FRA
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- Data API.
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- GUI APP.
Forward Rate Agreement (FRA) Valuation
FinPricing provides valuation models for:
- FRA
- Swap
- Check FinPricing valuation models
A forward rate agreement, or FRA, is an OTC contract between two parties in which one party will pay a fixed rate
while the other party will pay a reference interest rate for a set future period.
| 1. FRA Introduction |
FRAs are over-the-counter (OTC) derivatives. They are cash-settled with the payment based on the net difference
between the floating interest rate and the fixed (reference) rate in the contract. Similar to an
interest rate swap, a FRA has two legs: a fixed leg and a floating leg. But each leg only has one cash
flow. The party paying the fixed rate is usually referred to as the borrower, while the party paying the floating rate
is referred to as the lender.
A FRA can be used to hedge future interest rate or exchange rate exposure. The buyer hedges against the risk of
rising interest rate whereas the seller hedges against the risk of falling interest rates. In other words, the buyer
locks in the interest rate to protect against the increase of interest rates while the seller protects against the
possible decrease of interest rates. A speculator can also use FRAs to make bets on future directional changes in
interest rates. Market participants can also take advantage of price differences between an FRA and other interest
rate instruments. FRAs are money market instruments that are liquid in all major currencies.
| 2. FRA Valuation |
Some people believe that a FRA is equivalent to a one-period vanilla swap. That is not
completely true. A FRA is usually settled and paid at the end of a forwarding period, called settling in arrear,
while a regular swaplet is settled at the beginning of the forward period and paid at the end. Strictly speaking,
FRAs need convexity adjustment. However, given FRA is such a simple product, the adjustment is very simple as well.
The present value of a fixed leg is given by
The present value of a floating leg can be expressed as
Practical Notes
- Usually a FRA is settled at arrear, i.e, the end of a forwarding period while a swaplet is settled at the beginning of the forward period, although both are paid at the end. The denominators in (1) and (2) are reflected the adjustment to this difference.
- Using fixed leg as an example, we first calculate the payoff NRτ at the end of the forwarding period. Then the payoff needs to be discounted to the fixing date (the beginning of the period) as NRτ/(1+Rτ). Finally the amount is discounted from the payment date or end date.
- You need to construct zero curve by bootstring some most liquity interest rate instruments. FinPricing provides useful tools to build various curves, such as swap curve, basis curve, OIS curve, bond curve, treasury curve, etc. Go to the list of the tools
- Any compounded interest yield curve data can be used to compute discount factor, of course the formulas will be slightly different. The most common used one is continuously compounded zero rates.
- To use the formula, you need to compute simply compounded forward rate instead of any other compounding types.
- The accrual period or day count fraction is calculated according to the start date and end date of a cash flow plus day count convention
- We assume that the accrual period is the same as the reset period and the payment date is the same as the accrual end dates in the above formulas for brevity. But in fact, they are several days’ difference due to different market conventions.
- A forward rate should be computed based on the reset period (index reset date, index start date, index end date) that are determined by index definition, such as index tenor and convention.
| 3. Related Topics |