Financial modelling in an HMM-modulated regime-switching framework

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This research programme centres on the theme of regime-switching frameworks in financial modelling. The switching of regimes is governed by either a continuous- or discrete-time hidden Markov chain representing the "state of the world". New practical applications and further theoretical developments of hidden Markov models (HMM) are investigated. First, HMM filtering theory is extended to deal with the long range dependence of time series data illustrating that the Markovian assumption in HMM is not as restrictive as it first appears. This gives rise to weak HMMs driving the stochastic evolution of model parameters thereby capturing both regime-switching and memory properties. Second, Kalman filtering and other non-linear filtering techniques are coupled with optimal HMM filtering theory to produce adaptive and high performance algorithms in the parameter estimation and modelling of financial variables and other phenomena in nonlinear time series. Third, methodologies are devised for efficient valuation of annuity-linked contracts and mortality-linked securities where the dynamics of both financial and demographic factors are assumed correlated, and both interest and mortality rates are HMM-modulated. Fourth, the recovery of time-varying parameters for HMM-based models in option pricing and bond valuation is considered. This inverse problem in finance may be addressed either by using an ansatz approach or by reformulating it as a generalisation of the inverse Stieltjes moment problem of mathematical analysis. In some cases such as in bond pricing, generating functions, which can be viewed as a transform of one of the components of the bond price solution, will be constructed. Whilst all of these investigations have direct relevance to quantitative finance and actuarial science, other fields of applications including economics, engineering and other branches of applied sciences could also positively benefit from the results of this research programme.