Let's now look at the settlement of an FRA transaction.

Using a concrete example.

Suppose an investor buys a six by 12 FRA on a notional of 100 million euros at an FRA rate of 2.082%.

That means they're locking in a six month interest rate for borrowing, starting six months from spot.

More precisely. The relevant underlying rate is six month. Your eye O observed six months after the trade date.

As with all RAs, there's no exchange of notional.

Instead, the trade settles in cash based on the net difference between the agreed FRA rate and the open market six month arrival rate at the time of fixing that, being the beginning of the notional borrowing period.

What's unusual about RAs compared to most other interest rate derivatives like swaps is that settlement occurs at the start of the interest period.

In our example, the payoff is calculated and settled six months from spot, even though the underlying rate refers to the six month period that follows.

Let's walk through how the settlement is calculated.

The standard formula shown here from the perspective of the FRA buyer first calculates a hypothetical interest differential amount, which is the difference between the six month arrival rate and the FRA rate agreed at the beginning of the FRA multiplied by the notional principle.

Since your IOR interest is paid in arrears, this interest differential amount is the difference in interest that would need to be paid on a real world borrowing at the six month IOR rate.

And what would've been paid had money been borrowed at the FRA rate, these cash flows would all be at the end of the six month period.

So the interest differential amount is discounted back to the start of the hypothetical period, which is the settlement date.

Mathematically, the formula is FRA settlement equals notional times floating rate minus FRA rate times days divided by 360 divided by one plus the floating rate times, days divided by 360.

The numerator gives the value of the interest differential while the denominator discounts that value to present terms using the current market UIO rate.

Now, let's plug in the numbers.

The client agreed a six by 12 FRA at 2.0882%.

Let's say that in six months time, the six month arrival is observed at 2.158%.

The notional is a hundred million euros, and the interest period is 182 days.

So we calculate the FRA settlement as 100 million times the difference between the 2.158% and the 2.082% multiplied by 180 2 over 360, and that's all divided by one plus the 2.158% times 180 2 out of 360.

To discount it back to the present value, this gives a result of 38007.56 euros, which the buyer receives.

This is because the floating rate fixed above the FRA rate.

So why do FRA settle at the beginning of the period? The main advantage is that the trade is shortened reducing credit risk.

In this example, the FRA buyer receives the payment upfront rather than waiting six months and taking on counterparty risk over that time.

But this early settlement also introduces an important feature.

It makes FRA payoffs non-linear.

If we only considered the numerator the difference in rates, the payout would be linear.

But because we discount the cash cashflow using the floating rate, the result is a concave payoff for the FRA buyer.

That means they still benefit as rates rise, but each additional basis point gives slightly less value in present terms than the one before.

In other words, the buyer is short convexity.

This chart shows the present value of the FRA payoff across different IO fixing scenarios.

As you can see, it's not a straight line.

It curves downward. That's the impact of discounting using the floating rate.