As examples, in Figs. 1.1–1.7 we showed how the prices of assets vary with time t. Fig. 2.1 shows the stock price of Microsoft Inc. in the period March 30, 1999, to June 8, 2000. From these figures, we can see the following: the graphs are jagged, and the size of the jags changes all the time. This means that we cannot express S as a smooth function of t, and it is difficult to predict exactly the price at time t from the price before time t. It is natural to think of the price at time t as a random variable. Now let us give a model for such a random variable.
KeywordsIncome Hull Lution Volatility Vanilla
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