A new approach for scenario generation in risk management

We provide a new approach to scenario generation for the purpose of risk management in the banking industry. We connect ideas from standard techniques – like historical and Monte Carlo simulation – to a hybrid technique that shares the advantages of standard procedures but reduces several of their drawbacks. Instead of considering the static problem of constructing one or ten day ahead distributions, we embed the problem into a dynamic framework, where any time horizon can be consistently simulated. Second, we use standard models from mathematical finance for each risk factor, bridging this way between the worlds of trading and risk management. Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. Furthermore we are able to easily incorporate “middle-size” and “large-size” events within our framework. Results of a concrete implementation are provided. The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager.