3.FUTURES & FORWARDS

3(a) On July 10, 2020, a speculator took a short position on 4 contracts of Bitcoin futures traded on CME when the futures price was $9,200 for August 2020 delivery. Each Bitcoin futures contract is based on 5 Bitcoins. The initial and maintenance margins are $18,000 and $15,000 per contract, respectively. On July 24, 2020, Bitcoin futures price rose to $10,000.

(i)Compute the gain or loss for the speculator on July 24, 2020.

(ii)Determine if she will get a margin call and how much cash will she need to transfer to her futures account.

3(b) The following table provides the prices of U.S. Treasury securities:

Bond principal Time to maturity Annual coupon* Bond price

$100 0.5 year $0.00 $97

$100 1.0 year $0.00 $94

$100 1.5 years $4.00 $102

*Half the stated coupon is assumed to be paid every 6 months.

Calculate the zero rates for maturities of:

(i)6 months,

(ii)12 months, and

(iii)18 months.

What are the forward rates for the following periods:

(iv) 6 to 12 months, and

(v) 12 to 18 months?