Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define nonlinear partial integro–differential equations that are solved numerically for the three...

We report on the adequacy of using Sato processes to value equity structured products. In models used to price options on realized variance, the latter must be a random variable with a positive variance. An analysis of this variance of realized variance for Sato processes shows that these...

Index option pricing on world market indices are investigated using Levy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a rally before a...

When firms access unbounded liability exposures and are granted limited liability, then an all equity firm holds a call option, whereby it receives a free option to put losses back to the taxpayers. We call this option the taxpayer put, where the strike is the negative of the level of reserve...

The concept of the gamma of a financed return as the highest level of stress that a return distribution can withstand is introduced. Stress is measured by positive expectation under a concave distortion of the return distribution accessed. Four distortions introduced in Cherny and Madan (2008)...

Time consistency of the models used is an important ingredient to improve risk management. The empirical investigation in this article gives evidence for some models driven by Levy processes to be highly consistent. This means that they provide a good statistical fit of empirical distributions...

Models driven by Levy processes are attractive since they allow for better statistical fitting than classical diffusion models. The dynamics of the forward swap rate process is derived in a semimartingale setting and a Levy swap market model is introduced. In order to guarantee positive rates,...

One of the fundamental problems in financial mathematics is to develop efficient algorithms for pricing options in advanced models such as those driven by Lévy processes. Essentially there are three approaches in use. These are Monte Carlo, Fourier transform and partial integro-differential...

We study sufficient conditions under which a sequence of stochastic processes (Xn(t))t >= 0 can be approximated almost surely by another sequence of stochastic processes (Yn(t))t >= 0. Two different approaches are discussed.

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the...