Analytical Approach to Value Options with State Variables of a Levy System

Abstract

In this paper we present an analytical method in pricing European contingent assets, whose state variables follow a multi-dimensional Levy process. We give an explicit formula for the hypothetical European "two-price" call option price by means of the conditional characteristic transform. The work not only unifies and extends the option pricing literature, which focuses on the use of the characteristic function, but also provides the way to formalize and and unify the valuation of the option price, the valuation of the discount bond price, the valuation of the scaled-forward price, and the valuation of the pricing measure in incomplete markets.

Keywords: Levy process, Jump-Diffusion process, Option Pricing, Fourier Transform, Characteristic Function

JEL Classification: G13