An index swap revolves around a hedging contract where two parties agree to exchange predetermined cash flows on a specific date, typically determined based on a debt, equity, or price index.
An overnight index swap (OIS) specifically leverages an overnight rate index like the federal funds rate. These swaps are a category within conventional fixed-rate swaps, which can span durations from three months to over a year.
Key Insights
- The interest from the overnight rate portion compounds and is paid out on reset dates, influencing each party’s valuation of the swap.
- The present value (PV) of the floating leg is calculated by compounding the overnight rate, or using the geometric average over a period.
- Similar to other interest rate swaps, generating an interest rate curve is essential to ascertain the present value of expected cash flows.
The Inner Workings of an Overnight Index Swap
An OIS entails swapping the overnight rate for an agreed-upon fixed interest rate. The floating rate leg of the swap typically relates to an overnight rate index, while the fixed leg’s rate is mutually agreed upon. The compounded interest from the overnight rate part of the swap is settled on reset dates, adding to the swap’s overall value for each participant.
The finite present value (PV) of the floating leg is calculated either by daily compounding the overnight rate or using its geometric average over the specified period.
Popular among financial institutions, OIS transactions are viewed as low-risk indicators of the interbank credit market, favoring them over traditional interest rate spreads.
Calculating an Overnight Index Swap
Bank’s financial benefits from an OIS can be calculated in eight key steps:
- Calculate Daily Rate: Multiply the overnight rate by the number of days in the swap period. For instance, a Friday swap equates to three days, while a non-weekend day covers a single day. E.g., a 0.005% overnight rate becomes 0.015% (0.005% x 3 days).
- Annualize the Rate: Divide the effective rate by 360, adhering to industry practice: 0.005% / 360 = 1.3889 x 10^-5^
- Add One: Sum one to the result: 1.3889 x 10^-5^ + 1 = 1.000013889
- Calculate Principal Impact: Multiply this new rate by the principal amount. For instance, a $1 million principal results in: 1.000013889 x $1,000,000 = $1,000,013.89.
- Repeat for Periods: Apply these computations daily, adjusting the principal accordingly.
- Re-apply Steps 2 & 3: Follow similar steps by dividing the overnight rate with 360 and adding 1. Assuming an overnight rate of 0.0053%, the result is: 0.0053% / 360 + 1 = 1.00001472.
- Power Calculation: Raise this adjusted rate to the power of the loan’s duration and multiply by the principal: 1.00001472^1 x $1,000,000 = $1,000,014.72.
- Determine Profit: Subtract the two sums to calculate the profit earned through the swap: $1,000,014.72 - $1,000,013.89 = $0.83.
Through this meticulous process, the potential gains facilitated by an OIS can be comprehensively assessed, assisting financial institutions in making informed hedging decisions.
Related Terms: fixed interest rate, principal, swap contracts, interest rate swaps, overnight rate.
References
- Cbonds. “Overnight Index Swap”.
