Time-Changed Lévy Processes and Option Pricing

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 ...

Numerical Algorithms for Pricing Discrete Variance and Volatility Derivatives under Time-changed Lévy Processes

We propose robust numerical algorithms for pricing discrete variance options and volatility swaps under general time-changed Lévy processes. Since analytic pricing formulas of these derivatives are not available, some of the earlier pricing methods use the quadratic variation approximation for the discrete realized variance. While this approximation works quite well for long-maturity options on...

Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes

We derive efficient and accurate analytical pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes. We extend the conditioning variable approach to derive the lower bound on the Asian option price and construct a sharp upper bound based on the lower bound. We also consider the general partially exact and bounded (PEB) approximations, which incl...

Review of Option Pricing under Stochastic Volatility and Lévy Processes

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.