Pricing Options on Realized Variance in the Heston Model with Jumps in Returns and Volatility - Part II: An Approximate Distribution of Discrete Variance

Journal Of Computational Finance, 2012, Vol. 16, No. 2, pp. 3-32

23 Pages Posted: 25 Aug 2010 Last revised: 21 May 2014

See all articles by Artur Sepp

Artur Sepp

Sygnum Bank's Asset Management

Date Written: January 17, 2012

Abstract

We analyse the effect of the discrete sampling on the valuation of options on the realized variance in the Heston (1993) stochastic volatility model. It has been known for a while (Buehler (2006)) that, even though the quadratic variance can serve as an approximation to the discrete variance for valuing longer-term options on the realized variance, this approximation underestimates option values for short-term maturities (with maturities up to three months). We propose a method of mixing of the discrete variance in a log-normal model and the quadratic variance in a stochastic volatility model, which allows to accurately approximate the distribution of the discrete variance in the Heston model. As a result, we can apply semi-analytical Fourier transform methods developed by Sepp (2008) for pricing shorter-term options on the realized variance.

Keywords: realized variance, discrete variance, quadratic variance, variance swap, volatility derivatives, Heston model

JEL Classification: C00

Suggested Citation

Sepp, Artur, Pricing Options on Realized Variance in the Heston Model with Jumps in Returns and Volatility - Part II: An Approximate Distribution of Discrete Variance (January 17, 2012). Journal Of Computational Finance, 2012, Vol. 16, No. 2, pp. 3-32, Available at SSRN: https://ssrn.com/abstract=1664267

Artur Sepp (Contact Author)

Sygnum Bank's Asset Management ( email )

Uetlibergstrasse 134a
Zurich, 8045
Switzerland

HOME PAGE: http://artursepp.com

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