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
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: Suggested Citation
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