Abstract

http://ssrn.com/abstract=2232131
 
 

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


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

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.

Number of Pages in PDF File: 21

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

JEL Classification: G13


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Date posted: March 12, 2013 ; Last revised: February 21, 2016

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: http://ssrn.com/abstract=2232131 or http://dx.doi.org/10.2139/ssrn.2232131

Contact Information

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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