Smile from the Past: A general option pricing framework with multiple volatility and leverage components

In the current literature, the analytical tractability of discrete time option pricing models is guarantee only for rather specific type of models and pricing kernels. We propose a very general and fully analytical option pricing framework encompassing a wide class of discrete time models featuring multiple components structure in both volatility and leverage and a flexible pricing kernel with multiple risk premia. Although the proposed framework is general enough to include either GARCH-type volatility, Realized Volatility or a combination of the two, in this paper we focus on realized volatility option pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model of Corsi et al. (2012) to incorporate heterogeneous leverage structures with multiple components, while preserving closed-form solutions for option prices. Applying our analytically tractable asymmetric HARG model to a large sample of S&P 500 index options, we evidence its superior ability to price out-of-the-money options compared to existing benchmarks

Discrete-time volatility forecasting with persistent leverage effect and the link with continuous-time volatility modeling

We first propose a reduced-form model in discrete time for S&P 500 volatility showing that the forecasting performance can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly. We then estimate continuous-time stochastic volatility models that are able to reproduce the statistical features captured by the discrete-time model. We show that a single-factor model driven by a fractional Brownian motion is unable to reproduce the volatility dynamics observed in the data, while a multifactor Markovian model fully replicates the persistence of both volatility and leverage effect. The impact of jumps can be associated with a common jump component in price and volatility

Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models

We propose a general likelihood evaluation method for nonlinear non-Gaussian state-space models using the simulation-based method of efficient importance sampling. We minimize the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer to this method as numerically accelerated importance sampling. We show that the likelihood function for models with a high-dimensional state vector and a low-dimensional signal can be evaluated more efficiently using the new method. We report many efficiency gains in an extensive Monte Carlo study as well as in an empirical application using a stochastic volatility model for U.S. stock returns with multiple volatility factors. Supplementary materials for this article are available online