HW11solutions_fall11

HW11solutions_fall11 - put price. 5. A. The delta of the...

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Homework 11, FINA 471 Fall, 2011 1. B. You can use the spreadsheet from the textbook to solve this problem. To do this on your own, you need to build a 2-step tree first. The up- and down- multipliers are: u = e (0.05-0.03)*0.25+0.30*0.5 = 1.1677 and d = e (0.05-0.03)*0.25-0.3*0.5 = 0.8650. The terminal stock prices are: S uu =54.537, S ud =40.402, S dd =29.931. The risk-neutral probability is: p* = (e (0.05-0.03)*0.25 – 0.8650)/(1.1677 – 0.8650) = 0.4626. The European put price is P=e -0.05*0.5 (0*p* 2 +0*p*(1-p*)+(1-p*) 2 *(40-29.931)) = 2.84. 2. B. There are several ways to solve the problem. You can follow the previous solution by building a tree. You can use the spreadsheet from the textbook. Or you can use the put-call parity. C = P+Se -δT -Ke -rT = 2.84+40 e -0.03*0.5 -40e -0.05*0.5 = 3.23. 3. C. The price is obtained from the Black-Scholes formula. 4. B. You can either use the Black-Scholes formula or the put-call parity as in problem 2 to find the
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Unformatted text preview: put price. 5. A. The delta of the inverse butterfly spread = -0.84 + 2*0.58 - 0.32 = 0. 6. C. To hedge, the trader should long 1500 euros. The interest rates are irrelevant. 7. A. Net delta = 100*0.33+100*0.5-200*0.63 =-43. 8. D. From Problem 7, he should long 43 shares. 9. D. To delta hedge short put options on 200 shares of stock, we must short 200*0.42 = 84 shares. 10. B. The total value of the hedged position in the previous problem is 84*50 + 2.5*200 = 4700, which is the amount you will initially lend. In one day, you will earn 4700*(e 0.08/365-1) = $1.03 interest. If the stock price falls to 49 and the option is worth 2.93, you will profit (2.50 - 2.93)*200 = -$86 on the puts you wrote and make (50-49)*84 = $84 on the stocks you bought. Including interest, our one day profit is: -86 + 84 + 1.03 = -$0.97....
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This note was uploaded on 01/16/2012 for the course FINA 442 taught by Professor Ms.etheridge during the Fall '11 term at South Carolina.

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