Estimation of objective and risk-neutral distributions based on moments of integrated volatility

Abstract

a b s t r a c tIn this paper, we present an estimation procedure which uses both option prices and high-frequency spot price feeds to estimate jointly the objective and risk-neutral parameters of stochastic volatility models. The procedure is based on a method of moments that uses analytical expressions for the moments of the integrated volatility and series expansions of option prices and implied volatilities. This results in an easily implementable and rapid estimation technique. An extensive Monte Carlo study compares various procedures and shows the efficiency of our approach. Empirical applications to the Deutsche mark-US dollar exchange rate futures and the S&P 500 index provide evidence that the method delivers results that are in line with the ones obtained in previous studies where much more involved estimation procedures were used.

Parametric and Nonparametric Volatility Measurement

“…In particular, following Hull and White (1987) and ignoring the return variation associated with the conditional mean, options prices only depend on the expected notional volatility (see also Garcia, Ghysels and Renault, 2002;and Garcia, Lewis and Renault, 2001). …”

Indirect inference with time series observed with error

“…Table 1 reports the Monte Carlo summary statistics of the indirect inference estimates of the Heston model parameters with and without accounting for the presence of MN, using different sampling frequencies, 30 seconds, 1, 5 and 30 minutes to construct the daily RV . The true parameter set is calibrated to values close to those found in empirical works, see Bollerlsev and Zhou (2002) and Garcia et al (2011), and are relative to percentage returns. The long-run mean parameter, ω, is set equal to 0.5 and 0.8, which corresponds to an annualized volatility of 11.2% and 14.2% respectively.…”

Econometrics of Option Pricing

“…Garcia, Lewis and Renault (2001) propose an estimation procedure which uses both option prices and high-frequency spot price feeds to estimate jointly the objective and risk-neutral parameters of stochastic volatility models. This procedure is based on series expansions of option prices and implied volatilities and on a method-of-moment estimation that uses analytical expressions for the moments of the integrated volatility.…”

“…A more informative exercise is to use option prices to calibrate the parameters under the risk neutral process given some version of a nonlinear least-squares procedure as in Bakshi, Cao and Chen (1997) and Bates (2000). An even more ambitious program is to use both the time series data on stock returns and the panel data on option prices to characterize the dynamics of returns with stochastic volatility and with or without jumps as in , Pan (2002), Poteshman (2000) and Garcia, Lewis and Renault (2001).…”