3. Exercise Consider a stock with price (St) 120. (i) Consider a bull spread at current...

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3. Exercise Consider a stock with price (St) 120. (i) Consider a bull spread at current time t = 0, consisting of a long call option with strike $10 and a short call option with strike $30, both with maturity T = 1. Compute its payoff and draw its graph. Show that it is non-negative for all values of ST. (ii) Use monotonicity theorem to conclude that the value of the bull spread in (i) at current time t = 0 is strictly positive. Hence when entering into this bull spread, one needs to pay an up-front fee, which we may assume to be c = $5 for the following problems. (iii) Compute the profit of this spread at maturity and draw its graph. (iv) Suppose P(ST = 5) = P(ST= 20) = P(ST=40) = 1/3, that is, the stock price ST at matu- rity can take three values $5, $20, and $40 with equal probabilities. What is the expec- tation and standard deviation of the profit of this bull spread? 3. Exercise Consider a stock with price (St) 120. (i) Consider a bull spread at current time t = 0, consisting of a long call option with strike $10 and a short call option with strike $30, both with maturity T = 1. Compute its payoff and draw its graph. Show that it is non-negative for all values of ST. (ii) Use monotonicity theorem to conclude that the value of the bull spread in (i) at current time t = 0 is strictly positive. Hence when entering into this bull spread, one needs to pay an up-front fee, which we may assume to be c = $5 for the following problems. (iii) Compute the profit of this spread at maturity and draw its graph. (iv) Suppose P(ST = 5) = P(ST= 20) = P(ST=40) = 1/3, that is, the stock price ST at matu- rity can take three values $5, $20, and $40 with equal probabilities. What is the expec- tation and standard deviation of the profit of this bull spread?