State-Space Approaches for Modelling and Control in Financial Engineering by Gerasimos G. Rigatos

Author:Gerasimos G. Rigatos
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

8. Corporations’ Default Probability Forecasting Using the Derivative-Free Nonlinear Kalman Filter

Gerasimos G. Rigatos1

(1)Unit of Industrial Automation, Industrial Systems Institute, Rion, Patras, Greece

Gerasimos G. Rigatos

Email: [email protected]

8.1 Outline

The purpose of this chapter is to demonstrate how state-space models of finance systems can be used in risk management and particularly in firms’ default probability forecasting. In the recent years the problems of option pricing, dynamic hedging and risk management in firms, including the energy sector, have been widely studied [79–81]. Investments planning in electric power generation and in the electricity grid is highly affected by the credit risk assessment of power corporations and may be canceled or severely modified in case that electric power corporations undergo financial distress [1, 136, 144, 235, 271]. Of particular importance is the problem of bankruptcy prediction and of the early detection of indexes that reveal the financial stresses of such a company, as well as the company’s distance to default [6, 22, 125, 194, 229, 280, 287]. Software and computational packages for monitoring and assessing the default risk make to a great extent use of Merton’s model for a company’s proximity to bankruptcy [22, 56, 253, 260, 279].

The present chapter proposes a nonlinear filtering method for forecasting default probabilities for financial firms with particular interest in risk management for electric power corporations. First, results from credit risk theory are used [6, 22, 125, 194, 229, 280, 287]. The probability or default of equivalently the distance to default is computed as a function of the company’s assets value, of the assets value volatility and of the company’s accumulated debts [22, 56, 253, 260, 279]. Since the first two parameters are not directly measurable they are estimated through the processing of measurements of the company’s market value, that is of the company’s options price. Therefore, if one is in position to forecast the company’s market value he can finally forecast the company’s probability of default or the company’s distance to default.

Forecasting of the company’s market (options) value is a non-trivial problem. The dynamics of options’ value is known to be described by the Black–Scholes partial differential equation [102, 111, 189, 217, 218, 222]. This theory has been used for credit risk assessment [29, 160]. It has been shown however, that starting from the Black–Scholes PDE and by applying a new nonlinear filtering method, the so-called Derivative-free nonlinear Kalman Filter, forecasting of the options’ value can be succeeded [216, 222, 225, 228]. The proposed filtering method is based on a transformation of the initial option price dynamics into a state-space model of the linear canonical form. The transformation has been proven to be in accordance to differential flatness theory, and finally provides a model of the option price dynamics for which state estimation is possible by applying the standard Kalman Filter recursion [34, 77, 134, 156, 191, 220, 231, 247, 265]. Moreover, by redesigning the Kalman Filter as a m-step ahead predictor it becomes possible to obtain estimates of the future options’ price. This estimated future market value of the company can be finally used to compute bankruptcy risk and the probability of default.

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