Il y a plus d'outils que d'ouvriers. (La Bruyère)
Market prices simulation is the basis of ALM and is required in:
In risk sections, we have already developed some simulation tools for credit risk, stock market risk, etc.
Nowadays the most common simulations are stochastic simulations and for this reason, we start with the presentation of some basic stochastic calculation principles.
The Brownian motion is defined in mathematics by the use of a continuous-time stochastic process called the Wiener process. The term Brownian comes from Robert Brown and the term Wiener process from Norbert Wiener. This process Wt is characterized by three facts:
This means that for 0 < s < t < t2 < t3:
(Wt − Ws) follows N(0, t − s)
(Wt − Ws) and (Wt2 − Wt3) are independant variables
In addition, for an infinitesimal increment, the relationship continues:
To simulate a Wiener process, the A/L manager will use this relationship introducing normal distributions.
The normal distribution is also called a Gaussian ...