Expositor: Rogemar Mamon, University of British Columbia, Vancouver
Resumen:
This talk will consider two applications of Markov chains in continuous time, which represents the "state of the economy". First, a Black-Scholes market is studied in which the underlying economy, as modelled by the parameters and volatility of the processes, switches between a finite number of states. The switching is modelled by a Markov chain. European options are valued and a Black-Scholes PDE derived. The second application will focus on the extension of the classical Vasicek model, where the mean-reverting level evolves according to the dynamics of a Markov chain. This model is applicable in situations where some reference level for interest rates is set by regulatory authorities such as the central banks. The term structure characterisation is given through the analytic solution of the bond price and a simulation demonstrates the plausibility of the proposed model.