# What is the difference between open interest and trading volume?

Problem Set 1

Please show all work. Please use four decimal places for all calculations.

What is the difference between open interest and trading volume?

What does it mean to say someone has a long position in a futures contract?

A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price would lead to a margin call? Under what circumstances could $1,500 be withdrawn from the margin account. Note:The size of the wheat futures contract is 5,000 bushels.

Assume the interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding? Comment on your answers for problem a, b and c and explain why they make sense.

Use the data in the following table, determine the zero rates for maturities of 6 months, 1 year, and 18 months expressed in terms of continuous compounding. Bond 2 and 3 have semiannual coupon payments.

Bond

Number Bond Principal Time to maturity

(years) Annual Coupon Bond Price

1 100 0.5 0 97

2 100 1.0 7 102

3 100 1.5 9 103

Please fill in the following table and show your work.

Time (years) Annual Zero Rate

(continuous compounding)

0.5

1

1.5

Find the cash price for a 1.5 year bond with a 5% coupon rate. Assume payments are semiannual and the next payment is in 6 months. Zero rates (expressed with continuous compounding) are 5%, 6%, and 7% for 6 months, 12 months, and 18 months respectively. Assume the bond has a face value of 100.

A deposit account pays 10% per annum with continuous compounding, but interest is actually paid semiannually. How much interest will be paid in the first six months on a $100,000 deposit?

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