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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 7496539, 9 pages
http://dx.doi.org/10.1155/2016/7496539
Research Article

Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model

School of Economics and Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China

Received 11 December 2015; Accepted 8 March 2016

Academic Editor: Leonid Shaikhet

Copyright © 2016 Congyin Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Market crashes often appear in daily trading activities and such instantaneous occurring events would affect the stock prices greatly. In an unstable market, the volatility of financial assets changes sharply, which leads to the fact that classical option pricing models with constant volatility coefficient, even stochastic volatility term, are not accurate. To overcome this problem, in this paper we put forward a dynamic elasticity of variance (DEV) model by extending the classical constant elasticity of variance (CEV) model. Further, the partial differential equation (PDE) for the prices of European call option is derived by using risk neutral pricing principle and the numerical solution of the PDE is calculated by the Crank-Nicolson scheme. In addition, Kalman filtering method is employed to estimate the volatility term of our model. Our main finding is that the prices of European call option under our model are more accurate than those calculated by Black-Scholes model and CEV model in financial crashes.