We model the stock price as SIT) -scp {( + | (7 t) +0(W(T) W(t)} = se, where z follows the normal distribution with mean (r - 102) (T t) and standard deviation oVT-t. As a result, F(t, s) = e-r(T-1)E(S(T))] (20) =e- (1-1) L 0(se?)(2) dz where f means the PDF of the normal distribution with the above-mentioned mean and standard deviation. The above integral should be evaluated individually for specific contract functions . Consider an option which pays a certain amount if the price of the stock at a certain date falls within a specified interval. Otherwise, nothing will be paid out. Suppose that the option pays K to the holder at date 7 if the stock price at time I is in the interval (a.pl. Determine the arbitrage- free price, in terms of the standard normal cumulative distribution function N. You should use the stock price expression in p. 165 of the lecture slides. We model the stock price as SIT) -scp {( + | (7 t) +0(W(T) W(t)} = se, where z follows the normal distribution with mean (r - 102) (T t) and standard deviation oVT-t. As a result, F(t, s) = e-r(T-1)E(S(T))] (20) =e- (1-1) L 0(se?)(2) dz where f means the PDF of the normal distribution with the above-mentioned mean and standard deviation. The above integral should be evaluated individually for specific contract functions . Consider an option which pays a certain amount if the price of the stock at a certain date falls within a specified interval. Otherwise, nothing will be paid out. Suppose that the option pays K to the holder at date 7 if the stock price at time I is in the interval (a.pl. Determine the arbitrage- free price, in terms of the standard normal cumulative distribution function N. You should use the stock price expression in p. 165 of the lecture slides