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Show why the frequency of payments and the dates on which options can be exercised alter the exposure profile of different securities.

FRM® Part II · Credit Risk Measurement and Management · Future Value and Exposure · FRM2.CR.19.e

The idea

Payment frequency and exercise dates change the amortisation that shapes exposure. When net payments are exchanged more often, for example quarterly rather than annually, value is settled sooner and less accumulates before a default, so exposure is lower. A zero-coupon swap has a single payment at maturity, so it has no interim amortisation. Its exposure keeps rising until close to maturity, higher than a coupon swap. For options, exposure follows the value of the exercise rights. A Bermudan option has several exercise dates, so it is worth at least as much as a European one with the same final expiry, and its exposure is at least as large. A physically settled swaption turns into a swap on exercise, so exposure continues after expiry. For a cash-settled swaption, exposure ends at settlement.

A practice question

From the question bank, with the reason each wrong option is wrong.

Other things equal, how does moving a swap from annual to quarterly settlement affect its expected exposure?

  1. It lowers exposure, since net payments settle value sooner and less builds up before a default - correct
  2. It raises the exposure because more payment dates add more cash flows that might not be paidWhy not: Each payment reduces what is owed later, so more payments amortise exposure.
  3. It leaves the exposure unchanged, since only the notional and volatility matterWhy not: Frequency changes how much value is settled early, so it does matter.
  4. It raises the exposure because frequent payments increase the PV01 of the swapWhy not: Changing frequency has only a small effect on PV01; the main effect is earlier settlement.

Net settlement of mark-to-market gains at each payment date removes exposure. With more frequent payments less value builds up between dates, so the exposure profile is lower.

A harder one

A European payer swaption expires in two years into a swap. Which statement about exposure just after expiry is correct?

  1. It falls to zero in both cases, because the option has expired and no further claim remainsWhy not: A physically settled swaption becomes a swap in exercised scenarios, so exposure continues.
  2. It continues as a swap in both cases, since cash settlement is economically identical to physical deliveryWhy not: Cash settlement pays the value at expiry, so no swap and no exposure remain.
  3. It rises in the cash-settled case because the settlement payment is outstanding until the swap maturesWhy not: The cash amount is paid at expiry and is not outstanding for the swap's life.
  4. Physically settled, exposure continues as the swap's positive value where exercised; cash-settled, it ends at payment - correct

On physical settlement the holder enters the swap, so exposure persists on exercised paths and then follows the swap's own profile. A cash-settled swaption pays the value at expiry and leaves no further exposure.

The hardest tier

A bank has a physically settled European payer swaption. Four equally likely scenarios give the underlying swap value (USD million) at expiry as 10, 6, -2, -8, and one year later as 12, 3, 5, -4 respectively. What is the expected exposure one year after expiry?

  1. USD 5.00 millionWhy not: Includes the third scenario's value of 5, although the option lapsed unexercised when the swap was worth -2.
  2. USD 7.50 millionWhy not: Averages over only the two exercised scenarios instead of all four equally likely scenarios.
  3. USD 3.75 million - correct
  4. USD 0 millionWhy not: Treats the option as cash settled, so no exposure remains after expiry.

Only scenarios 1 and 2 were in the money at expiry and so were exercised. One year later their swap values are 12 and 3 (both positive), and the others contribute zero: EE = (12 + 3 + 0 + 0)/4 = 3.75.

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