Stochastic volatility Gaussian Heath-Jarrow-Morton models

Applied Mathematical Finance

Volumn 11, Issue 4, 2004, Pages 347-368

  Valchev, Stoyan ^a  

^a UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

Continuous time Markov chains; Heath Jarrow Morton model; Piecewise deterministic Markov processes; Stochastic volatility; Term structure of interest rates

Indexed keywords

EID: 10244226781     PISSN: 1350486X     EISSN: None     Source Type: Journal    
DOI: 10.1080/1350486042000231902     Document Type: Article

References (26)

1. Amin, K. and Morton, A. (1994) Implied volatility functions in arbitrage free term structure models, Journal of Financial Economics, 35, 141-80.
2. Ball, C. and Torous, W.N. (1999) The stochastic volatility of short-term interest rates: some international evidence, Journal of Finance, 6, 2339-59.
3. Bansal, R. and Zhou, H. (2002) Term structure of interest rates with regime shifts, Journal of Finance, 5, 1997-2043.
4. Brace, A., Gatarek, D. and Musiela, M. (1997) The market model of interest rate dynamics, Mathematical Finance, 7, 127-54.
5. Chen, R.R. and Scott, L. (2002) Stochastic volatility and jumps in interest rates: an empirical analysis, Working Paper.
6. Davis, M. (1984) Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models, Journal of Royal Statistical Society B, 46, 353-88.
7. Davis, M. (1998) A note on the forward measure. Finance and Stochastics, 2, 19-28.
8. Elliott, R., Aggoun, L. and Moore, J. (1995) Hidden Markov Models: Estimation and Control, Applications of Mathematics, Springer-Verlag, New York.
9. Elliott, R., Fischer, P. and Platen, E. (1999) Hidden Markov model filtering for a mean reverting interest rate model, Canadian Applied Mathematics Quarterly, 7, 381-400.
10. Elliott, R. and Wilson, C. (2001) The term structure of interest rates when a Markov chain is driving drift and volatility parameters of the short rate diffusion process. Working Paper.
11. Hansen, A. and Poulsen, R. (2000) A simple regime switching term structure model, Finance and Stochastics, 4, 409-29.
12. Harrison, J. and Kreps, D. (1979) Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, 20, 381-408.
13. Harrison, J. and Pliska, S. (1981) Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and Their Applications, 11, 215-60.
14. Heath, D., Jarrow, R. and Morton, A. (1990a) Bond pricing and the term structure of interest rates: a discrete time approximation, Journal of Financial and Quantitative Analysis. 25, 419-40.
15. Heath, D., Jarrow, R. and Morton, A. (1990b) Contingent claim valuation with a random evolution of interest rates, Review of Futures Markets, 9, 54-76.
16. Heath, D., Jarrow, R. and Morton, A. (1992) Bond pricing and the term structure of interest rates: a new methodology, Econometrica, 60, 77-105.
17. Ho, T.S.Y. and Lee, S.B. (1986) Term structure movements and the pricing of interest rate contingent claims, The Journal of Finance, 41, 1011-29.
18. Hull, J. and White, A. (1990) Pricing interest rate derivative securities, Review of Financial Studies, 3, 573-92.
19. Hull, J. and White, A. (1993) One-factor interest rate models and the valuation of interest rate derivative securities, Journal of Financial and Quantitative Analysis. 28, 235-54.
20. Landen, C. (2000) Bond pricing in a hidden Markov model of the short rate. Finance and Stochastics, 4, 371-89.
21. Miltersen, K. (1994) An arbitrage theory of the term structure of interest rates. Annals of Applied Probability, 4, 953-67.
22. Miltersen, K., Sandmann, K. and Sondermann, D. (1997) Closed form solutions for term structure derivatives with lognormal interest rates. Journal of Finance, 52, 409-30.
23. Morton, A. (1989) Arbitrage and martingales. Doctoral dissertation, Cornell University.
24. Musiela, M. and Rutkowski, M. (1997) Martingale Methods in Financial Modelling, Springer-Verlag, New York.
25. Rebonato, R. (2002) Modern Pricing of Interest Rate Derivatives. Princeton University Press, Princeton, NJ.
26. Vasicek, O. (1977) An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177-88.