# Simulation Methods

• Hans-Peter Deutsch
Part of the Finance and Capital Markets Series book series (FCMS)

## Abstract

In the calculation of the value at risk by means of Monte Carlo simulations, all of the risk factors influencing a portfolio are simulated over the liquidation, period St as stochastic processes satisfying, for example, Equation 2.13 or even more general processes of the form, 2.15. The value at risk of the risk factors themselves are taken into complete consideration using Equation 19.15 sometimes neglecting the drift in the simulation if the liquidation period is short:

$$\matrix{ {{\rm{Va}}{{\rm{R}}_{{\rm{long}}}}\left( c \right)\, \approx \,NS\left( t \right)\,\left[ {1\, - \,\exp \,\left( { + \,Q_{1\, - \,c}^{{\rm{N}}\left( {0,\,1} \right)}\sigma \sqrt {\delta t} } \right)} \right]} \hfill \cr {{\rm{Va}}{{\rm{R}}_{{\rm{short}}}}\left( c \right) \approx \, - \,NS\left( t \right)\,\left[ {1\, - \,\exp \,\left( {t\, - \,Q_{1\, - \,c}^{{\rm{N}}\left( {0,\,1} \right)}\sigma \sqrt {\delta t} } \right)} \right]} \hfill \cr }$$

As explained in Section 19.1, the value at risk of a long position in an underlying is only then equal to that of a short position if the drift is neglected and the linear approximation has been used. Since the linear approximation is usually not assumed in the Monte Carlo method, the VaRs of a long position will not equal that of a short position on the same underlying.

## Keywords

Simulated Scenario Historical Simulation Short Position Relevant Risk Factor Market Scenario
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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