Title: Continuous-time regime switching models with jumps and filter-based volatility
Authors: Elisabeth Leoff - University of Kaiserslautern (Germany)
Vikram Krishnamurthy - University of British Columbia (Canada)
Joern Sass - University of Kaiserslautern (Germany) [presenting]
Abstract: In finance, a continuous time regime switching model, where the observation process is a diffusion process whose drift and volatility coefficients jump governed by a continuous time Markov chain, can explain some of the stylized facts of asset returns. But due to the switching volatility, in continuous time the underlying Markov chain could be observed and no filtering is needed (in theory). Therefore, if in finance explicit theoretical results are obtained, they may not provide a good approximation for the discretely observed model in which we have to filter. On the other hand, a continuous-time hidden Markov model (HMM), where only the drift switches and the volatility is constant, allows for explicit calculations but has no such good econometric properties. We first discuss estimation, model choice and portfolio optimization in both models. To combine useful aspects of both models, we then look at a HMM where the volatility depends on the filter for the underlying Markov chain. This volatility model can be motivated by social learning arguments. We analyze its relation to Markov switching models and, using examples from portfolio optimization, we illustrate that we can still get quite explicit results and that these provide a good approximation to the discretely observed model. Further, we extend these results to a jump-diffusion model where also the intensity of the driving Poisson process is switching. This allows for jumps in the observation.