HW11solutions_fall11

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

This preview shows page 1. Sign up to view the full content.

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
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

## 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.

Ask a homework question - tutors are online