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.
Highlights
Nowadays, more and more researchers focus on stock option pricing problems
The volatility term is a compound function based on stock prices to the power of a nonparametric function, which implies that the model has dynamic elasticity of variance
First we put forward a new model, dynamic elasticity of variance (DEV) model, by extending the constant elasticity of variance (CEV) model to fit the process of stock prices in crashes
Summary
More and more researchers focus on stock option pricing problems. In different environments, such as bull markets or bear markets, the returns of stock prices have different properties and distributions to follow, based on which many different models (see [1,2,3,4,5,6,7]) are proposed and some analytic formulae or approximations are provided. Yoon et al in [21, 22] study problems of option pricing under stochastic elasticity of variance model and their works enhance the existing option price structures in view of flexibility and applicability through the market prices of elasticity risk For these processes, there exist some certain distributions they followed. In this paper we put forward a semiparametric model with parametric drift coefficient and nonparametric volatility term to imitate the motion of stock prices in crashes In this model, the volatility term is a compound function based on stock prices to the power of a nonparametric function, which implies that the model has dynamic elasticity of variance. Our main contributions and findings in this paper include that we first put forward a dynamic elasticity of variance model to explain the big changes of volatility and of option prices in crashes. In the last section we make some conclusions
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