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
Indian Statistical Institute, Kolkata
North Dakota State University
January 24, 2014
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
Date posted: March 12, 2013 ; Last revised: February 21, 2016
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