Fin & math doc seminar

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Spring Semester 2013

Date / Time

Speaker

Title

Location

9 April 2013
11:15-12:00

Oleg Reichmann

Event Details

Fin & Math Doc Seminar

Title	Numerical option pricing beyond Lévy models
Speaker, Affiliation	Oleg Reichmann,
Date, Time	9 April 2013, 11:15-12:00
Location	HG G 43
Abstract	In this talk we consider the numerical approximation of option prices in different market models beyond Lévy processes. The Lévy setup is extended in several directions. The arising partial integrodifferential equations and inequalities are solved with the finite element method. European as well as American type contracts are considered. Spatially inhomogeneous market models are analyzed, specifically certain Feller processes are considered. The well-posedness of the arising pricing equations is proved using pseudodifferential operator theory. The resulting pricing equations need no longer be parabolic and can exhibit degeneracies under certain conditions. Classical continuous Galerkin methods are therefore inapplicable for the numerical solution of the corresponding pricing equations. Thus we employ a discontinuous Galerkin discretization. Besides the spatial inhomogeneity, also the assumption of temporal homogeneity of the coefficients of the partial integrodifferential equations is weakened. The well-posedness for pricing equations with degenerate coefficients in time is shown via a weak space-time formulation. The main problem arising in the discretization of such equations is the non-applicability of classical time-marching schemes due to the possible degeneracy of the coefficients. Therefore two alternative approaches are considered. First, a continuous Galerkin method for the space-time discretization is used, in this case optimality of the solution algorithm can be shown. Second, a discontinuous Galerkin discretization for the temporal domain is studied, in which case exponential convergence of the algorithm can be shown.

Numerical option pricing beyond Lévy modelsread_more

HG G 43

28 May 2013
11:15-12:00

Felix Matthys

Event Details

Fin & Math Doc Seminar

Title	The Term Structure of Interest Rates and Exchange Rate Dynamics under Uncertainty about Government and Monetary Policy
Speaker, Affiliation	Felix Matthys,
Date, Time	28 May 2013, 11:15-12:00
Location	HG G 43
Abstract	We develop a continuous time two country Lucas economy where the agents have incomplete information about government and monetary policy. Using the variational approach as in Grossman & Shiller (1982), we derive semi-closed formulas for the equilibrium exchange rate, the corresponding nominal short rate and term structure of interest rates for the two countries when both their agents face uncertainty about monetary and government policies. For two different standard utility functions of the country's representative agent, we discuss the effects of this uncertainty on the dynamics of the resulting equilibrium exchange rate and show that under non-separable power utility, the exchange rate is first, only driven by monetary quantities and second, only influenced by the relative uncertainty about monetary policy between the two countries. For separable power utility functions, the resulting equilibrium exchange rate will be on the one hand side driven by both monetary and real quantities and on the other hand affected by both uncertainty about monetary and government policy. We extend the analysis to determine the equilibrium forward rate and show that incorporating uncertainty about either government or monetary policy is able to give new answers to the forward premium puzzle. This is joint work with Markus Leippold.

The Term Structure of Interest Rates and Exchange Rate Dynamics under Uncertainty about Government and Monetary Policy read_more

HG G 43

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Organizers: Martin Herdegen

Archive: SS 15 AS 14 SS 14 AS 13 SS 13 AS 12