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Closed-form convexity and cross-convexity adjustments for Heston prices


Drimus, Gabriel G (2011). Closed-form convexity and cross-convexity adjustments for Heston prices. Quantitative Finance, 11(8):1137-1149.

Abstract

We present a new and general technique for obtaining closed-form expansions for prices of options in the Heston model, in terms of Black–Scholes prices and Black–Scholes Greeks up to arbitrary order. We then apply the technique to solve, in detail, the cases for the second-order and third-order expansions. In particular, such expansions show how the convexity in volatility, measured by the Black–Scholes volga, and the sensitivity of delta with respect to volatility, measured by the Black–Scholes vanna, impact option prices in the Heston model. The general method for obtaining the expansion rests on the construction of a set of new probability measures, equivalent to the original pricing measure, and which retain the affine structure of the Heston volatility diffusion. Finally, we extend the method to the pricing of forward-starting options in the Heston model.

We present a new and general technique for obtaining closed-form expansions for prices of options in the Heston model, in terms of Black–Scholes prices and Black–Scholes Greeks up to arbitrary order. We then apply the technique to solve, in detail, the cases for the second-order and third-order expansions. In particular, such expansions show how the convexity in volatility, measured by the Black–Scholes volga, and the sensitivity of delta with respect to volatility, measured by the Black–Scholes vanna, impact option prices in the Heston model. The general method for obtaining the expansion rests on the construction of a set of new probability measures, equivalent to the original pricing measure, and which retain the affine structure of the Heston volatility diffusion. Finally, we extend the method to the pricing of forward-starting options in the Heston model.

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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:2011
Deposited On:14 Feb 2012 09:45
Last Modified:05 Apr 2016 15:24
Publisher:Routledge / Taylor & Francis
ISSN:1469-7688 (P) 1469-7696 (E)
Publisher DOI:https://doi.org/10.1080/14697688.2010.549835
Other Identification Number:merlin-id:4239

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