Next Article in Journal
Multiplicative Expression for the Coefficient in Fermionic 3–3 Relation
Next Article in Special Issue
Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility
Previous Article in Journal
On Diff(M)-Pseudo-Differential Operators and the Geometry of Non Linear Grassmannians
Article Menu

Export Article

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

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

Department of Mathematics, Jadavpur University, West Bengal 700032, India
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]   |  


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

Figure 1

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).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top