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

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

Option pricing under the double stochastic volatility with double jump model

In this paper, we deal with the pricing of power options when the dynamics of the risky underling asset follows the double stochastic volatility with double jump model. We prove efficiency of our considered model by fast Fourier transform method, Monte Carlo simulation and numerical results using power call options i.e. Monte Carlo simulation and numerical results show that the fast Fourier tra...

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...