A3SOLUTION

# A3SOLUTION - Assignment 3 Solutions Question 1 Put-call...

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Assignment 3 Solutions Question 1. Put-call parity gives 0 S p Ke D c rT + = + + 29 30 5 . 0 5 . 0 2 12 / 6 %* 10 12 / 5 %* 10 12 / 2 %* 10 + = + + + p e e e p=2.51 The price of this put option should be \$2.51. Question 2. The present value of all dividends: D=0.5e -10%*2/12 +0.5*e -10%*5/12 =0.9713 Since c+D+Xe -rT =p+S 0 p=C+D+ Xe -rT -S 0 =2+0.9713+30* e -10%*6/12 -29=2.5082 If the put option is traded at \$3, there is an arbitrage opportunity. ± Short a put option at \$3 and a share of stock at \$29 ± Long a call option at \$2 and invest 0.9713+30 e -10%*6/12 into the market money account with an interest rate of 10%. The rest (29+3-2-0.9713-30 e -10%*6/12 =0.4918) is your arbitrage profit. At the end of 2 nd month, withdraw \$0.5 to pay the dividend. At the end of 5 th month, withdraw \$0.5 to pay the dividend. At the maturity (the 6 th month), hold a long position of a call, a short position of a put and a short positon of a share of stock.Withdraw an amount of \$30. If the stock price is greater than \$30, the call will be exercised and pay \$30 to buy the share. If the stock price is smaller than \$30, the put will be exercised and pay \$30 to buy back the share. If the stock price is equal to \$30, no option will be exercised. Buy back the share with the \$30.

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Question 3. Choose one portfolio: A (long call options with strike prices K1 and K3, short two options with strike price K2) If , all options with strike prices K1, K2 will be exercised, A value: 3 K S T 0 2 3 1 2 = K K K If , options with strike prices K1, K2 will be exercised, A value: 2 3 K S K T > 0 2 1 2 > T S K K If , just option with strike price K1 will be exercised, the value of A: 1 2 K S K T > 0 1 > K S T If , all the options will not be exercised, the value of A: =0 1 K S T < The value of A is always non-negative, so the price of portfolio A should also be non-
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A3SOLUTION - Assignment 3 Solutions Question 1 Put-call...

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