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Pricing and Hedging of Quantile Options in a Flexible Jump Diffusion Model

Part of: Integral transforms, operational calculus Markov processes

Published online by Cambridge University Press:  14 July 2016

Ning Cai
Ning Cai*
Affiliation:
The Hong Kong University of Science and Technology
*
∗ Postal address: Department of Industrial Engineering and Logistics Management, Room 5521, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. Email address: ningcai@ust.hk
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Abstract

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This paper proposes a Laplace-transform-based approach to price the fixed-strike quantile options as well as to calculate the associated hedging parameters (delta and gamma) under a hyperexponential jump diffusion model, which can be viewed as a generalization of the well-known Black-Scholes model and Kou's double exponential jump diffusion model. By establishing a relationship between floating- and fixed-strike quantile option prices, we can also apply this pricing and hedging method to floating-strike quantile options. Numerical experiments demonstrate that our pricing and hedging method is fast, stable, and accurate.

Keywords

Jump diffusionoption pricinghyperexponentialquantile optionEuler inversion

MSC classification

Secondary: 60J75: Jump processes 44A10: Laplace transform
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 637 - 656
Copyright
Copyright © Applied Probability Trust 2011 

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