FRM Exam Part II · Future Value and Exposure

Exposure Profiles by Product Type: Loans, Forwards, Swaps, Options

Updated 11 October 2026 · Fact-checked

An exposure profile shows how expected or potential credit exposure to a counterparty changes over time. Two forces shape it: diffusion, where uncertainty about market values grows with time, and amortization, where cash flows are paid and exposure shrinks. Their balance gives each product its shape: rising, humped or declining.

Understand Exposure Profiles by Product Type

Counterparty exposure is the loss you would suffer if the counterparty defaulted today, ignoring recovery. It is the larger of the contract's value and zero, because you lose only if the contract is an asset to you. Looking forward, you do not know that value, so you describe it with a profile: expected exposure (EE) or potential future exposure (PFE) at each future date.

Two effects drive the profile. The diffusion effect says that market variables wander further from today's level as time passes. Their standard deviation grows roughly with √t. More dispersion means a bigger chance of large positive values, so exposure rises. The amortization effect says that as payments are made and the contract nears maturity, there are fewer remaining cash flows that can lose or gain value. This pulls exposure down toward zero.

Products differ in which effect wins. A loan or bond you hold has fixed, known payments, so its exposure is approximately the outstanding principal, ignoring changes in market value from interest rates and credit spreads. It is roughly flat for a bullet loan or bond, which repays all principal at maturity, and it declines for an amortizing loan as principal is repaid. A forward has one payment at maturity, so there is no amortization before the end and exposure keeps rising with diffusion. An interest rate swap exchanges many payments, so diffusion wins early and amortization wins late. The result is a hump, with the peak typically around the first third to half of the life, depending on the curve and the swap terms.

A cross-currency swap also exchanges notionals at maturity, and the FX rate moves a lot. The notional exchange stays exposed to FX diffusion until the end, so the profile keeps rising and peaks late, near maturity. It then drops to zero at the final exchange. For comparable notional the peak is usually higher than for a single-currency swap, because FX volatility generally exceeds the interest-rate-driven value volatility. A bought option has a known upfront premium and the holder is exposed only to positive value. Its exposure is its mark-to-market value, which can rise or fall with the underlying and the option's moneyness. Expected exposure generally rises with time up to expiry, because diffusion increases the chance of a large payoff. At expiry the exposure equals the payoff, and once the payoff is settled the exposure drops to zero. The seller of an option has no exposure to the buyer once the premium is paid.

For the exam, always ask: Is there a single end payment or many? Is the notional exchanged at the end? Which side of the trade are you on? Then pick the shape.

Key formulas to remember

Exposure at time t: Exposure(t) = max(V(t), 0); V is the contract's value to you. Exposure is never negative. Ignores netting and collateral.
Expected exposure (EE): EE(t) = E[max(V(t), 0)]; The average positive value at future date t. Plotting EE against t gives the expected exposure profile.
Potential future exposure (PFE): PFE(t) = the α-percentile of max(V(t), 0); A high quantile, such as 95% or 97.5%, of the exposure distribution at t. It is typically well above EE.
Diffusion scaling: Standard deviation of a risk factor ∝ σ × √t; Uncertainty grows with the square root of time, so diffusion alone gives a rising, concave profile.
Forward exposure at the money: EE(t) ∝ σ × √t (for an at-the-money forward); Rises until maturity. Exposure is largest at the end, since no amortization occurs.
Profile shapes by product: Loan or bond: flat if bullet, declining if amortizing; Forward: rising; IR swap: hump; Cross-currency swap: rising, late peak; Bought option: value-based, generally rising to expiry, then zero once the payoff is settled; Use this as a memory map for exam questions.

How to solve Exposure Profiles by Product Type questions

Use the same logic for any question asking you to identify or sketch an exposure profile.

1Identify the product and your side: do you hold a loan, a forward, a swap or a bought or sold option?
2Find the risk factor and whether exposure can be positive. A sold option after premium has zero exposure to the buyer.
3Count the cash flows. One payment at the end means no amortization until maturity. Many payments mean amortization builds up.
4Check whether the notional is exchanged at maturity. If yes, as in a cross-currency swap, the exposure stays high until the end.
5Apply diffusion: uncertainty grows with √t, so exposure rises early.
6Apply amortization: as payments are made, remaining sensitivity falls, so exposure drops near maturity.
7Combine: diffusion only gives rising; amortization only gives falling; both gives a hump. Pick the answer that matches.
8Check the metric. EE is an average, PFE is a high percentile and is typically well above EE.

Quickest way: Product to shape in ten seconds

When to use it: Use for multiple-choice questions that ask which profile fits a product, or which effect dominates at a point in time.

Loan or bond you hold: exposure is approximately the outstanding principal, ignoring market-value changes from rates and spreads. Roughly flat for a bullet loan, declining for an amortizing loan.
Forward or one-payment contract: rising line to maturity.
Single-currency interest rate swap: hump, peak typically in the first third to half of the life depending on the curve and terms, zero at maturity.
Cross-currency swap: rising to a late peak near maturity because of FX diffusion on the final notional exchange, then zero after the exchange. The peak is usually higher for comparable notional because FX volatility is generally larger.
Bought option: exposure equals its mark-to-market value. Expected exposure generally rises with time up to expiry because of diffusion. At expiry it equals the payoff, then drops to zero once settled. The seller has none.
Early life: diffusion dominates. Late life: amortization dominates.

Common mistakes in Exposure Profiles by Product Type

Drawing a swap profile that keeps rising until maturity.
Students remember that uncertainty grows with time and forget that payments are exchanged along the way.
Fix: For a swap, include amortization. Exposure falls to zero at maturity because no cash flows remain.
Treating a cross-currency swap like an interest rate swap.
Both are called swaps, so the hump shape is applied to both.
Fix: Remember the final notional exchange. It keeps FX exposure large until the end, so the peak is later and the profile does not fall as early.
Giving a sold option positive exposure to the buyer.
Students think any derivative creates two-way credit risk.
Fix: After the premium is paid, the option seller owes the buyer and has no credit exposure to the buyer. Only the buyer has exposure.
Confusing EE with PFE.
Both are plotted against time and look similar.
Fix: EE is the average of positive exposure. PFE is a high percentile. At a high confidence level, PFE is typically well above EE.
Letting exposure go negative on the profile.
Students plot the mark-to-market value rather than its positive part.
Fix: Exposure is max(V, 0). Negative value is a liability, not exposure.
Saying forward exposure falls near maturity.
Students copy the swap hump onto every derivative.
Fix: A forward has one payment at maturity, so there is no amortization. Exposure keeps rising until the end.

Worked examples

Example 1

A bank enters a 10-year plain vanilla USD interest rate swap with a corporate. Describe the shape of its expected exposure profile and explain why. At what point does each effect dominate?

Show the solution

Product: single-currency interest rate swap with periodic net payments and no notional exchange.
Early life: many payments remain, and rate uncertainty grows with √t. Diffusion dominates, so exposure rises.
Later life: each payment reduces the number of remaining cash flows. Sensitivity of the swap value to rates falls. Amortization dominates.
Maturity: no cash flows remain, so value and exposure are zero.
Combining these gives a hump with a peak well before maturity, typically around the first third to half of the life, depending on the curve and swap terms.

Answer: The profile is hump-shaped: rising early because of diffusion, peaking before maturity, then falling to zero at maturity because of amortization.

Example 2

A bank holds a 5-year EUR/USD cross-currency swap with notional exchange at maturity, and a 5-year USD interest rate swap on a comparable notional value. Which has the later and higher peak in expected exposure, and why?

Show the solution

The interest rate swap has no final notional exchange. Amortization of the net coupon payments reduces exposure, so it humps and falls to zero.
The cross-currency swap exchanges notionals at maturity. Its value depends on the FX rate, which stays uncertain until the end.
Because the final notional exchange stays exposed to FX diffusion, exposure keeps rising with √t to a late peak near maturity. It then drops to zero once the final exchange is made.
FX volatility generally exceeds the interest-rate-driven value volatility of a net coupon stream, so for comparable notional the cross-currency peak is higher.
Therefore the cross-currency swap has the later and higher peak.

Answer: The cross-currency swap. FX diffusion on the final notional exchange keeps exposure rising to a late, usually higher peak near maturity, before it drops to zero at the final exchange. The interest rate swap peaks earlier and falls to zero.

Exam tips

Questions are often conceptual: match the product to the shape, or name the effect that dominates early or late.
Expect a trap on cross-currency versus single-currency swaps. Look for notional exchange.
Check which party is the option buyer. Only the buyer has credit exposure.
If asked about PFE versus EE, remember PFE is a high percentile and is typically well above EE.
Netting and collateral reduce exposure but are separate topics. Do not apply them unless the question states them.

Practice questions from Future Value and Exposure

Exposure Profiles by Product Type in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

CFA Level IIICurrency Swaps and Cross-Currency Exposure

Exposure Profiles by Product Type: frequently asked questions

Why is the interest rate swap exposure profile hump shaped?

Two effects work against each other. Early on, rate uncertainty builds with time and pushes exposure up. As payments are exchanged, fewer cash flows remain and exposure falls to zero at maturity.

How do I draw the expected exposure profile of a forward?

Draw a line rising from zero at today for an at-the-money forward, with a concave shape roughly following √t. It peaks at maturity because there is a single payment and no amortization.

What is the difference between the diffusion effect and the amortization effect?

Diffusion is the growth in uncertainty about market values as time passes, which raises exposure. Amortization is the reduction in remaining cash flows as payments are made, which lowers exposure.

How does a cross-currency swap profile differ from an interest rate swap?

A cross-currency swap exchanges notionals at maturity and is exposed to FX moves. Its profile keeps rising to a late peak near maturity, then drops to zero at the final exchange. For comparable notional the peak is usually higher, because FX volatility generally exceeds interest-rate-driven value volatility. A single-currency swap peaks earlier and falls away.