Original scientific paper
https://doi.org/10.1080/1331677X.2017.1421989
Estimation of market prices of risks in the G.A.R.C.H. diffusion model
Xinyu Wu
; School of Finance, Anhui University of Finance and Economics, Bengbu, P.R. China
Hailin Zhou
; School of Finance, Anhui University of Finance and Economics, Bengbu, P.R. China
Shouyang Wang
; Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China
Abstract
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.
Keywords
Market prices of risks; G.A.R.C.H. diffusion model; option pricing; efficient importance sampling; maximum likelihood; particle filter
Hrčak ID:
200638
URI
Publication date:
3.12.2018.
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