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Homework 1 Solution

# Homework 1 Solution - STAT 473 HW 1 Solution 1 Recall C K T...

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STAT 473 HW 1 Solution 1. Recall Since both options are at-the money, . We have Therefore, in order to be consistent with Call Put Formula, We must have 2. Therefore, there is an arbitrage opportunity. Buy Low Sell High: Long RHS & Short LHS: The profit after one year = \$ 1.3952 C K , T ( ) P K , T ( ) = S 0 K e rT K = S 0 C K , T ( ) P K , T ( ) = S 0 S 0 e rT = S 0 1 e rT ( ) T > 0, r T < 0 e r T < 1 RHS = S 0 1 e rT ( ) > 0 C K , T ( ) > P K , T ( ) C K , T ( ) P K , T ( ) = S 0 e δ T K e rT LHS = 2.34 8.00 = 5.66 RHS = 40 × e 2% × 1 50 × e 8% × 1 ≈ − 6.95 LHS > RHS Transaction @ t = 0 Cash Flow @ t = 0 If S(T) > K If S(T) < K Long Stock -40 e^(-0.02) = -39.2079 S(T) S(T) Short Call + 2.34 - [S(T) - K] Not Exercised: 0 Long Put - 8.00 Not Exercised: 0 K - S(T) Short Treasury 50 e^(-0.08) = 46.1558 - K - K Lend Money -1.2879 1.2879 e^(0.08) = 1.3952 1.2879 e^(0.08) = 1.3952 TOTAL 0 \$ 1.3952 \$ 1.3952 Page of 1 3

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STAT 473 HW 1 Solution 3. Notice that the second dividend is 9 months from today, but the agreement period is only 6 months.
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