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

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.

Reconstruction of the Time-Dependent Volatility Function Using the Black–Scholes Model

“…According to [3], the authors proposed the accurate computations for Greeks using the numerical solutions of the Black-Scholes partial differential equation. The wellknown standard Black-Scholes (BS) model is not adequate for calibrating the market option data because it uses the constant volatility [4][5][6]. As an alternative to the BS equation with constant volatility [7], local volatility models were introduced to explain the volatility smiles or skews observed in the market.…”