1. Let S(t) > O be the price at time t of a non-dividend paying stock. A European style derivative with expiration T = 3 months has the pay-off depicted in the figure in the next page (blue line). Find a constant portfolio on European put options that replicates the value of the derivative (max 2 points). Assuming that the stock price is given by a geometric Brownian motion with zero mean of log-return, 50 % volatility and S(0) = 1, compute the probability that the derivative expires in the money. Express the result in terms of the standard normal distribution (max 2 points). 1.0 0.8 0.6 0.4 0.2 1 2. 3 4 5 6 7 Remark: For S(T) > 7 the pay-off is identically zero. 1. Let S(t) > O be the price at time t of a non-dividend paying stock. A European style derivative with expiration T = 3 months has the pay-off depicted in the figure in the next page (blue line). Find a constant portfolio on European put options that replicates the value of the derivative (max 2 points). Assuming that the stock price is given by a geometric Brownian motion with zero mean of log-return, 50 % volatility and S(0) = 1, compute the probability that the derivative expires in the money. Express the result in terms of the standard normal distribution (max 2 points). 1.0 0.8 0.6 0.4 0.2 1 2. 3 4 5 6 7 Remark: For S(T) > 7 the pay-off is identically zero