The Mean Reversion Stochastic Processes Applications in Risk Management

Radkov, Petar (2010): The Mean Reversion Stochastic Processes Applications in Risk Management.

Abstract

In this study we investigate using the mean reversion processes in financial risk management, as they provide an good description of stock price uctuations and market risks. This paper does not aim at being exhaustive, but gives examples for practically implementable models allowing for stylised features in the data. After introducing several widely used the mean reversion processes, we discuss this methods for risk management with Monte Carlo simulations. We also explain how the process can be calibrated based on historical data of Bulgarian 5 year Credit Default Swap and to find out Value at Risk.

• Item Type: MPRA Paper
• Language: English
• Keywords: Risk Management, Stochastic Processes, Mean Reversion, Monte Carlo Simulation, Calibration interest rate processes,
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C26 - Instrumental Variables (IV) Estimation; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation

References

[1] Brigo, D. and F. Mercurio (2006). Interest Rate Models: Theory and Practice - With Smile, In ation and Credit. New York, NY: Springer Verlag.

[2] Cox, J., J. Ingersoll, and S. A. Ross (1985a). An intertemporal general equilibrium model of asset prices. Econometrica 53, 363-384.

[3] Cox, J., J. Ingersoll, and S. A. Ross (1985b). A theory of the term structure of interest rates. Econometrica 53, 385-408.

[4] Dickey, D. and W. Fuller (1979). Distribution of the stimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427431

[5] Kwiatkowski, D., P. C. B. Phillips, P. Schmidt, and Y. Shin (1992). Testing the null hypothesis of stationary against the alternative of a unit root. Journal of Econometrics 54, 159178;

[6] Phillips, P. and P. Perron. (1988). Testing for unit root in time series regression. Biometrica 75, 335-346.

[7] Poterba, J. and L. J. Summers (1988). Mean reversion in stock prices: Evidence and implications. Journal of inancial Economics 22, 27-59.

[8] Said, S. and D. Dickey (1984). Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71, 599607.

[9] Vasicek, O. A. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics 5, 177-188.