We provide a new dynamic approach to scenario generation for the purposes of risk management in the banking industry. We connect ideas from conventional techniques - like historical and Monte Carlo simulation - and we come up with a hybrid method that shares the advantages of standard procedures but eliminates several of their drawbacks. Instead of considering the static problem of constructing one or ten day ahead distributions for vectors of risk factors, we embed the problem into a dynamic framework, where any time horizon can be consistently simulated. Additionally, we use standard models from mathematical finance for each risk factor, whence bridging 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 evaluation of the respective SDEs. The empirical calibration procedure presented in this paper can be seen as the SDE-counterpart of the so called Filtered Historical Simulation method; the behavior of volatility stems in our case out of the assumptions on the underlying SDEs. Furthermore, we are able to easily incorporate "middle-size" and "large-size" events within our framework always making a precise distinction between the information obtained from the market and the one coming from the necessary a-priori intuition of the risk manager. Results of one concrete implementation are provided.
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