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Barrier Option Under Lévy Model: A PIDE and Mellin Transform Approach

21 Pages Posted: 12 Mar 2013 Last revised: 12 Feb 2017

Sudip Ratan Chandra

University of Kent, Canterbury - School of Mathematics, Statistics and Actuarial Science; Indian Statistical Institute, Kolkata

Diganta Mukherjee

Indian Statistical Institute, Kolkata

Indranil SenGupta

North Dakota State University

Date Written: January 24, 2014

Abstract

We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Lévy processes leading to the market inherently incomplete, and dynamic hedging is no longer risk free. We first develop a PIDE for fixed type Barrier options, and apply the Mellin transform to derive a pricing expression. Our main contribution is to develop a PIDE with its closed form pricing expression for the contract. The procedure is easy to implement for all class of Lévy processes numerically. Finally, the algorithm for computing numerically is presented with results for a set of Lévy processes.

Keywords: Barrier Option pricing, Levy Process, Incomplete Market, Numerical Inverse Mellin Transform, Simulation

JEL Classification: G13

Suggested Citation

Chandra, Sudip Ratan and Mukherjee, Diganta and SenGupta, Indranil, Barrier Option Under Lévy Model: A PIDE and Mellin Transform Approach (January 24, 2014). Available at SSRN: https://ssrn.com/abstract=2232131 or http://dx.doi.org/10.2139/ssrn.2232131

Sudip Ratan Chandra (Contact Author)

University of Kent, Canterbury - School of Mathematics, Statistics and Actuarial Science ( email )

Cornwallis Building
Canterbury, CT2 7NF
United Kingdom

Indian Statistical Institute, Kolkata ( email )

203 B.T. Road
Kolkata, West Bengal 700108
India

Diganta Mukherjee

Indian Statistical Institute, Kolkata ( email )

203 B.T. Road
Kolkata, West Bengal 700108
India

Indranil SenGupta

North Dakota State University ( email )

Fargo, ND 58105
United States

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