Estimating and testing non‐affine option pricing models with a large unbalanced panel of options

Abstract

Summary In this paper, we consider joint estimation of objective and risk‐neutral parameters for stochastic volatility option pricing models using both stock and option prices. A common strategy simplifies the task by limiting the analysis to just one option per date. We first discuss its drawbacks on the basis of model interpretation, estimation results and pricing exercises. We then turn the attention to a more flexible approach, that successfully exploits the wealth of information contained in large heterogeneous panels of options, and we apply it to actual S&P 500 index and index call options data. Our approach breaks the stochastic singularity between contemporaneous option prices by assuming that every observation is affected by measurement error, essentially recasting the problem as a non‐linear filtering one. The resulting likelihood function is evaluated using a Monte Carlo Importance Sampling (MC‐IS) strategy, combined with a Particle Filter algorithm. The results provide useful intuitions on the directions that should be followed to extend the model, in particular by allowing jumps or regime switching in the volatility process.

Empirical Analysis of Affine Versus Nonaffine Variance Specifications in Jump-Diffusion Models for Equity Indices

“…That is, for modeling jumps we employ a jump model with stochastic jump sizes and constant jump intensity, a framework that is frequently used in the literature; see e.g. Eraker et al (2003), Broadie et al (2007), Durham (2013), or Ferriani and Pastorello (2012). The variance process in Equation (2) nests several specifications used in the literature.…”

“…However, some recent papers find jump components that do not fit these results. For example, Ferriani and Pastorello (2012) and Durham (2013) estimate very frequent jumps that have a slightly positive mean. Both papers use options, meaning that their information sets are different from ours.…”

Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets

“…See, e.g., Pan (2002), Eraker (2004), Broadie et al (2007), Christoffersen et al (2010), Johannes et al (2009) and Duan and Yeh (2011). However, as underlined in Ferriani and Pastorello (2012), most papers filtering information from option prices rely on one option per day or a limited set of options. Limiting the amount of data results in a computationally less intensive empirical exercise, but it ignores a large part of the information present in the markets.…”

Empirical Analysis of Affine vs. Non-Affine Variance Specifications in Jump-Diffusion Models for Equity Indices

“…For example, Ferriani and Pastorello (2012) and Durham (2013) estimate very frequent jumps that have a slightly positive mean. Both papers use options, meaning that their information sets are different from ours.…”

“…That is, for modeling jumps we employ a jump model with stochastic jump sizes and constant jump intensity, a framework that is frequently used in the literature; see e.g. Eraker et al (2003), Broadie et al (2007), Durham (2013), or Ferriani andPastorello (2012). The variance process in Equation (2) nests several specifications used in the literature.…”