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Stochastic volatility Gaussian Heath-Jarrow-Morton models

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  • Stoyan Valchev

Abstract

This paper extends the class of deterministic volatility Heath-Jarrow-Morton models to a Markov chain stochastic volatility framework allowing for jump discontinuities and a variety of deformations of the term structure of forward rate volatilities. Analytical solutions for the dynamics of the volatility term structure are obtained. Semimartingale decompositions of the interest rates under a spot and forward martingale measures are identified. Stochastic volatility versions of the continuous time Ho-Lee and Hull-White extended Vasicek models are obtained. Introducing a regime shift in volatility that is an exponential function of time to maturity leads to a Vasicek dynamics with regime switching coefficients of the short rate.

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  • Stoyan Valchev, 2004. "Stochastic volatility Gaussian Heath-Jarrow-Morton models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(4), pages 347-368.
    • Handle: RePEc:taf:apmtfi:v:11:y:2004:i:4:p:347-368
    DOI: 10.1080/1350486042000231902
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    3. Lian, Yu-Min & Chen, Jun-Home, 2022. "Foreign exchange option pricing under regime switching with asymmetrical jumps," Finance Research Letters, Elsevier, vol. 46(PA).
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    5. Mikael Elhouar, 2008. "Finite-dimensional Realizations of Regime-switching HJM Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 331-354.
    6. Lian, Yu-Min & Chen, Jun-Home & Liao, Szu-Lang, 2016. "Option pricing on foreign exchange in a Markov-modulated, incomplete-market economy," Finance Research Letters, Elsevier, vol. 16(C), pages 208-219.
    7. Olivier Le Courtois & François Quittard-Pinon & Xiaoshan Su, 2020. "Pricing and hedging defaultable participating contracts with regime switching and jump risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 303-339, June.
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