Research Workshop and Conference on
Statistical methods in finance
July 13-17, 2015
Chennai, India

Organized by

Chennai Mathematical Institute
and
Indian Statistical Institute, Chennai

Pricing a Class of Lévy Driven Barrier Options using PIDE

Diganta Mukherjee, ISI Kolkata

Abstract: We propose a stochastic model to develop a pricing partial integro-differential equation (PIDE) and its Mellin transform expression for fixed type Single Barrier options based on the Itô-Lévy calculus. 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. Finally, the model is calibrated with the market data and its accuracy is presented.