Financial pricing models in continuous time and Kalman filtering (Q5943405)

This book deals with the application of Kalman filter algorithms to efficiently estimate financial models of contingent claim pricing. The author uses different types of Kalman filter algorithms to estimate current pricing problems in the equity market, the bond market and the electricity market. In each market the new contingent claim valuation models to price selected financial instruments in continuous time are derived. In Part I modeling and estimation principles are described. The state space formulation of a financial model is presented. The state space form is based on the measurement equation which relates the state variables to the variables that can only be observed with measurement noise, and the transition equation describes the dynamic evolution of the unobservable variables. Then the author presents the derivation of the Kalman filter under the normality assumption and obtains the Kalman filter for the general case of non-normality by exploiting the given linear relationships of the observations and dynamics stated, respectively, in the state space equations. For the nonlinear functional relationships of non-normally distributed state variables in the measurement and transition equations the extended Kalman filters are considered. In Part II the closed-end funds is considered. The capital markets for closed-end funds provide two important prices for financial analysis: the market value of the closed-end funds' shares and the net asset value of their foreign assets which is reported by the investment companies. The proposed stochastic pricing model takes into account both the price risk of the funds as well as their risk associated with altering discounts. Based on a state space formulation of the pricing model the author estimates the relevant model parameters using Kalman filter framework. For the empirical adaptation of the valuation model a sample of closed-end equity funds that invest in emerging markets and are traded on the New York Stock Exchange is used. Then the forecasting power is tested and portfolio strategies using trading rules are implemented. In Part III a new approach in modeling the term structure of interest rates and the pricing of fixed income instruments is used. The suggested models choose the short interest rate and its market price of risk as the two explaining state variables whereupon the author establishes an affine term structure model. The closed-form solution for arbitrage-free prices of discount bonds is derived and then the implied term structure of interest rates and volatilities is analyzed. Then the management of interest rate risk is considered. The author shows how to implement the duration technique for considered model and how to price the term structure derivatives such as bond option, swap contracts, cap and floor agreements. The calibration of the proposed term structure model to standard fixed income instruments is considered. The implemented maximum likelihood estimation is based on a linear as well as an extended Kalman filter algorithm. Using the filtering technique the author extracts the dynamic behaviour of the risk attitudes of fixed income investors. In Part IV the author develops a continuous time pricing model for valuation of short-term electricity forwards. From properly chosen model assumptions, especially capturing the unique characteristic of non-storability of electricity and the marked volatility in electricity prices being both high and variable over time, the author builds an appropriate valuation model to price electricity forwards. Thereupon a closed-form solution on valuing electricity forward contracts using risk neutral pricing technique is presented. Next the author empirically adopts a theoretical pricing model in state space form dealing with state variables that follow a non-Gaussian distribution. Using maximum likelihood estimation based on extended Kalman filtering the author presents empirical results on electricity data from the largely deregulated Californian electricity market.