Power corporations´ default probability forecasting using the Derivative-free nonlinear Kalman Filter

The paper proposes a systematic method for forecasting default probabilities for financial firms with particular interest in electric power corporations. According to credit risk theory a company´s proximity to default is determined by the distance of its assets´ value from its debts. The assets´ value depends primarily on the company´s market (option) value through a complex nonlinear relation. Therefore, by forecasting with accuracy the enterprize´s option value it becomes also possible to estimate the future value of the enterprize´s asset value and the associated probability of default. This paper proposes a systematic method for forecasting the probability to default for companies (option / asset value forecasting methods) using a new nonlinear Kalman Filtering method under the name Derivative-free nonlinear Kalman Filter. The company´s option value is considered to be described by the Black-Scholes nonlinear partial differential equation. Using differential flatness theory the partial differential equation is transformed into an equivalent state-space model in the so-called canonical form. Using the latter model and by redesigning the Derivative-free nonlinear Kalman Filter as a m-step ahead predictor, estimates are obtained of the company´s future option values. Thus, by forecasting the company´s market (option) values, it becomes also possible to forecast the associated asset value and volatility and finally to estimate the company´s future default risk.