enough to cope wit ..."
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Cited by 42 (1 self)
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In this survey we discuss models with leveldependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical BlackScholes model; they have been developed in an effort to build models that are flexible enough to cope with the known deficits of the classical BlackScholes model. We start by briefly recalling the standard theory for pricing and hedging derivatives in complete frictionless markets and the classical BlackScholes model. After a review of the known empirical contradictions to the classical BlackScholes model we consider models with leveldependent volatility. Most of this survey is devoted to derivative asset analysis in stochastic volatility models. We discuss several recent developments in the theory of derivative pricing under incompleteness in the context of stochastic volatility models and review analytical and numerical approaches to the actual computation of option values.
A Market Model For Stochastic Implied Volatility
, 1998
"... In this paper a stochastic volatility model is presented that directly prescribes the stochastic development of the implied BlackScholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic movements of a full term structure of implied volatilities. T ..."
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Cited by 41 (1 self)
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In this paper a stochastic volatility model is presented that directly prescribes the stochastic development of the implied BlackScholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic movements of a full term structure of implied volatilities. The conditions are derived that have to be satisfied to ensure absence of arbitrage in the model and its numerical implementation is discussed.
Reconstructing The Unknown Local Volatility Function
 Journal of Computational Finance
, 1998
"... Using market European option prices, a method for computing a smooth local volatility function in a 1factor continuous diffusion model is proposed. Smoothness is introduced to facilitate accurate approximation of the true local volatility function from a finite set of observation data. It is emphas ..."
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Cited by 39 (5 self)
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Using market European option prices, a method for computing a smooth local volatility function in a 1factor continuous diffusion model is proposed. Smoothness is introduced to facilitate accurate approximation of the true local volatility function from a finite set of observation data. It is emphasized that accurately approximating the true local volatility function is crucial in hedging even simple European options, and pricing exotic options. A spline functional approach is used: the local volatility function is represented by a spline whose values at chosen knots are determined by solving a constrained nonlinear optimization problem. The optimization formulation is amenable to various option evaluation methods; a partial differential equation implementation is discussed. Using a synthetic European call option example, we illustrate the capability of the proposed method in reconstructing the unknown local volatility function. Accuracy of pricing and hedging is also illustrated. Moreover, it is demonstrated that, using a different constant implied volatility for an option with different strike/maturity can produce erroneous hedge factors. In addition, real market European call option data on the S&P 500 stock index is used to compute the local volatility function; stability of the approach is demonstrated.
Semiparametric Pricing of Multivariate Contingent Claims
, 1999
"... This paper derives and implements a nonparametric, arbitragefree technique for multivariate contingent claims (MVCC) pricing. This technique is based on nonparametric estimation of a multivariate riskneutral density function using data from traded options markets and historical asset returns. “New ..."
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Cited by 36 (3 self)
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This paper derives and implements a nonparametric, arbitragefree technique for multivariate contingent claims (MVCC) pricing. This technique is based on nonparametric estimation of a multivariate riskneutral density function using data from traded options markets and historical asset returns. “New ” multivariate claims are priced using expectations under this measure. An appealing feature of nonparametric arbitragefree derivative pricing is that fitted prices are obtained that are consistent with traded option prices and are not based on specific restrictions on the underlying asset price process or the functional form of the riskneutral density. Nonparametric MVCC pricing utilizes the method of copulas to combine nonparametrically estimated marginal riskneutral densities (based on options data) into a joint density using a separately estimated nonparametric dependence function (based on historical returns data). This paper provides theory linking objective and riskneutral dependence functions, and empirically testable conditions that justify the use of historical data for estimation of the riskneutral dependence function. The nonparametric MVCC pricing technique is implemented for the valuation of bivariate underperformance and outperformance options on the S&P500 and DAX index. Price deviations are
Implied Trinomial Trees of the Volatility Smile
 Journal of Derivatives
, 1996
"... This material is for your private information, and we are not soliciting any action based upon it. This report is not to be construed as an offer to sell or the solicitation of an offer to buy any security in any jurisdiction where such an offer or solicitation would be illegal. Certain transactions ..."
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Cited by 33 (0 self)
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