A stock price is log-normally distributed, i.e.,

ln S T ( ln S 0 + ( r 2 2 ) T , T ) .

Consider a derivative on the stock with the time to expiration T and the following payoff: { 0 if S T < K 1 S T if K 1 S T < K 2 0 if K 2 S T . What is the present value of the derivative? Provide an analytic form using N ( ), the cumulative probability distribution function of a standard normal random variable.