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CFA® Level I · Derivatives · free lesson
Pricing and Valuation of Interest Rate and Other Swaps
The interest rate swap is the largest derivative market in the world by notional amount. This module shows that a swap is a bundle of forward contracts on interest rates, derives the fixed swap rate from discount factors so that the swap is worth zero at inception, values a swap after rates have moved, and compares swaps with forwards and futures in terms of settlement and credit exposure.
What you will learn
1. Explain how an interest rate swap can be viewed as a series of forward contracts and calculate the fixed swap rate from spot rates or discount factors.
- A swap is a series of FRAs, all at one fixed rate; individual FRAs are off-market.
- The swap rate makes the swap's value zero at inception.
- Adding notional to both legs: floating leg = par FRN; fixed leg = fixed-rate bond priced at par.
- Swap rate s = (1 - DF_N) / (sum of DF_i), a periodic rate for non-annual settlements.
- The swap rate is a discount-factor-weighted average of implied forward rates.
2. Calculate and interpret the value of an interest rate swap after initiation when market swap rates have changed.
- Value to fixed payer = (current swap rate - original swap rate) x notional x sum of remaining DFs.
- Rates up: fixed payer gains; rates down: fixed receiver gains.
- Use only remaining settlement dates and current discount factors.
- Bond view: pay-fixed swap = long floating-rate note + short fixed-rate bond.
- A receive-fixed swap behaves like a leveraged long bond position.
3. Compare interest rate swaps with forwards and futures and explain how the credit exposure on a swap evolves over its life.
- Forwards settle once, futures daily, swaps periodically.
- Credit exposure exists only when the swap has positive value to you.
- Swap exposure starts at zero, can grow with rate moves, and declines as maturity nears.
- Netting, collateral and central clearing reduce swap credit exposure.
- Exposure is a small fraction of notional because only net interest differences are exchanged.
Module at a glance
- A swap is a portfolio of FRAs written at one fixed rate; the embedded forwards are off-market.
- Par swap rate s = (1 - DF_N) / sum of DF_i; annualize periodic rates.
- The swap rate is a discount-factor-weighted average of forward rates.
- Value to the fixed payer = (s_t - s_0) x notional x sum of remaining discount factors.
- Rates up benefits the fixed payer; rates down benefits the fixed receiver.
- Swaps settle periodically; exposure starts at zero, peaks mid-life and declines toward maturity.
- Netting, collateral, clearing and legal certainty all limit swap counterparty risk.
This free module has 3 lessons, 13 practice questions with full explanations.