## Derivative Pricing – Interest Rate Swaps and Futures – Calculation reference

*in*Derivatives

# 1. Interest Rate Swap

## a. 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.

# 2. Futures

## a. 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:

## b. Futures Contracts on Currencies

The futuresprice is as follows:

Where F_{0} is the futures price in local currency of one unit of foreign currency

S_{0} 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

## c. Futures Contracts on Commodities

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

The future sprice 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 futures contract.

## d. 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.