Pricing and Rate Risk · Swaps Trading Guide

A fair fixed swap rate balances the present value of two payment streams. Learn the calculation before interpreting a quoted rate as a forecast.

Start with dated payments

A payment tomorrow is not equivalent to the same payment several years away. A discount factor converts each future amount into a value today. Project the floating payments using the relevant forward rates, then discount both legs consistently with the valuation framework. Already fixed floating coupons use their known fixings rather than a new projection.

Solve for the balancing rate

For a simple fixed leg, present value equals notional multiplied by the fixed rate multiplied by the sum of accrual fractions times discount factors. The par rate is the floating leg present value divided by that notional weighted sum. This expression assumes no additional upfront payment or optional feature.

Work through a small example

Assume a $1,000,000 notional and two annual payments with discount factors of 0.96 and 0.92. Suppose the projected floating leg has a present value of $75,200. The fixed leg annuity is 1.88. The balancing fixed rate is $75,200 divided by $1,880,000, or 4%. These invented inputs illustrate the arithmetic rather than a tradable quote.

Separate valuation from prediction

A par rate incorporates the full payment schedule and market curve. It is not simply the central bank rate expected on the final date. Dealer spreads, credit terms, collateral and fees can also make an executable offer differ from a clean model value.

Try it yourself

A $2,000,000 swap has an annuity of 2.5 and a floating leg present value of $200,000. What fixed rate balances it?

Show the worked answer

Divide $200,000 by $2,000,000 times 2.5. The result is 0.04, or 4%. This is a simplified par calculation before additional adjustments.

Further reading

Educational material, not a recommendation to transact. Numerical examples are hypothetical and simplify contract terms. Access, documentation, collateral and regulatory requirements depend on the product, jurisdiction and counterparties.

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