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SELF EXCITING THRESHOLD INTEREST RATES MODELS

Marc Decamps A · Marc J. Goovaerts · Wim Schoutens

52 citations0/0 files storedInternational Journal of Theoretical and Applied Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

Abstract

In this paper, we study a new class of tractable diffusions suitable for model primitives of interest rates. We consider scalar diffusions with scale s'(x) and speed m(x) densities discontinuous at the level x*. We call that family of processes Self Exciting Threshold (SET) diffusions. Following Gorovoi and Linetsky (2004), we obtain semianalytical expressions for the transition density of SET (killed) diffusions. We propose several applications to interest rates modeling. We show that SET short rate processes do not generate arbitrage possibilities and we adapt the HJM procedure to forward rates with discontinuous scale density. We also extend the CEV and the shiftedlognormal Libor market models. Finally, the models are calibrated to the U.S. market. SET diffusions can also be used to model stock price, stochastic volatility, credit spread, etc.

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References

1985A Theory of the Term Structure of Interest Rates 1999Continuous Martingales and Brownian Motion 1977An equilibrium characterization of the term structure 1992Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation 1991Continuous Martingales and Brownian Motion 19965 Stochastic volatility 1997The Market Model of Interest Rate Dynamics 1996Testing Continuous-Time Models of the Spot Interest Rate

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2007Chapter 6 Spectral Methods in Derivatives Pricing 2014Skew Ornstein–Uhlenbeck processes and their financial applications 2015Quasi-likelihood estimation of a threshold diffusion process 2018Statistical estimation of the Oscillating Brownian Motion

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