Estimation of Value at Risk with Extreme Value Theory approach and using Stochastic Differential Equation

Subject Areas : Financial engineering

Amir Shafiee ¹ , reza raei ² , Hossein Abdoh Tabrizi ³ , saeed falahpor ⁴

1 - Department of finance and insurance, Faculty of Management, Tehran University, Tehran, Iran
2 - Department of finance and insurance, Faculty of Management, Tehran University, Tehran, Iran
3 - Faculty of management and Accounting, Shahid Beheshti University, Tehran, Iran
4 - Department of finance and insurance, Faculty of Management, Tehran University, Tehran, Iran

Received: 2019-03-29 Accepted : 2019-05-26 Published : 2019-09-23

Keywords: Value at Risk, Stochastic Differential Equation, Brownian Motion, Extreme Value Theory, Peak over Threshold Approach, Stochastic Process,

Abstract :

The occurrence of financial crises in recent decades has caused a lot of damage to the economy as well as economic enterprises in many countries. The Extreme Value Approach is a new approach to the phenomenon of financial crisis, which has been able to analyze the events that are less likely to occur but the damage caused by them is significant. In this study, we use the Extreme Value theory and Stochastic differential equations to find a new method for estimating the more precisely the value at risk. For this purpose, after estimating the parameters of the Stochastic differential equations, which includes the geometric Brownian motion, the geometric Brownian motion with the jump, the nonlinear GARCH model, and the Heston model, simulate the Monte Carlo simulations of future paths and then use peak over threshold approach, to estimate the value We at risk. The results of the simultaneous use of Stochastic differential equations and Extreme value theory ​​are compared with historical simulations and variance-covariance approaches for value at risk. The results of Back-test techniques on value at risk indicate the superiority of the Heston model in estimation of value at risk.