Option Pricing Under a Mixed-Exponential Jump Diffusion Model

This paper aims to extend the analytical tractability of the Black-Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exp...

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Vydáno v:	Management science Ročník 57; číslo 11; s. 2067 - 2081
Hlavní autoři:	Cai, Ning, Kou, S. G.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Hanover, MD INFORMS 01.11.2011 Institute for Operations Research and the Management Sciences
Témata:	Algorithms Alternative approaches Applications Applied sciences Approximation Asset pricing barrier options Calibration Call options Diffusion index Diffusion models Distribution Distribution theory Economic models European option Exact sciences and technology Experimental economics Experiments first passage times Insurance, economics, finance jump diffusion Jump diffusion model Laplace transformation Laplace transforms lookback options Management science Mathematical economics Mathematical models Mathematics Merton's normal jump diffusion model Microelectromechanical systems mixed-exponential distributions Modeling Monte Carlo methods Normal distribution Operational research and scientific management Operational research. Management science Option pricing Options (Finance) Portfolio theory Prices Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Securities prices Size distribution Statistics Stochastic models Studies United States Euler equation Exponential distribution Differential equation Black Scholes model Gaussian distribution Inversion Modeling jump diffusion mixed-exponential distributions Stock exchange Pricing Diffusion process Jump process barrier options Integrodifferential equation Analytical solution Mixed distribution Heavy tail Calibration Mean estimation Weighting first passage times lookback options Mixed model Merton's normal jump diffusion model First passage time Distribution tail Laplace transformation Financial option Tariffication Maturity
ISSN:	0025-1909, 1526-5501
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Shrnutí:	This paper aims to extend the analytical tractability of the Black-Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing models, such as hyperexponential and double-exponential jump diffusion models, because the mixed-exponential distribution can approximate any distribution as closely as possible, including the normal distribution and various heavy-tailed distributions. The mixed-exponential jump diffusion model can lead to analytical solutions for Laplace transforms of prices and sensitivity parameters for path-dependent options such as lookback and barrier options. The Laplace transforms can be inverted via the Euler inversion algorithm. Numerical experiments indicate that the formulae are easy to implement and accurate. The analytical solutions are made possible mainly because we solve a high-order integro-differential equation explicitly. A calibration example for SPY options shows that the model can provide a reasonable fit even for options with very short maturity, such as one day. This paper was accepted by Michael Fu, stochastic models and simulation.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	0025-1909 1526-5501
DOI:	10.1287/mnsc.1110.1393