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Québécoisation method for the pricing of Parisian options with jump risk


Chesney, Marc; Vasiljevic, Nikola (2016). Québécoisation method for the pricing of Parisian options with jump risk. , University of Zurich.

Abstract

In this paper, a new technique for pricing of European and American Parisian options, that we call the québécoisation method, is developed. We study the pricing of Parisian options in a hyper-exponential jump-diffusion model using the double Laplace-Carson transform with respect to the time to maturity and the residual Parisian time (time to expiration of the Parisian window) of the system of two partial integro-differential equations describing the option price dynamics. The transformed, i.e., québécoised, option price and hedging parameters delta and gamma are computed in a closed form, and the final results are obtained via the two-dimensional Gaver-Stehfest inversion algorithm. Our pricing method is analytically tractable, and it provides important economic insights for pricing and hedging of European and American Parisian options in the presence of jumps.

Abstract

In this paper, a new technique for pricing of European and American Parisian options, that we call the québécoisation method, is developed. We study the pricing of Parisian options in a hyper-exponential jump-diffusion model using the double Laplace-Carson transform with respect to the time to maturity and the residual Parisian time (time to expiration of the Parisian window) of the system of two partial integro-differential equations describing the option price dynamics. The transformed, i.e., québécoised, option price and hedging parameters delta and gamma are computed in a closed form, and the final results are obtained via the two-dimensional Gaver-Stehfest inversion algorithm. Our pricing method is analytically tractable, and it provides important economic insights for pricing and hedging of European and American Parisian options in the presence of jumps.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:10 February 2016
Deposited On:10 Jun 2016 10:34
Last Modified:10 Jun 2016 10:37
Other Identification Number:merlin-id:13148

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