Filtering and parameter estimation for a mean reverting interest rate model (Q2713012)

The authors consider interest rates described by a mean reverting model NEWLINE\[NEWLINEdL_t= \gamma(\overline {L_1}-L_t)dt +\zeta dW_t,NEWLINE\]NEWLINE where \((\overline {L_t})_t\) is a finite-space continuous-time Markov chain written as \(\overline {L_t}= \langle X_t,\lambda \rangle\) where \(\lambda\) is a parameter. The process \((L_t)_t\) is observed; the unknown parameters are \(\lambda\) and \((A_t)_t\), the family of transition intensity matrices associated with \(X\).NEWLINENEWLINENEWLINEThe estimation of \(\theta= (\lambda,A)\) is performed through the EM algorithm to maximize the likelihood, via standard filtering techniques. The method can be extented to include \(\gamma\) in the set of parameters. Simulations using British interest rates are given. This technique, fairly general, could be used with other financial models.