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Mathematics 2016, 4(1), 2; doi:10.3390/math4010002

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

1
Department of Mathematics, Jadavpur University, West Bengal 700032, India
2
Indian Statistical Institute, Kolkata, West Bengal 700108, India
*
Author to whom correspondence should be addressed.
Academic Editor: Anatoliy Swishchuk
Received: 22 November 2015 / Accepted: 14 December 2015 / Published: 4 January 2016
(This article belongs to the Special Issue Mathematical Finance)
View Full-Text   |   Download PDF [832 KB, uploaded 4 January 2016]   |  

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. View Full-Text
Keywords: Barrier option pricing; Lévy process; numerical inverse Mellin transform; simulation Barrier option pricing; Lévy process; numerical inverse Mellin transform; simulation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Chandra, S.R.; Mukherjee, D. Barrier Option Under Lévy Model : A PIDE and Mellin Transform Approach. Mathematics 2016, 4, 2.

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