Research Of Dynamic Implied Volatility Models Based On Hong Kong Market

Implied volatility is the volatility that yields the same price as the market for a European option when substituted into the BS formula. For a particular underlying asset, the surface which reflects the implied volatility as a function of the strike price and the time to maturity was called implied volatility surface. Research for this surface is one of the most important pricing literature. Market traders not only care about the shape of the surface, but also pay much attention to the dynamic process of the whole surface. And for the purpose of derivatives pricing, it is also important to specify the evolution rule under the risk-neutral world.Based on the HSI option data, this paper makes some empirical study on the implied volatility surface of the HSI option. This paper applies the theory framework of no-arbitrage restrict condition for the evolution of the implied volatility surface under the risk-neutral world, which was first studied by Schonbucher(1999). So, this paper focuses on the empirical modeling and estimating of the dynamic process of the implied volatility surface under the real world. Firstly, this paper tests the three popular determined evolution rules of the implied volatility surface, and the results shows that, no matter in the long-time period or in the short-time period, all the three simple determined rules can't explain the dynamic process of the implied volatility. So, stochastic implied volatility model was applied. This paper applies the parametrical factor-based model method, and finally constructs a five-factor stochastic implied volatility model after a series of tests and analysis. As for the estimation of the model, the simple two-stage method may yield a large error because of the overfitting problem which is caused by the deficiency of the cross section data during the sample periods. Pointed to this problem, this paper applies the Extended Kalman Filter method which is based on the incomplete panel-data. The final result shows that the five-factor stochastic implied volatility model estimated by Kalman Filter method fits well in the revolution of the implied volatility surface under the real world.