Using an Euler discretization to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretization is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case...

Guo and Hung (2007) recently studied the complex logarithm present in the characteristic function of Heston's stochastic volatility model. They proposed an algorithm for the evaluation of the characteristic function that is claimed to preserve its continuity. We show their algorithm is correct,...

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all of its extensions, involve multivalued functions such as the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages,...

In this paper we derive a market value for Guaranteed Annuity Optionusing martingale modeling techniques. Furthermore, we show how to construct a static replicating portfolio of vanillainterest rate swaptions that replicates the Guaranteed Annuity Option. Finally, we illustrate with historical...

Double barrier options have become popular instruments in derivative markets. Several papers_new have already analyseddouble knock-out call and put options using different methods. In a recent paper, Geman and Yor (1996) deriveexpressions for the Laplace transform of the double barrrier option...