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         - Historical Simulation
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Full Valuation / Monte Carlo

B&Cweiß

The Full Valuation approach tries to evaluate every instrument with its "full" valuation function. These can be the classical functions derived by hedge portfolios (e.g. Black-Scholes), by discounting future cash flows (e.g. bonds) or by numerical evaluation of scenario paths (e.g. exotic derivatives or structured products).

Generally, a large number of risk factor scenarios is generated in a Monte Carlo Simulation. It can be based on a straightforward distribution assumption like a (geometric) Brownian motion that is calibrated to historical market data via variances and covariances of (logarithmic) instrument returns. Alternatively, more elaborate market models can be used that include stochastic volatility (e.g. Heston) or mean reversion behavior of interest rates on single or multiple state variables (e.g. Vasicek, Black-Karasinsky, Hull-White, Cox-Ingersoll-Ross). Dependencies between risk factors can be considered in the second moments only (VCV), or by coupling terms in the stochastic differential equations.

For every scenario generated by the Monte Carlo Simulation each instrument return is calculated and the distribution of the portfolio return is aggregated from them. The usual risk measures like VaR and TailVaR can be calculated (simply read off) from the portfolio distribution with high accuracy. There are in principle no limitations on pushing models to highest sophistication, be it advanced instrument models, advanced market models or aging and portfolio roll down effects.

A Full Valuation / Monte Carlo Simulation engine is an extremely powerful tool for modeling market risk, especially when correlated non-linear assets are involved. However, one has to take into account the high initial development effort and the necessary computing time due to the relatively large numerical effort.