Parisian Options with Jumps: A Maturity–Excursion Randomization Approach

46 Pages Posted: 9 Aug 2017

See all articles by Marc Chesney

Marc Chesney

University of Zurich - Department of Banking and Finance

Nikola Vasiljevic

University of Zurich, Department of Banking and Finance; Swiss Finance Institute

Date Written: August 8, 2017

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.

Keywords: Parisian Options, Maturity–Excursion Randomization, Hyper-Exponential Jump–Diffusion Model, Excursion Disentanglement

JEL Classification: G13, C02, C65

Suggested Citation

Chesney, Marc and Vasiljevic, Nikola, Parisian Options with Jumps: A Maturity–Excursion Randomization Approach (August 8, 2017). Available at SSRN: https://ssrn.com/abstract=3015460 or http://dx.doi.org/10.2139/ssrn.3015460

Marc Chesney (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

HOME PAGE: http://https://www.bf.uzh.ch/en/persons/chesney-marc

Nikola Vasiljevic

University of Zurich, Department of Banking and Finance ( email )

Plattenstrasse 14
Zurich, CH-8032
Switzerland

Swiss Finance Institute

c/o University of Geneve
40, Bd du Pont-d'Arve
Geneva, CH-1211
Switzerland

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