Question

4. Assume that we are pricing a four month contract on the S & P 500 index that provides a continuous dividend yield of 5% per annum. Its current index value is 1350. The risk free rate is currently 5.5% for all maturities.

a. Calculate the futures price for a nine month contract on the index.

b. Under what circumstances would the spot and futures prices be equal to one another?

c. How does settlement of an index contract differ from say, a commodity contract like soybeans?

Answer 1

Answer-a The futures priceof a contract can be calculated as follows:

F = S × e^[(r-y)×t]

Where, F= futures price

S= spot price

r = risk free rate of interest

y = dividend yield and

t = time

So, F = 1350 × e^[(0.055-0.05)×9/12]

= 1350 × e^0.00375

= 1350 × 1.00375

= 1355.0625

Answer-b The value of index futures is ascertained using the cost of carry model where, cost of carry and interest rates are two important factors. This model takes into consideration the cost of money, dividends and the carrying costs.

The spot and futures prices can be equal to one another only if all the above factors are absent.

Answer-c Settlement of index contract:

Index futures contracts are settled using the cash settlement approach where the settlement price is the closing value of the index as on the date of expiry of the contract.

Settlement of commodity contract:

Commodity futures can be settled by physical delivery or through cash settlement based on the underlying spot price. In a cash settlement, the seller does not deliver actual asset but transfers the associated cash position i.e. the difference between the spot price and futures price. Whereas in a physical settlement, delivery of actual commodity has to be given.