The valuation of a European-style contingent claim is discussed in a hidden Markov regime-switching jump-diffusion market, where the evolution of a hidden economic state process over time is described by a continuous-time, finite-state, hidden Markov chain. A two-stage procedure is used to discuss the option valuation problem. Firstly filtering theory is employed to transform the original market with hidden quantities into a filtered market with complete observations. Then a generalized version of the Esscher transform based on a Dolé-Dade stochastic exponential is employed to select a pricing kernel in the filtered market. A partialdifferential- integral equation for the price of a European-style option is presented.
|Title of host publication||Hidden Markov Models in Finance|
|Subtitle of host publication||Further Developments and Applications, Volume II|
|Editors||Rogemar S. Mamon, Robert J. Elliott|
|Place of Publication||Heidelberg|
|Publisher||Springer, Springer Nature|
|Number of pages||25|
|Publication status||Published - 2014|