### Overnight indexed swap

For periods beyond twelve months the following general formula for bootstrapping the OIS discount factors is used:. An overnight indexed swap OIS is an interest rate swap where the periodic floating payment is generally based on a return calculated from a daily compound interest investment.

## Your Answer

An overnight index swap OIS is a swap in which one party pays a fixed rate of interest known as the OIS rate which depends on the term of the swap and is known at trade inception.

It is linked to the cost of unsecured lending. The other party pays the rate equivalent to the daily compounded index rate over the life time of the OIS.

This is not known until the end of the life of the OIS. To make the OIS swap have zero initial value at inception, which is how it is traded, the OIS rate therefore must equal the market's expectation of what the compounded daily geometric average index rate will be over the lifetime of the OIS. In USD the index rate is the fed funds rate which is linked to the cost of unsecured lending.

The main use of OIS swaps is to allow banks to lock in the cost of unsecured overnight funding in advance. Finally, your confusion may be due to the use of OIS for discounting of collateralised non-cleared derivatives.

This is market practice since The OIS rate is used because it is close to the typical interest rate paid on the collateral that is held. It becomes the best estimate of the risk-neutral risk-free rate in a world where the collateral has effectively eliminated counterparty risk. USD 1 per unit to the present value of cash flows, where each individual cash flow is discounted from the date of its settlement to the date of inception.

For example at period 5 the at-par bond has the following cash flows. Coupon payments at a fixed rate of 2. Coupon payments at periods 1 to 4 will be discounted by the LIBOR discount factors determined earlier. The sum of these discounted payments is deducted from the par value of the bond to arrive at the discounted value of the final principal and interest payment at the end of period 5.

Dividing this value with the undiscounted principal and interest cash flow for period 5 will result in the discount factor applicable from the period 5 settlement date to inception.

What we are doing in cell F6 in the screenshot above is multiplying the first coupon 2. We repeat this process for the cash flows at periods Then we subtract the sum of discounted cash flows from 1 and divide the resulting value with the coupon and principal cash flow of period 5 to arrive at the LIBOR discount rate for period 5, as follows indicated in the second half of the EXCEL formula [boxed in red]:.

Another important term is that of the implied forward rate IFR , which is also known as the projected forward rate for a 3-month LIBOR between n-1 and n periods. It is derived from successive discount factors and calculated using the following formula:.

The implied LIBOR forward curve is useful in pricing options on swaps and non-standard interest rate swaps. An example of a non-standard interest rate swap is of a swap whose notional principal varies over its tenor.

The value of the interest rate swap is determined by calculating the value of the two bonds implicit in the interest rate swap. The difference in the price of these bonds is equal to the market value of the swap, which is as follows:. For the Fixed bond, this is the coupon payment at 5. For example, the cash flow at period 8 is:. For the Floating rate bond, this is the coupon payment at the implied forward rate for the period adjusted for the days in the period with respect to a day year times the notional amount for each of the eight periods and the principal notional amount at maturity at the end of period 8.

The cash flows are discounted using the calculated discount factor for the period. For period 8 both the fixed and the floating rate cash flows are discounted by 0. The discounted cash flows for period 8 are:. The sum of the discounted cash flows gives the price of the Fixed and Floating Rate bonds respectively.

The difference between the prices gives the value of the IRS:. The net cash flow for the receiver of the fixed rate leg of the swap is the Notional x fixed rate minus at-market swap rate for the given tenor at each settlement date. In our example, the fixed rate is 5. This reflects counterparty credit risk premiums in contrast to liquidity risk premiums.

This changed abruptly, as the spread jumped to a rate of around 50 bps in early August as the financial markets began to price in a higher risk environment. Within months, the Bank of England was forced to rescue Northern Rock from failure. The spread continued to maintain historically high levels as the crisis continued to unfold.

As markets improved, the spread fell and as of October , stood at 10 bps once again, only to rise again as struggles of the PIIGS countries threatened European banks.

The spread varied from 10 to 50 bps up through February From Wikipedia, the free encyclopedia. Economic Synopses, Number 25, Federal Reserve Bank of St.