Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Levy processes and other jump diffusions as well as stochastic volatility models with...

Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Levy processes and other jump diffusions as well as stochastic volatility models with...

We study the first hitting time of integral functionals of time-homogeneous diffusions, and characterize their Laplace transforms through a stochastic time change. We obtain explicit expressions of the Laplace transforms for the geometric Brownian motion (GBM) and the mean-reverting GBM process....

In this paper, we propose a general framework for the valuation of options in stochas-tic local volatility (SLV) models with a general correlation structure, which includes the Stochastic Alpha Beta Rho (SABR) model and the quadratic SLV model as special cases. Standard stochastic volatility...

We propose numerical schemes for pricing Asian options when the underlying asset price follows a very general state-dependent regime-switching jump-diffusion process. Under this model, the price of the option can be obtained by solving a highly complex system of coupled two-dimensional parabolic...

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in Palmowski & Rolski (2002). With this generic approach, we first derive explicit...

This paper presents a generic probabilistic approach to study elasticities and sensitivities of financial quantities under stochastic volatility models. We describe the shock elasticity, the quantile sensitivity and the vaga value of cash flows with respect to perturbation of the volatility...

We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local...

We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local...

Many financial assets, such as currencies, commodities, and equity stocks, exhibit both jumps and stochastic volatility, which are especially prominent in the market after the financial crisis. Some strategic decision making problems also involve American-style options. In this paper, we develop...