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SUMMARY: We study the term structure models which are driven by a Lévy process, from the point of view of arbitrage and completeness. Exactly as for the Heath–Jarrow–Morton model, which fits into our class of models, we observe that the conditions on the coefficients for having no arbitrage opportunity are rather stringent. For the completeness problem, the(More)
Distributional assumptions for the returns on the underlying assets play a key role in valuation theories for derivative securities. Based on a data set consisting of daily prices of the 30 DAX shares over a three-year period, we investigate the distributional form of compound returns. After performing a number of statistical tests, it becomes clear that(More)
The complexity of modern financial derivatives very often leads to valuation problems that require the knowledge of the joint distribution of several random variables. This thesis aims to simplify and solve such valuation problems. Duality is related to the simplification of the valuation problem. We investigate changes of probability measures in an effort(More)
In this paper we consider the valuation of an option with time to expiration T and pay-oo function g which is a convex function (as is a European call option), and constant interest rate r, in the case where the underlying model for stock prices (S t) is a purely discontinuous process (hence typically the model is incomplete). The main result is that, for(More)
In this paper we present a model for the dynamic evolution of the term structure of default-free and defaultable interest rates. The model is set in the Libor market model framework but in contrast to the classical diffusion-driven setup, its dynamics are driven by a time-inhomogeneous Lévy process which allows us to better capture the real-world dynamics(More)
The purpose of this paper is to describe the appropriate mathematical framework for the study of the duality principle in option pricing. We consider models where prices evolve as general exponential semimartingales and provide a complete characterization of the dual process under the dual measure. Particular cases of these models are the ones driven by(More)
Statistical analysis of data from the nancial markets shows that generalized hyper-bolic (GH) distributions allow a more realistic description of asset returns than the classical normal distribution. GH distributions contain as sub-classes hyperbolic as well as normal inverse Gaussian (NIG) distributions which have recently been proposed as basic(More)