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.