Interest Rate Swaps and Future Contracts

Pricing Interest Rate Swap
Pricing Net Cash Flow
Valuing Futures contracts
Valuing Stock Index Futures
Pricing Futures Contracts on Currencies
Pricing Futures Contracts on Commodities
Pricing Futures Price for Treasury Bond futures contracts

Interest Rate Swap

Net Cash Flow

The net cash flow for the buyer of the contract (receiver of floating leg and payer of fixed leg) at each payment date is:

Where t-1 is the payment date on which the floating rate interest was observed and is one payment date prior to the payment date on which the net cash flow is paid.

“days” are the period of time in the interest rate period (in years) based on the appropriate day count convention.

Futures

Stock Index Futures

These futuresare used to offset the exposure to a well diversified equity portfolio, in particular the systemic risk associated with the portfolio.

The futures price of stock indices with known yield is as follows:

Futures Contracts on Currencies

The futuresprice is as follows:

Where F₀ is the futuresprice in local currency of one unit of foreign currency
S₀ is the current spot price in local currency of one unit of foreign currency
r is the domestic risk free rate
r_f is the foreign risk free rate

Futures Contracts on Commodities

The futuresprice of a commodity with no storage cost or income is as follows:

The futuresprice of a commodity with storage cost and income is as follows:

Where U is the discounted value of the storage costs net of income during the life of the futurescontract.

Futures Price for Treasury Bond futures  contracts

Where I is the present value of the coupons during the life of the contract discounted at the risk free rate.