7. We can now use the model to price a call or a put with maturity T on a single stock. In order to do that, we divide the interval [0, T] into N subintervals, so that we can refer to the N-period model discussed above and we study the asymptotic case when N goes to innity, r =

RT/N, log(d/(1 + r))=−¾

p T/N and log(u/(1 + r))=¾

p T/N. The real number R is to be interpreted as the instantaneous interest rate at all times between 0 and T. Indeed, we have eRT =limN!1(1 + r)N. The number ¾2T can be seen as the limit variance, under the measure P¤, of the random variable log(SN), when N goes to innity. The number ¾2 is the limit variance of the increase in the log-price over a time interval with unit length.