Psychological barriers and option pricing in a local volatility model

In this paper, we investigate the possible existence of psychological barriers in the SSE 50 Index and find that the volatility of the index returns and the implied volatility around psychological barriers are significantly different. To capture this special behavior, a local volatility model (LVM) is introduced, and the price of the European call option is derived under this framework with the help of the Laplace transform approach. We also report the LVM's empirical and delta hedging performance relative to the Black-Scholes (BS) model, constant elasticity of variance (CEV) model and Jang et al.'s threshold model and find that for 50ETF and S&P 500 option pricing, the LVM is superior to the other three models.