Problem set #2 Solution

# Problem set #2 Solution - Problem Set 2 Solutions Econ 136,...

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Unformatted text preview: Problem Set 2 Solutions Econ 136, Fall 2009 A note about grading: 5: no major or minor errors 4: no more than a few minor errors 3: a major or many minor errors 2: multiple major errors 1: multiple major errors and portions left blank 0: blank or never turned in. 1. Puts and calls (a) Verify the put-call parity conditions, C + X 1+ R f = S + P , for the options with the following strike prices, X = { \$22 , \$24 , \$26 } . Use bid prices for both put and call options, assume R f = 0 . 00, and S = 24 . 11. X C bid P bid C bid + X 1 . 00 24 . 11 + P bid Deviation from Parity 22 2.17 0.06 24.17 24.17 0.00 24 0.59 0.47 24.59 24.58 0.01 26 0.05 1.93 26.05 26.04 0.01 The last column is just the difference between the left and the right hand side of the parity equation C + X 1 + R f- ( S + P ) . Yes, there are deviations from parity. An arbitrage portfolio for the options with strike price \$26 would include short selling the call option and lending \$26, which would give you \$26.05, then using the proceeds to buy the stock and buy a put option, which would cost a total of \$26.04. For each contract this will allow you to earn a penny (\$0.01) today with no gain or loss when the options expire. There are no gains or losses at expiration because you will be using the call option and the money in the bank to cover the put option and stock you shorted. (b) To check put-call parity, we used bid prices. If it does not hold, i.e. C + X/ (1+ R f ) 6 = S + P , then an arbitrage opportunity might exist. To take advantage of it, we should: sell (short) the expensive portfolio, buy the cheaper portfolio, and pocket the difference. Bid prices are prices at which the dealer is willing to buy a security and ask prices (or asked prices) are prices at which the dealer is willing to sell a security. The dealer is holding the opposite position from what you want to do. So if you want to sell, the dealer will buy from you, so you need to find the dealers bid prices....
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## Problem set #2 Solution - Problem Set 2 Solutions Econ 136,...

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