In this paper we propose an estimation procedure which uses joint data on the underlying asset and option prices to extract market prices of return and volatility risks in the context of the G.A.R.C.H. diffusion model. The procedure is flexible and simple to implement. Firstly, a quasi-closed form pricing formula for European options in the G.A.R.C.H. diffusion model is derived. This result greatly eases the computational burden for computing option prices, and well suited for our model estimation. Then, based upon the joint data, we develop an efficient importance sampling-based maximum likelihood (E.I.S.-M.L.) estimation method for the objective and risk-neutral parameters of the G.A.R.C.H. diffusion model and a particle filter algorithm for latent state variable. Hence, this allows us to infer the market prices of risks that link the objective measure and the risk-neutral measure. Finally, we illustrate our approach using actual data on the Hang Seng Index (H.S.I.) and index warrant prices. The results show that both the return and volatility risks are priced by the market. Moreover, an option pricing study demonstrates that the market price of the volatility risk plays an important role in fitting option prices.

This paper extends the realized EGARCH-MIDAS (REGARCH-MIDAS) model to incorporate implied volatility (IV) derived from option prices. The extension allows us to examine the incremental information content of IV for forecasting volatility. An empirical investigation with S&P 500 index shows that IV contains valuable information for forecasting volatility. Our proposed model provides more accurate out-of-sample volatility forecasts compared to the EGARCH, the REGARCH and the REGARCH-MIDAS models as well as the EGARCH-IV and the REGARCH-IV models.

This paper proposes an extended conditional autoregressive range (EXCARR) model to describe the range-based volatility dynamics of financial assets.