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Parisian Options with Jumps: A Maturity-Excursion Randomization Approach


Chesney, Marc; Vasiljevic, Nikola (2018). Parisian Options with Jumps: A Maturity-Excursion Randomization Approach. Quantitative Finance, 18(11):1887-1908.

Abstract

This paper introduces an analytically tractable method for the pricing of European and American Parisian options in a flexible jump-diffusion model. Our contribution is threefold. First, using a double Laplace-Carson transform with respect to the option maturity and the Parisian (excursion) time, we obtain closed-form solutions for different types of Parisian contracts. Our approach allows us also to analytically disentangle contributions of the jump and diffusion components for Parisian options in the excursion region. Second, we provide numerical examples and quantify the impact of jumps on the option price and the greeks. Finally, we study the non-monotonic effects of volatility and jump intensity close to the excursion barrier, which are important for shareholders’ investment policy decisions in a levered firm.

Abstract

This paper introduces an analytically tractable method for the pricing of European and American Parisian options in a flexible jump-diffusion model. Our contribution is threefold. First, using a double Laplace-Carson transform with respect to the option maturity and the Parisian (excursion) time, we obtain closed-form solutions for different types of Parisian contracts. Our approach allows us also to analytically disentangle contributions of the jump and diffusion components for Parisian options in the excursion region. Second, we provide numerical examples and quantify the impact of jumps on the option price and the greeks. Finally, we study the non-monotonic effects of volatility and jump intensity close to the excursion barrier, which are important for shareholders’ investment policy decisions in a levered firm.

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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
Scopus Subject Areas:Social Sciences & Humanities > Finance
Social Sciences & Humanities > General Economics, Econometrics and Finance
Language:English
Date:25 April 2018
Deposited On:31 Jan 2019 07:54
Last Modified:29 Jul 2020 09:04
Publisher:Taylor & Francis
ISSN:1469-7688
OA Status:Closed
Publisher DOI:https://doi.org/10.1080/14697688.2018.1444785
Related URLs:https://www.tandfonline.com/doi/abs/10.1080/14697688.2018.1444785 (Publisher)
Other Identification Number:merlin-id:16227

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