Exercise 4 (Bull and bear spreads with negative value). (See Example 8.8 in Lecture note 1.) Con- sider an asset with price (S) 120. We are going to construct bull and bear spreads on this asset with strictly negative initial value. Fix K1 0. (1) Consider a bull spread consisting of a long put with strike Ky and a short put with strike K2. Compute its payoff and draw its graph. Show that it is non-positive for all values of St. (it) Use a no-arbitrage argument to show that the bull spread in (i) has strictly negative initial value. Hence one receives an up-front payment, say CK,,K, when entering into this spread. Let K1 = 10, K2 = 30, and CK,K, = 15. Compute the profit of this spread at maturity and draw its graph. (iii) Consider a bull spread consisting of a long call with strike K2 and a short call with strike K. Compute its payoff and draw its graph. Show that it is non-positive for all values of St. (iv) Do (ii) for the bull spread in (iii). Profit of K1, K2 bull spread Profit of Ky, K, bear spread Short call, strike Ki profit profit Short put, strike K2 0 long call, strike K2 long put, strike K K K2 Stock price Sy Ki K2 Stock price Sy FIGURE 1. Profit of bull (using put) and bear (using call) spreads with strike K and K2