2013 FNCE605 MAF Derivatives HW1 with ans.doc

FNCE605 MAF Derivatives / Prof KG Lim / Semester I 2013
Home Work Set I (25%) with Answers
There are 5 Questions. Please answer all 5 questions. You can submit individually or in a group of no more than 3 persons. Submit your answers in class to TA Nelson Yap on either 24th or 25th October.
Suppose you own a dividend-paying stock that is selling now at $100. You plan to sell it in 150 days. To hedge against possible price decline, you sell a forward contract on the stock. The forward contract expires in 150 days. Risk-free rate is 2%. The stock will pay the following dividends: $2 in 30 days, $2 in 120 days, and $2 in 210 days. What is the appropriate forward price of your stock expiring in 150 days? After 60 days, the stock price is $105. Risk-free interest adjusts to 3%. Calculate the value of your forward contract at that point of time after 60 days.
PV(D,0,150) = 2/()30/365 + 2/()120/365 = $. Forward price = (100-)()150/365 = $. After 60 days, PV(D,60,150) = 2/()60/365= $.
Value of a long forward after 60 days = $[105 – PV(D,60,150)] – /()90/65 = $. Therefore since you short, your short forward value is now -$ (a loss).
The spot exchange rate for GBP pound per Euro is . . and Euro interest rate for a maturity or term of 180 days are 4% and 2% respectively. Find the arbitrage-free 180-day forward exchange