Research Of Volatility Risk Premium

How to model the dynamic process for the price of assets is an important issue for both academe and practitioners. This task becomes more difficult and more necessary when derivatives become prevalent in the market. Because the price of derivatives are computed with the dynamics process of the price of the underlying asset under the risk-neutral measure, but they are hedged in the real-life measure. And the dynamic processes under these two measures are different because of the risk premium. The traditional method for estimation of the dynamics process of asset price uses the information of the underlying asset or the information of the derivatives only. This induces the discrepancy between the results obtained from the information of the underlying asset and the counterpart obtained from the information of derivatives, which is quite dangerous for the risk management. In such a world which includes two sources of risk, the asset price and the volatility, the premium of the volatility risk is a key factor to combine the dynamics processes under the two measures, with which we can estimate the dynamics processes using both the information of the underlying asset and the derivatives.This paper uses the Hang Seng Index (HSI) and prices of options written on HIS to investigate the volatility risk premium on Hang Kong security market. By constructing a dynamic delta-neutral portfolio of call options written on HIS, this paper distills the information of the volatility risk premium from the return of the delta-neutral portfolio, and try to find out the factors influence the volatility risk premium. The results show the volatility risk premium in the Hong Kong security market is priced to be negative. And it is time variable, and is negatively correlative with the level of volatility, the scope and speed of the change of the underlying asset price, while it is positively correlative to the scope of the change of the volatility.Then, this paper proposes some kinds of the function for the volatility risk premium, which are based on the results of the first part of empirical research. Assuming the dynamic process of the price of the underlying asset follows the Heston (1993) model and the volatility risk premium functions are those this paper proposes, I estimate the dynamics process under both two measures jointly. The results show that the functions of the volatility risk premium which I propose improve the estimation evidently, while the Heston (1993) model and the traditional assumption of the volatility risk premium functions are not suitable to describe the dynamics process of the HIS.