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FRM Part II · FRM Exam Part II

Future Value and Exposure for FRM Part II

Future value and exposure is the study of how much you could lose if a derivatives counterparty defaults, estimated by simulating future market values. You solve questions by identifying the metric (EE, PFE or EPE), applying netting and collateral, then reading the profile. Positive values only count, because you lose only when the contract is in your favour.

What this chapter covers

This chapter is about counterparty credit exposure. A derivative has no fixed amount owed today. Its value changes as markets move, so your exposure to the counterparty at a future date is uncertain. The chapter teaches you to describe that uncertainty with a distribution of future values and to summarise it with a few metrics.

You start with the core metrics: expected exposure (EE), potential future exposure (PFE) and expected positive exposure (EPE). Exposure is the positive part of value, max(V, 0). You then see how profiles differ by product, how Monte Carlo simulation builds them, how netting and collateral reduce them, how wrong-way risk distorts them, and how the numbers feed capital and limits.

This chapter connects directly to the Credit Risk topic in Part II. Exposure is the input to credit valuation adjustment, counterparty capital and default loss estimates. It also links to Market Risk, because the simulation uses market risk factor models, and to Liquidity, because margin calls create funding needs.

Counterparty exposure questions are applied and case-like, which is the style of all 80 questions in Part II. They reward candidates who can state the metric, run a short calculation and interpret the result. The chapter also feeds other credit topics, so a solid grasp here lifts your accuracy on CVA, capital and margin questions. The concepts are few and the same ideas repeat, so effort here pays back well.

Future Value and Exposure: topics in the order to study them

  1. 1Counterparty Exposure Metrics (EE, PFE, EPE)Every other topic uses these definitions, so learn them first.
  2. 2Exposure Profiles by Product TypeOnce you know the metrics, you can see how their shape changes for swaps, forwards and options.
  3. 3Monte Carlo Simulation for Exposure ModellingThis explains how the profiles you just saw are actually produced.
  4. 4Netting, Collateral and Margin Effects on ExposureMitigants modify the simulated exposure, so you need the base profile first.
  5. 5Wrong-Way and Right-Way RiskIt adds the link between exposure and counterparty default to the picture you have built.
  6. 6Exposure Measures for Capital and LimitsThis is the end use, and it makes sense only after the earlier topics.

How to prepare Future Value and Exposure

Aim to be able to define each metric, compute it from a small data set, and explain how a change in the setup moves it. Use short daily sessions that suit phone study.

  1. Write the definitions of EE, PFE and EPE in your own words. Remember that exposure is max(V, 0) and that PFE is a high percentile of the exposure distribution, such as 95% or 99%.
  2. Sketch the exposure profile for an interest rate swap, a forward, and a bought option. Note when each peaks and why, and what happens as maturity approaches.
  3. Work a tiny simulation by hand with five or six scenario values. Take the positive parts, then average for EE and pick the percentile for PFE.
  4. Practise netting with two or three trades under one netting agreement. Compare the sum of individual exposures with the exposure of the net portfolio, then layer on collateral and a margin period of risk.
  5. Build one wrong-way risk example and one right-way example. State clearly which direction exposure and default probability move together.
  6. Finish with capital and limits questions. Link PFE to limit setting and EPE to capital and CVA, and then do mixed MCQs under timed conditions.

Common mistakes in Future Value and Exposure

    Last-day revision: Future Value and Exposure

    • Exposure = max(V, 0). You lose only when the contract has positive value to you.
    • EE at a date is the average of the positive exposures across scenarios at that date.
    • PFE is a chosen high percentile of exposure at a date, used for limits.
    • EPE is the time average of the EE profile over a period.
    • Swap exposure rises, peaks mid-life, then falls as payments are made and fewer cash flows remain.
    • A forward's exposure typically rises with time as uncertainty grows (the standard deviation of value scales roughly with the square root of time), peaks at maturity, and drops to zero on settlement.
    • The option buyer's exposure equals the option's value (never negative). The seller has no exposure to the buyer on the option, because the buyer has no further obligations once the premium is paid.
    • Netting lets you offset positive and negative values only within a legally enforceable netting set.
    • Netted exposure is never greater than the sum of the individual exposures.
    • Collateral reduces exposure but leaves residual risk over the margin period of risk.
    • Wrong-way risk is a positive dependence between exposure and the counterparty's default probability. Exposure tends to rise as its credit quality falls.
    • Right-way risk is a negative dependence between exposure and the counterparty's default probability. Exposure tends to fall as its credit quality falls.

    Future Value and Exposure practice questions

    Future Value and Exposure in other exams

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

    Future Value and Exposure: frequently asked questions