Abstract:

On February 9， 2015， the Shanghai Stock Exchange （SSE） launched its first exchange-traded option， the SSE 50 ETF option. The SSE 50 ETF option is an European-style option written on the 50 ETF. The SSE 50 ETF option provides an effective hedging instrument for the investors in China's stock market. One of the important issues for the development of derivatives markets is to address the question on how derivatives can be valued correctly. It aims to develop an appropriate model for pricing the SSE 50 ETF option in this paper.Classical option pricing theory （such as the Black-Scholes model） is based on the assumption that the underlying asset returns are normally distributed with constant volatility. However， the assumptions are inconsistent with empirical findings， resulting in option pricing biases. It is well recognized that asset returns exhibit characteristics such as skewness and heavy tails， which cannot be captured by using a normal distribution. Moreover， asset returns exhibit the volatility clustering property： the volatility changes over time and its degree shows a tendency to persist. To overcome the drawbacks of the conventional option pricing approach， the GARCH option pricing models have been developed. In particular， the GJR-GARCH-FHS option pricing model has been proved to be useful in fitting the option prices.However， the GJR-GARCH-FHS option pricing model does not exploit the high-frequency information for pricing options. The usefulness of high-frequency information to price options has been well established in the literature. In light of this， this paper proposes the REGARCH-FHS model which combines the realized EGARCH （REGARCH） model with the filtered historical simulation （FHS） method for pricing option. The model extends the conventional GJR-GARCH-FHS option pricing model by incorporating the rich high-frequency intraday information from the realized measure to price options. The model is easy to implement， allows for flexible change of measure and is able to capture volatility asymmetry （leverage effect） as well as non-Gaussian innovation distribution.Empirical analysis based on SSE 50 ETF options shows that our proposed REGARCH-FHS model outperforms the Black-Scholes and GJR-GARCH-FHS models in both in-sample and out-of-sample option pricing. Specifically， the root-mean-square error （RMSE） of the REGARCH-FHS model is 77.70% and 15.64% lower than the RMSE of the Black-Scholes and GJR-GARCH-FHS models in in-sample option pricing， while it is 64.16% and 5.40% lower than the RMSE of the Black-Scholes and GJR-GARCH-FHS models in out-of-sample option pricing. Moreover， the REGARCH-FHS model improves the GJR-GARCH-FHS model most significantly for the pricing of the short-term （days to maturity less than 60 days） in-sample and for the pricing of the short-term （days to maturity： 30-60 days） out-of-sample. Our results are robust to alternative criteria for pricing performance evaluation. In summary， our study highlights the value of incorporating the realized measure （price range） and the flexible FHS method for option pricing.

Key words: option pricing, realized EGARCH, GJR-GARCH, FHS, price range