Realizing Smiles: Options Pricing with Realized Volatility

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Bates, our referee, for helpful comments and suggestions. We are also grateful to Torben Andersen, Giovanni Barone-Adesi, Francesco Permanent repository linkCorielli, Christian Gourieroux, Peter Gruber, Patrick Gagliardini, Loriano Mancini, Nour Meddahi, Alain Monfort, Fulvio Pegoraro, Roberto Renó, Viktor Todorov, and Fabio Trojani for their constructive discussions and remarks. We also thank the participants at the SoFiE conference held in Chicago. All errors are our own responsibility. The authors acknowledge the Swiss National Science Foundation Pro*Doc program, the NCCR FinRisk, and the Swiss Finance Institute for partial financial support. AbstractWe develop a discrete-time stochastic volatility option pricing model exploiting the information contained in the Realized Volatility (RV), which is used as a proxy of the unobservable log-return volatility. We model the RV dynamics by a simple and effective long-memory process, whose parameters can be easily estimated using historical data. Assuming an exponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An empirical analysis of Standard and Poor's 500 index options illustrates that our model outperforms competing time-varying and stochastic volatility option pricing models.

Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach

“…In Corsi et al (2013), deep out-of-momey is defined as S/K > 1.06 or S/K < 0.94. 10 The analytical approximation (7) ensures that the Vega-adjusted option pricing error is free from sampling error and therefore a well defined objective function.…”

“…where z t and u t are independent standard normal random variables. This specification of risk-neutralization has also been adopted in option pricing models using realized variance, such as those of Corsi et al (2013), Christoffersen et al (2014), andMajewski et al (2015). This specification of risk-neutralization degenerated to the locally risk-neutral valuation relationship (LRNVR) of Duan (1995)…”

“…Their paper also suggests the need for further research on pricing, using non-affine models and modeling leverage effect separately for both return and realized measures. A related framework is that in Corsi, Fusari, and Vecchia (2013), who employ a Heterogeneous Autoregressive Gamma (HARG) model. This model assumes that the realized variance follows a simple process (with linear long-memory features) and option pricing can be obtained using Monte Carlo simulation.…”

“…This transformation makes the model more stable, especially during periods with high volatility of volatility.A quasi closed-form option pricing formula is very hard to obtain for a non-affine model, using the standard method based on the moment-generating function and the inverse Fourier transformation. When a closed-form expression is unavailable one can resort to Monte Carlo methods, see, for example, Corsi et al (2013) and Kanniainen, Lin, and Yang (2014). While this method is straight forward to apply, it can be very time consuming to achieve a desirable accuracy.…”

VIX term structure and VIX futures pricing with realized volatility

“…The appealing feature of such mapping is that it preserves the structure of the model and, as a result, the closed-form pricing formula. Following studies such as Corsi et al (2013) and others, we use this "upgraded" benchmark model (referred to as HNG hereafter) to ensure fairness in the comparison.…”