Options on Realized Variance by Transform Methods: A Non-Affine Stochastic Volatility Model

Quantitative Finance, 12(11), 1679-1694, (2012)

30 Pages Posted: 21 Nov 2009 Last revised: 7 Nov 2012

See all articles by Gabriel G. Drimus

Gabriel G. Drimus

Institute of Banking and Finance, University of Zürich

Date Written: September 19, 2009

Abstract

In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model, by developing efficient transform based pricing methods. This non-affine model gives prices of options on realized variance which allow upward sloping implied volatility of variance smiles. Heston's (1993) model, the benchmark affine stochastic volatility model, leads to downward sloping volatility of variance smiles - in disagreement with variance markets in practice. We show a robust method, using control variates, to express the Laplace transform of the variance call function in terms of the Laplace transform of realized variance. The proposed method works in any model where the Laplace transform of realized variance is available in closed form. Additionally, we apply a new numerical Laplace inversion algorithm which gives fast and accurate prices for options on realized variance, simultaneously at a sequence of variance strikes. The method is also used to derive hedge ratios for options on variance with respect to variance swaps.

Keywords: options on realized variance, transform pricing, variance swaps, stochastic volatility, 3/2 model, Heston model

JEL Classification: C63, G12, G13

Suggested Citation

Drimus, Gabriel G., Options on Realized Variance by Transform Methods: A Non-Affine Stochastic Volatility Model (September 19, 2009). Quantitative Finance, 12(11), 1679-1694, (2012). Available at SSRN: https://ssrn.com/abstract=1485648

Gabriel G. Drimus (Contact Author)

Institute of Banking and Finance, University of Zürich ( email )

Plattenstrasse 14
Zürich, CH-8032
Switzerland

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