PIDE and Solution Related to Pricing of Lévy Driven Arithmetic Type Floating Asian Options

Abstract

We propose a stochastic model to develop a pricing partial integro-differential equation (PIDE) and its Fourier transform expression for floating Asian 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 floating Asian options, and apply the Fourier 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.

Keywords:

• Asian option pricing
• Lévy Process
• Partial Integro-differential equations (PIDE)
• Equivalent Martingale measure
• Calibration

Mathematics Subject Classification:

• 91G80
• 91G20
• 91G60
• 91G70