Question

1(a) Pacific Airline decides to use a collar to hedge the oil price risk. The lower strike is 55 and the higher strike is 60. The options mature in 6 months and the annualized 6-month interest rate is 6% (p.a.). Below is the relevant put and call premiums:

Strike	Call premium	Put premium
55	6.23	3.42
60	3.92	6.04

(i) What is the cost of the collar position?

(ii) As Pacific Airline is your client, you have become the counterparty. What is the oil price in 6 months such that you will break-even?

(b) Pacific Airline wants to borrow $100,000 6 months later for 3 months with a Forward Rate Agreement. The following table shows bond market information.

Maturity (month)	Zero Coupon Bond Price
3	0.988
6	0.971
9	0.953
12	0.933

(I) What is the forward rate of the FRA (effectively for 3 months)?

(ii) Suppose 6 months later, the 3-month annualized spot rate is 5%. What is the settlement amount of the FRA if settle in arrears?

(iii) Instead of using an FRA directly, what positions in zero coupon bonds could Pacific Airline use to synthetically create the FRA borrower position?

a. Long 6 months ZCB, Short 9 months ZCB

b. Long 6 months ZCB, Long 9 months ZCB

c. Short 6 months ZCB, Long 9 months ZCB

d. Short 6 months ZCB, Short 9 months ZCB

Answer 1

1.

a.qn 1:

lower strike is 55 -put premium is 3.42 and the higher strike is 60 call premium is 3.92

Collar= buy put at lower strike and sell call at higher strike., cost per collar is 3.92-3.42 = 0.50 $ per share

qn 2:

Break even is obtained when price of underlying goes above the call price by 0.5$ and the call is exercised by the buyer, put owned by us goes worthless. = at 60.5$ of oil price., you pay 0.5 to call buyer, net = 0.5 - 0.5 = 0.

b. qn1: borrow $100,000 6 months later for 3 months. It is a 6*9 FRA.

If 6 months later, rate becomes 5%, since we were long on FRA at 8%, we have a loss of , 3% * 3/12 on notional, also this has to be discounted to T= 6 months by dividing with 1+ (rate of 6 to 9 month which is 2%)