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...

Full description

Saved in:
Bibliographic Details
Published in:Management science Vol. 57; no. 11; pp. 2067 - 2081
Main Authors: Cai, Ning, Kou, S. G.
Format: Journal Article
Language:English
Published: Hanover, MD INFORMS 01.11.2011
Institute for Operations Research and the Management Sciences
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography: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