Abstract: In the past decades, with the rapid development of China's financial markets, more and more derivative products, such as warrants, currency options and covertible bonds have been introduced into the markets. Specially, the SSE 50ETF option, the first stock option in China, was introduced in February 2015. The introduction of the SSE 50ETF options makes the China's equity market more complete. The purpose of this paper is to develop reasonable model for the pricing of the options. It is of great importance for investors and risk managers.
Traditionally, the pricing of options is based on the classical Black-Scholes (B-S) option pricing model. However, an extensive empirical literature has documented the empirical biases of the B-S option pricing model. Most prominently among these biases, observed market prices for out-of-the-money puts and in-the-money calls are higher than the B-S prices. This stylized fact is known as the "volatility smirk". To modeling the smirk, stochastic volatility (SV) models have been introduced. The SV models are popular in the option pricing literature, which have been proved to be helpful in modeling the smirk.
However, in the conventional SV option pricing, investors are supposed to have constant risk preferences. Numerous recent studies have found that the market participants' risk preferences exhibit time-varying characteristics. In contrast to conventional SV option pricing with constant risk aversion, this paper concentrates on the issue of option pricing under time-varying risk aversion. Firstly, by extending the conventional (non-affine) SV option pricing model with constant risk aversion (hereafter CRA-SV option pricing model), a SV option pricing model with time-varying risk aversion (hereafter TVRA-SV option pricing model) is developed to price options, and further the effect of time-varying risk aversion on option prices is examined. Secondly, an estimation approach, the continuous particle filter-based maximum likelihood estimation method, is presented for joint estimation of the objective and risk-neutral parameters of the pricing model, using information provided by the underlying asset and options data. Finally, using the actual financial market data on the SSE 50ETF options, empirically the performance of the developed pricing model is investigated. The results show that the TVRA-SV option pricing model leads to substantial improvements in the empirical fit over the conventional CRA-SV option pricing model, and can describe the volatility dynamics of the underlying SSE 50ETF returns more adequately under both the objective and risk-neutral measures. Moreover, the TVRA-SV option pricing model produces much more accurate option prices than the conventional B-S option pricing model and CRA-SV option pricing model.

Key words: option pricing, time-varying risk aversion, two-factor non-affine stochastic volatility, SSE 50ETF options, continuous particle filters