Term Structure Models Driven by Wiener Processes and Poisson Measures: Existence and Positivity

Damir Filipović · Stefan Tappe · Josef Teichmann

96 citations0/0 files storedSIAM Journal on Financial Mathematics

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Stochastic processes and financial applications Economic theories and models Fuzzy Systems and Optimization

Abstract

In the spirit of [T. Björk et al., Finance Stoch., 1 (1997), pp. 141–174], we investigate term structure models driven by Wiener processes and Poisson measures with forward curve dependent volatilities. This includes a full existence and uniqueness proof for the corresponding Heath–Jarrow–Morton-type term structure equation. Furthermore, we characterize positivity preserving models by means of the characteristic coefficients. A key role in our investigation is played by the method of the moving frame, which allows us to transform term structure equations to time-dependent SDEs.

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References

1985A Theory of the Term Structure of Interest Rates 1992Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation 1971On the uniqueness of solutions of stochastic differential equations 1997Bond Market Structure in the Presence of Marked Point Processes 1997Towards a general theory of bond markets 2001Consistency Problems for Heath-Jarrow-Morton Interest Rate Models 1999Term Structure Models Driven by General Lévy Processes 2009Term-Structure Models: A Graduate Course

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