A combined compact difference scheme for option pricing in the exponential jump-diffusion models

In the present paper, starting with the Black–Scholes equations, whose solutions are the values of European options, we describe the exponential jump-diffusion model of Levy process type. Here, a jump-diffusion model for a single-asset market is considered. Under this assumption the value of a Europ...

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Bibliographic Details
Published in:Advances in difference equations 2019-12, Vol.2019 (1), p.1-13, Article 495
Main Authors: Akbari, Rahman, Mokhtari, Reza, Jahandideh, Mohammad Taghi
Format: Article
Language:English
Subjects:
Analysis
Black-Scholes equation
Combined compact difference (CCD)
Contingency
Difference and Functional Equations
Differential equations
Diffusion
Economic models
Exact solutions
Functional Analysis
Jump-diffusion model
Mathematics
Mathematics and Statistics
Option pricing
Options markets
Ordinary Differential Equations
Partial Differential Equations
Securities prices
Stochastic processes
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Summary:In the present paper, starting with the Black–Scholes equations, whose solutions are the values of European options, we describe the exponential jump-diffusion model of Levy process type. Here, a jump-diffusion model for a single-asset market is considered. Under this assumption the value of a European contingency claim satisfies a general “partial integro-differential equation” (PIDE). With a combined compact difference (CCD) scheme for the spatial discretization, a high-order method is proposed for solving exponential jump-diffusion models. The method is sixth-order accurate in space and second-order accurate in time. A known analytical solution to the model is used to evaluate the performance of the numerical scheme.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2431-7