## Journal of Applied Probability

### Pricing and hedging of quantile options in a flexible jump diffusion model

Ning Cai

#### Abstract

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.

#### Article information

Source
J. Appl. Probab., Volume 48, Number 3 (2011), 637-656.

Dates
First available in Project Euclid: 23 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1316796904

Digital Object Identifier
doi:10.1239/jap/1316796904

Mathematical Reviews number (MathSciNet)
MR2884805

Zentralblatt MATH identifier
1230.60088

Subjects
Primary: 60J75: Jump processes
Secondary: 44A10: Laplace transform

#### Citation

Cai, Ning. Pricing and hedging of quantile options in a flexible jump diffusion model. J. Appl. Probab. 48 (2011), no. 3, 637--656. doi:10.1239/jap/1316796904. https://projecteuclid.org/euclid.jap/1316796904

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