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Studies in Nonlinear Dynamics & Econometrics

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Volume 18, Issue 2

Assessing the quality of volatility estimators via option pricing

Simona Sanfelici
Published Online: 2013-07-16 | DOI: https://doi.org/10.1515/snde-2012-0075

Abstract

The aim of this paper is to measure and assess the accuracy of different volatility estimators based on high frequency data in an option pricing context. For this, we use a discrete-time stochastic volatility model based on Auto-Regressive-Gamma (ARG) dynamics for the volatility. First, ARG processes are presented both under historical and risk-neutral measure, in an affine stochastic discount factor framework. The model parameters are estimated exploiting the informative content of historical high frequency data. Secondly, option pricing is performed via Monte Carlo techniques. This framework allows us to measure the quality of different volatility estimators in terms of mispricing with respect to real option data, leaving to the ARG volatility model the role of a tool. Our analysis points out that using high frequency intra-day returns allows to obtain more accurate ex post estimation of the true (unobservable) return variation than do the more traditional sample variances based on daily returns, and this is reflected in the quality of pricing. Moreover, estimators robust to microstructure effects show an improvement over the realized volatility estimator. The empirical analysis is conducted on European options written on S&P500 index.

This article offers supplementary material which is provided at the end of the article.

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Corresponding author: Simona Sanfelici, University of Parma, Department of Economics, Via J.F. Kennedy 6, 43125 Parma, Italy, e-mail:

Published Online: 2013-07-16

Published in Print: 2014-04-01

This means that $(σt2c|σt−12)~γ^(δ, βσt−12)$ or, equivalently, that $∃Z~P oiss(βσt−12)$ such that $((σt2c|σt−12)|Z)~γ(δ+Z).$

For each day in the sample and each time-to-maturity, ATM options are those having moneyness St/K closest to 1. According to this criterion, on each day the set of ATM options contains only one contract for each maturity.

The mispricing index $MISP=∑j=1NO(Cj−C^jC^j)/∑j=1NO|Cj−C^jC^j|$ ranges from -1 and 1 and indicates, on average, the overpricing (positive MISP) or underpricing (negative MISP) induced by the model. NO represents the total number of options in the sample.

Citation Information: Studies in Nonlinear Dynamics & Econometrics, Volume 18, Issue 2, Pages 103–124, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826,

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