REVISION: A Tale of Two Option Markets: Pricing Kernels and Volatility Risk
Date Posted: Feb 13, 2013
The S&P 500 and VIX option markets are closely connected as both options depend on the volatility dynamics. Capturing information in both option prices by nonparametric state-price densities (SPDs), we look into the dynamics of the index and its volatility, along with interactions between the two option markets. We find that SPDs of the index strongly depend on the current VIX level, and that such dependence is driven by information implied from VIX options beyond VIX time series, such as volati
New: Spot Variance Regressions
Date Posted: Feb 12, 2013
We study a nonlinear vector regression model for discretely sampled high-frequency data with the latent spot variance of an asset as a covariate. We propose a two-stage inference procedure by first nonparametrically recovering the volatility path from asset returns and then conducting inference based on the generalized method of moments (GMM). The GMM estimator is nonstandard in that the second-order asymptotics is dominated by a bias term, rendering the standard inference implausible. We propos
REVISION: Hermite Polynomial based Expansion of European Option Prices
Date Posted: Jan 03, 2013
We seek a closed-form series approximation of European option prices under a variety of diffusion models. The proposed convergent series are derived using the Hermite polynomial approach. Departing from the usual option pricing routine in the literature, our model assumptions have no requirements for affine dynamics or explicit characteristic functions. Moreover, convergent expansions provide a distinct insight into how and on which order the model parameters affect option prices, in contrast wi
REVISION: Econometric Analysis of Multivariate Realised QML: Estimation of the Covariation of Equity Prices un
Date Posted: Nov 11, 2012
Estimating the covariance and correlation between assets using high frequency data is challenging due to market microstructure effects and Epps effects. In this paper we extend Xiu’s univariate QML approach to the multivariate case, carrying out inference as if the observations arise from an asynchronously observed vector scaled Brownian model observed with error. Under stochastic volatility the resulting QML estimator is positive semi-definite, uses all available data, is consistent and asymp
REVISION: Quasi Maximum Likelihood Estimation of GARCH Models with Heavy-Tailed Likelihoods
Date Posted: Aug 06, 2012
The non-Gaussian maximum likelihood estimator is frequently used in GARCH models with the intention of capturing the heavy-tailed returns. However, unless the parametric likelihood family contains the true likelihood, the estimator is inconsistent due to density misspecification. To correct this bias, we identify an unknown scale parameter that is critical to the identification, and propose a two-step quasi maximum likelihood procedure with non-Gaussian likelihood functions. This novel approach
New: High Frequency Covariance Estimates with Noisy and Asynchronous Financial Data
Date Posted: Jun 28, 2010
This paper proposes a consistent and efficient estimator of the high frequency covariance (quadratic covariation) of two arbitrary assets, observed asynchronously with market microstructure noise. This estimator is built upon the marriage of the quasi-maximum likelihood estimator of the quadratic variation and the proposed Generalized Synchronization scheme. It is therefore not influenced by the Epps effect. Moreover, the estimation procedure is free of tuning parameters or bandwidths and readil
REVISION: Quasi-Maximum Likelihood Estimation of Volatility with High Frequency Data
Date Posted: Jun 28, 2010
This paper investigates the properties of the well-known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise, by extending the classic asymptotic results of quasi-maximum likelihood estimation. When trying to estimate the integrated volatility and the variance of noise, this parametric approach remains consistent, efficient and robust as a quasi-estimator under misspecified assumptions. Moreover, it shares the model-free feature with nonparametri