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Abstract
In this paper we develop a stochastic model incorporating a double-Markov modulated mean-reversion model. Unlike a price process the basis process X can take positive or negative values. This model is based on an explicit discretisation of the corresponding continuous time dynamics. The new feature in our model is that we suppose the mean reverting level in our dynamics as well as the noise coefficient can change according to the states of some finite-state Markov processes which could be the economy and some other unseen random phenomenon.
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References
- AGGOUN, L., and ELLIOTT, R.J. 2004. Measure Theory and Filtering: Introduction with Applications. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge.
- ELLIOTT, C. ELLIOTT, R.J. and MALCOLM, W.P. 2005. Commodity prices and regime switching bases, Conference on Stochastic Modelling of Complex Systems, Daydream Island, Queensland Australia, 10-16, July 2005.
- ELLIOTT, R.J., AGGOUN, L. and MOORE, J.B. 1995. Hidden Markov Models: Estimation and Control. Springer-Verlag, New-York. Applications of Mathematics No. 29.
- ELLIOTT, R.J. 1982. Stochastic Calculus and Applications. Springer-Verlag, New-York. Applications of Mathematics No. 18.
- ELLIOTT, R.J., FISCHER, P. and PLATEN, E. 1999. Filtering and parameter estimation for a mean-reverting interest rate model, Canadian Applied Mathematics Quarterly, 7: 381-400.
- ELLIOTT, R.J. and KOPP, P.E. 2005. Mathematics of Financial Markets, 2nd Edition, Springer-Verlag.
References
AGGOUN, L., and ELLIOTT, R.J. 2004. Measure Theory and Filtering: Introduction with Applications. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge.
ELLIOTT, C. ELLIOTT, R.J. and MALCOLM, W.P. 2005. Commodity prices and regime switching bases, Conference on Stochastic Modelling of Complex Systems, Daydream Island, Queensland Australia, 10-16, July 2005.
ELLIOTT, R.J., AGGOUN, L. and MOORE, J.B. 1995. Hidden Markov Models: Estimation and Control. Springer-Verlag, New-York. Applications of Mathematics No. 29.
ELLIOTT, R.J. 1982. Stochastic Calculus and Applications. Springer-Verlag, New-York. Applications of Mathematics No. 18.
ELLIOTT, R.J., FISCHER, P. and PLATEN, E. 1999. Filtering and parameter estimation for a mean-reverting interest rate model, Canadian Applied Mathematics Quarterly, 7: 381-400.
ELLIOTT, R.J. and KOPP, P.E. 2005. Mathematics of Financial Markets, 2nd Edition, Springer-Verlag.