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

Sudip Ratan Chandra and Diganta Mukherjee
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Sudip Ratan Chandra: Department of Mathematics, Jadavpur University, West Bengal 700032, India
Diganta Mukherjee: Indian Statistical Institute, Kolkata, West Bengal 700108, India

Mathematics, 2016, vol. 4, issue 1, 1-18

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; Lévy process; numerical inverse Mellin transform; simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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