A Gaussian approximation scheme for computation of option prices in stochastic volatility models

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

“…The estimates of the mean reversion rate of the volatility β differ considerably, implying that the estimated spot volatility process is much more persistent when estimated from the joint data than when estimated from the single data. This result is consistent with previous findings (see e.g., Cheng et al, 2008). The estimate of the volatility of volatility σ is noticeably smaller with the joint data than using the single data.…”

“…In order to perform the joint estimation of objective and risk-neutral parameters, we consider the additional information provided by the option prices. As is common in derivative pricing applications, the distribution of option prices is determined by both an option pricing formula, which is (11) in our case, and an assumption of pricing errors (Cheng et al, 2008;Eraker, 2004;Jacquier & Jarrow, 2000;Polson & Stroud, 2003). The pricing errors are not only required to permit application of likelihood-based methods but are also plausible reflections of market microstructure effects (e.g., price discreteness, infrequent trading, bid-ask bounce).…”

“…1 The fundamental advantage of this approach is that it is able to estimate jointly the objective and risk-neutral parameters of the model, as well as the market prices of return and volatility risks that govern the change of measure in a way that maintains the internal consistency of the objective and risk-neutral measures. 2 There is a large and growing literature on the use of joint data on the underlying asset and option prices for the joint estimation of the model in recent years (e.g., Bollerslev, Gibson, & Zhou, 2011;Cheng, Gallant, Ji, & Lee, 2008;Chernov & Ghysels, 2000;Eraker, 2004;Ferriani & Pastorello, 2012;Garcia, Lewis, Pastorello, & Renault, 2011;Johannes, Polson, & Stroud, 2009;Jones, 2003;Pan, 2002;Polson & Stroud, 2003).…”

“…(Bollerslev et al, 2011;Garcia et al, 2011;Pan, 2002) and M.C.M.C. (Cheng et al, 2008;Eraker, 2004;Jones, 2003). The estimation procedure we adopt in this paper is based on the maximum likelihood (M.L.)…”

“…The proposed approach is a more sophisticated updating procedure, which is able to estimate jointly the objective and risk-neutral parameters of the model, as well as the market prices of risks. Moreover, many studies have provided evidence that the use of option prices can lead to more accurate estimates of model parameters and volatility (see, e.g., Cheng et al, 2008;Chernov & Ghysels, 2000;Eraker, 2004;Johannes et al, 2009;Polson & Stroud, 2003). Thus, it is also advantageous to estimate the model parameters and volatility using additional option price information so that more precise parameter and volatility estimates can be obtained.…”