The term structure of interest rates in a hidden markov setting
Date
2007
Authors
Elliott, R.
Wilson, C.
Editors
Mamon, R.
Elliott, R.
Elliott, R.
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Book chapter
Citation
Hidden Markov Models in Finance, 2007 / Mamon, R., Elliott, R. (ed./s), vol.104, pp.15-30
Statement of Responsibility
Robert J. Elliot and Craig A. Wilson
Conference Name
Abstract
We describe an interest rate model in which randomness in the shortterm interest rate is partially due to a Markov chain. We model randomness through the volatility and mean-reverting level as well as through the interest rate directly. The short- term interest rate is modeled in a risk-neutral setting as a continuous process in continuous time. This allows the valuation of interest rate derivatives using the martingale approach. In particular, a solution is found for the value of a zero-coupon bond. This leads to a non-linear regression model for the yield to maturity, which is used to filter the state of the unobservable Markov chain.