Abstract
In this paper we model the forward rate process as a stochastic partial differential equation in a Sobolev space. We establish the existence of a martingale measure. We also derive the price of a general contigent claim as the solution to a partial differential equation in an appropriate Hilbert space. Moreover we obtain an explicit formula for the price of the interest rate cap in the Gaussian framework.
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References
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© 2001 Springer Basel AG
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Bagchi, A., Kumar, K.S. (2001). An Infinite Factor Model for the Interest Rate Derivatives. In: Kohlmann, M., Tang, S. (eds) Mathematical Finance. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8291-0_5
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DOI: https://doi.org/10.1007/978-3-0348-8291-0_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9506-4
Online ISBN: 978-3-0348-8291-0
eBook Packages: Springer Book Archive