Abstract
We present an overview of in project developed new techniques in computing key quantities of financial markets. Our approach is generic in the sense that the techniques apply essentially in the general frame work of markets which are described by systems of stochastic differential equations. We exemplify our methods in the LIBOR market model which is a standard interest rate market model widely used in practice and has its name from the daily quoted London interbank offered rates. The LIBOR market model has been developed in recent years beyond the classical framework in the direction of incomplete market models (with stochastic volatility and with jumps). Particular challenges are the high dimensionality (up to 20–40 factors), the calibration, and related problems of derivative prices evaluation and computation of sensitivities. We show how advanced Monte-Carlo techniques can be combined with analytic results about transition densities in order to obtain highly efficient and accurate numerical schemes for computing some of the key quantities in financial markets, especially hedging parameters.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Croitoru, C., Kampen, J.: Accurate numerical schemes and computation of a class of linear parabolic initial value problems. (in preparation)
Duffie, D.: Dynamic Asset Pricing Theory. Princeton, Princeton University Press (2001)
Fries, C., Kampen, J.: Proxy Simulation Schemes for generic robust Monte-Carlo sensitivities, process oriented importance sampling and high accuracy drift approximation (with applications to the LIBOR market model). Journal of Computational Finance, Vol. 10, Nr. 2
Fries, C., Kampen, J.: Proxy Simulation Schemes for generic robust Monte-Carlo sensitivities based on dimension reduced higher order analytic expansions of transition densities. (in preparation)
Fries, C.: Mathematical Finance. Theory, Modeling, Implementation. Wiley, Hoboken (2007), http://www.christian-fries.de/finmath/ book
Kampen, J.: The WKB-Expansion of the fundamental solution of linear parabolic equations and its applications. Book, submitted to Memoirs of the American Mathematical Society (electronically published at SSRN 2006)
Kampen, J.: How to compute the length of a geodesic on a Riemannian manifold with small error in arbitrarily regular norms. WIAS preprint (to appear)
Kampen, J.: Regular polynomial interpolation and global approximation of global solutions of linear partial differential equations. WIAS preprint (2007)
Kampen, J., Kolodko, A., Schoenmakers, J.: Monte Carlo Greeks for callable products via approximative Greenian Kernels. WIAS preprint, revised version to appear in SIAM Journal of computation (2007)
Krylov, N.V.: Lectures on Elliptic and Parabolic Equations in Hölder Spaces. Graduate Studies in Mathematics, Vol. 12, American Mathematical Society (1996)
Schoenmakers, J.: Robust Libor Modelling and Pricing of Derivative Products. Financial Mathematics. Chapman & Hall/CRC (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Croitoru, C., Fries, C., Jäger, W., Kampen, J., Nonnenmacher, DJ. (2008). On the Dynamics of the Forward Interest Rate Curve and the Evaluation of Interest Rate Derivatives and their Sensitivities. In: Krebs, HJ., Jäger, W. (eds) Mathematics – Key Technology for the Future. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77203-3_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-77203-3_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77202-6
Online ISBN: 978-3-540-77203-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)