Option Pricing with Lévy-Stable Processes

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 ...

Review of Option Pricing under Stochastic Volatility and Lévy Processes

Distinguished Limits of Lévy-Stable Processes, and Applications to Option Pricing

In this paper we derive analytic expressions for the value of European Put and Call options when the stock process follows an exponential Lévy-Stable process. It is shown that the generalised Black-Scholes operator for the Lévy-Stable case can be obtained as an asymptotic approximation of a process where the random variable follows a DampedLévy process. Finally, it is also shown that option pri...

Time-Changed Lévy Processes and Option Pricing

The classic Black-Scholes option pricing model assumes that returns follow Brownian motion, but return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non-normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. Time-change...

Option Pricing under Generalized Lévy Processes with State Dependent Parameters and the Volatility Surface

This paper presents a very general option pricing formula incorporating both the Lévy process methodology and the level dependent volatility approach. An approximate solution to the pricing problem is obtained throughout the construction of a parametrix by means of the pseudo differential calculus. Some examples are provided to illustrate the comprehensiveness of the framework. Finally, the imp...