m48-ch03 shrunk v02

# m48-ch03 shrunk v02 - Chapter 3 Insurance, Collars, and...

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Unformatted text preview: Chapter 3 Insurance, Collars, and Other Strategies Question 3.1. This question is a direct application of the Put-Call-Parity (equation (3.1)) of the textbook. Mim- icking Table 3.1., we have: S&R Index S&R Put Loan Payoff − (Cost + Interest) Profit 900.00 100.00 − 1000.00 0.00 − 95.68 − 95.68 950.00 50.00 − 1000.00 0.00 − 95.68 − 95.68 1000.00 0.00 − 1000.00 0.00 − 95.68 − 95.68 1050.00 0.00 − 1000.00 50.00 − 95.68 − 45.68 1100.00 0.00 − 1000.00 100.00 − 95.68 4.32 1150.00 0.00 − 1000.00 150.00 − 95.68 54.32 1200.00 0.00 − 1000.00 200.00 − 95.68 104.32 The payoff diagram looks as follows: We can see from the table and from the payoff diagram that we have in fact reproduced a call with the instruments given in the exercise. The profit diagram on the next page confirms this hypothesis. 21 Part 1 Insurance, Hedging, and Simple Strategies Question 3.2. This question constructs a position that is the opposite to the position of Table 3.1. Therefore, we should get the exact opposite results from Table 3.1. and the associated figures. Mimicking Table 3.1., we indeed have: S&R Index S&R Put Payoff − (Cost + Interest) Profit − 900.00 − 100.00 − 1000.00 1095.68 95.68 − 950.00 − 50.00 − 1000.00 1095.68 95.68 − 1000.00 0.00 − 1000.00 1095.68 95.68 − 1050.00 0.00 − 1050.00 1095.68 45.68 − 1100.00 0.00 − 1100.00 1095.68 − 4.32 − 1150.00 0.00 − 1150.00 1095.68 − 54.32 − 1200.00 0.00 − 1200.00 1095.68 − 104.32 On the next page, we see the corresponding payoff and profit diagrams. Please note that they match the combined payoff and profit diagrams of Figure 3.5. Only the axes have different scales. 22 Chapter 3 Insurance, Collars, and Other Strategies Payoff-diagram: Profit diagram: 23 Part 1 Insurance, Hedging, and Simple Strategies Question 3.3. In order to be able to draw profit diagrams, we need to find the future value of the put premium, the call premium and the investment in zero-coupon bonds. We have for: the put premium: \$51 . 777 × ( 1 + . 02 ) = \$52 . 81 , the call premium: \$120 . 405 × ( 1 + . 02 ) = \$122 . 81 and the zero-coupon bond: \$931 . 37 × ( 1 + . 02 ) = \$950 . 00 Now, we can construct the payoff and profit diagrams of the aggregate position: Payoff diagram: From this figure, we can already see that the combination of a long put and the long index looks exactly like a certain payoff of \$950, plus a call with a strike price of 950. But this is the alternative given to us in the question. We have thus confirmed the equivalence of the two combined positions for the payoff diagrams. The profit diagrams on the next page confirm the equivalence of the two positions (which is again an application of the Put-Call-Parity)....
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m48-ch03 shrunk v02 - Chapter 3 Insurance, Collars, and...

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