Consider two European call options on the same underlying, with the same strike price K, and expiration dates T1 and T2 (T1 < T2). A calendar spread strategy involves taking a short position in the short-dated option and a long position in the long-dated option. Suppose a calendar spread is entered into at date 0 and S0 = K.

1. (a) [10 marks] Represent graphically the value of the spread at date T1 as a function of ST1 . What is

   the limit of the spread value at date T1 as ST1 goes to infinity?

2. (b)How does the value of the calendar spread depend on realized volatility between dates 0 and T1? How does it depend on implied volatility at date T1?

3. (c)For this question, suppose that Black-Scholes assumptions are satisfied. Under Black- Scholes, the absolute value of the theta of an at-the-money call increases with time-to- expiration. Analyze how the value of the spread, between dates 0 and T1, is affected by the passage of time, assuming that the options remain at the money.

4. (d) For this question, suppose that Black-Scholes assumptions are satisfied. Under Black- Scholes, vega is increasing in time-to-expiration. Analyze how the value of the spread, between dates 0 and T1, is affected by a change in the level of the volatility parameter .