Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has...

We develop efficient fast Fourier transform algorithms for pricing and hedging discretely sampled variance products and volatility derivatives under additive processes (time-inhomogeneous L evy processes). Our numerical algorithms are non-trivial versions of the Fourier space time stepping...

This paper presents the willow tree algorithms for pricing variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB), where the underlying fund dynamics evolve under the Merton jump-diffusion process or constant-elasticity-of-variance (CEV) process. The GMWB rider gives the...

Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive Bessel function evaluations. We propose a new exact simulation scheme without the Bessel function, based on the observation that the conditional...