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Options on realized variance by transform methods: A non-affine stochastic volatility model


Drimus, Gabriel G (2012). Options on realized variance by transform methods: A non-affine stochastic volatility model. Quantitative Finance, 12(11):1679-1694.

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 that allow upward-sloping implied volatility of variance smiles. Heston's model [Rev. Financial Stud., 1993, 6, 327–343], the benchmark affine stochastic volatility model, leads to downward-sloping volatility of variance smiles—in disagreement with variance markets in practice. Using control variates, we propose a robust method to express the Laplace transform of the variance call function in terms of the Laplace transform of the 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 that 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.

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 that allow upward-sloping implied volatility of variance smiles. Heston's model [Rev. Financial Stud., 1993, 6, 327–343], the benchmark affine stochastic volatility model, leads to downward-sloping volatility of variance smiles—in disagreement with variance markets in practice. Using control variates, we propose a robust method to express the Laplace transform of the variance call function in terms of the Laplace transform of the 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 that 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.

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15 citations in Web of Science®
12 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:2012
Deposited On:20 Feb 2012 15:06
Last Modified:05 Apr 2016 15:25
Publisher:Taylor & Francis
ISSN:1469-7688
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1080/14697688.2011.565789
Related URLs:http://ssrn.com/abstract=1485648
Other Identification Number:merlin-id:4238

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