In the previous chapter, distributions were calibrated to historical data, and risk measures such as VaR and CVaR were calculated. Yet the valuation of financial products and the associated risk measures all deal with events in the future. Bonds, stocks, options, and so forth all have potential cash flows in the future, and therefore one needs a method to generate distributions at arbitrary times in the future, as indicated in Figure 4-1. This is the purpose of a stochastic (or random) process, which represents the evolution of a random variable in time.
Figure 4-1. Distributions moving forward in time