Duality and Derivative Pricing with Lévy Processes

Pricing Derivatives on Two-dimensional Lévy Processes∗

The aim of this work is to use a duality approach to study the pricing of derivatives depending on two stocks driven by a bidimensional Lévy process. The main idea is to apply Girsanov’s Theorem for Lévy processes, in order to reduce the posed problem to a problem with one Lévy driven stock in an auxiliary market, baptized as “dual market”. In this way, we extend the results obtained by Gerber ...

Review of Option Pricing under Stochastic Volatility and Lévy Processes

Modeling Financial Security Returns Using Lévy Processes

Lévy processes can capture the behaviors of return innovations on a full range of financial securities. Applying stochastic time changes to the Lévy processes randomizes the clock on which the processes run, thus generating stochastic volatilities and stochastic higher return moments. Therefore, with appropriate choices of Lévy processes and stochastic time changes, we can capture the return dy...

Pricing Foreign Equity Option with time-changed Lévy Process

In this paper we propose a general foreign equity option pricing framework that unifies the vast foreign equity option pricing literature and incorporates the stochastic volatility into foreign equity option pricing. Under our framework, the time-changed Lévy processes are used to model the underlying assets price of foreign equity option and the closed form pricing formula is obtained through ...

Option Pricing with Lévy-Stable Processes

In this paper we show how to calculate European-style option prices when the log-stock and stock returns processes follow a symmetric Lévy-Stable process. We extend our results to price European-style options when the log-stock process follows a skewed Lévy-Stable process.