Financial Pricing Models in Continuous Time and Kalman Filtering

Straight after its invention in the early sixties, the Kalman filter approach became part of the astronautical guidance system of the Apollo project and therefore received immediate acceptance in the field of electrical engineer ing. This sounds similar to the well known success story of the Black-Scholes model in finance, which has been implemented by the Chicago Board of Op tions Exchange (CBOE) within a few month after its publication in 1973. Recently, the Kalman filter approach has been discovered as a comfortable estimation tool in continuous time finance, bringing together seemingly un related methods from different fields. Dr. B. Philipp Kellerhals contributes to this topic in several respects. Specialized versions of the Kalman filter are developed and implemented for three different continuous time pricing models: A pricing model for closed-end funds, taking advantage from the fact, that the net asset value is observable, a term structure model, where the market price of risk itself is a stochastic variable, and a model for electricity forwards, where the volatility of the price process is stochastic. Beside the fact that these three models can be treated independently, the book as a whole gives the interested reader a comprehensive account of the requirements and capabilities of the Kalman filter applied to finance models. While the first model uses a linear version of the filter, the second model using LIBOR and swap market data requires an extended Kalman filter. Finally, the third model leads to a non-linear transition equation of the filter algorithm.