Estimation of market prices of risks in the G.A.R.C.H. diffusion model

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.

Quadrinomial trees with stochastic volatility to value real options

“…Considering the GARCH-diffusion model, over the time interval ½t i ; t k , where μ ∈ ℝ, α ≥ 0, θ > 0 and σ > 0 are constant, while fW ð1Þ t g t≥0 and fW ð2Þ t g t≥0 are independent one-dimensional standard Wiener motions, supposing further that S t ¼ S i and V t ¼ V i , probabilities of the transition and growth factors for the processes V t and S t , respectively, are defined as Pareja-Vasseur and Mar ın-S anchez ( 2019 Use multiple stock indexes to compare theoretical and empirical autocovariance. The conclusion was that this model captures autocovariance observed in data Plienpanich et al (2009) Integrated into the diffusion model a disturbance through a fractional noise, their results showed that the estimation of stock price of a commercial bank is better using this model than the traditional Black-Scholes model Wu et al (2012) Used the Hang Seng index (HSI) and concluded that using this model was better for predicting the price of warrants than the classic model Wu et al (2014) Studied Hong Kong stock market through American options and found the same advantage using this model against the traditional one Wu and Zhou (2016) Used the Chinese volatility index (iVIX); their findings indicated that the risk of volatility market values and risk premium volatility were negative, which implied that investors in the Shanghai stock exchange are risk averse Wu et al (2018) Wu et al (2020 They proposed an estimation procedure that uses joint data on the underlying asset and options prices. They used HSI data and index warrant prices.…”

“…Also, it has been used as a good model for adjusting financial option data (Christoffersen et al, 2010;Chourdakis and Dotsis, 2011;Kaeck and Alexander, 2012;Wu et al, 2012Wu et al, , 2014Wu et al, , 2018Wu et al, , 2020. The most recent applied research related to this model is summarized in Table 2.…”

Trading support method based on computational intelligence for speculators in the options market

“…Moments of future prices are important determinants on option markets and non-structural approach show potentials in estimating them (Šestanović et al, 2018). GARCH diffusion model proved to be valuable in estimating market prices risks according to the study of Wu et al (2018).…”

GARCH-type volatility in the multiplicative quadrinomial tree method: An application to real options

“…These conclusions were reaffirmed by Chourdakis and Dotsis (2011); although they also suggested that the model should consider a nonlinear drift against a linear one. Recent studies have indicated that this model gives a better description of the behavior and dynamics of financial series than other types of models, such as the well-known model of Heston (1993) (Aït-Sahalia & Kimmel, 2007Jones, 2003;Wu, Zhou, & Wang, 2018). It has been used as a good model for adjusting financial option data (Chourdakis & Dotsis, 2011;Christoffersen et al, 2010;Kaeck & Alexander, 2012;Wu et al, 2012).…”