FRM Part 2 – Credit Risk · FRM
Credit Risk in Options: All of It Sits With the Buyer
Counterparty credit risk on a derivative is the risk that the party who owes you money fails before paying. On most derivatives that risk runs in both directions and changes hands as the market moves. On an option it does not.
Once the premium has been paid, the buyer of an option can never owe the writer anything. The contract can only ever be worth zero or more to the buyer, so the buyer carries all of the credit exposure for the whole life of the trade and the writer carries none. Every other feature of option counterparty risk, from the shape of the exposure profile to the size of the credit valuation adjustment, follows from that single asymmetry, and it follows from the payoff rather than from anything about credit.
Key Takeaways
- Current exposure is the maximum of the mark to market value and zero, so only a positive position creates credit exposure.
- A purchased option can never have negative value to its holder, so the buyer carries all the exposure and the writer carries none.
- Forwards and swaps are two-way: the exposure changes hands as the market moves.
- Exposure profiles differ by instrument: forwards rise throughout, swaps hump and fall, purchased options rise with a floor at zero.
- CVA prices the exposure as loss given default times the sum of expected exposure, default probability and discount factor across time.
- Netting gives no benefit in a one-way option book, because there are no negative positions to offset, so collateral does the work instead.
Why an option’s credit exposure runs one way
Credit exposure on a derivative at any moment is the amount you would lose if the counterparty defaulted right then. If the contract has positive value to you, the counterparty owes you that amount and you lose it. If it has negative value, you owe them, and their default does not hurt you.
Current exposure = max(V, 0)
V is the current mark to market value of the position to you
Apply that to each instrument and the difference is immediate. A forward or a swap can have positive or negative value depending on where the market has gone, so the exposure moves back and forth between the two parties over the life of the trade. A purchased option cannot have negative value to its holder, because the holder is never obliged to do anything. So V is always at least zero, the maximum function never binds, and the exposure sits permanently with one side.
The premium is what makes this true. The buyer pays it at inception and thereafter has no further obligation. The writer receives it and thereafter carries only obligations. Everything the buyer might ever receive is a payment from the writer, and everything the writer might ever receive has already been received.
It is worth separating two things that the word risk runs together here. The writer of an option carries a great deal of market risk, potentially unlimited on a written call, and that is a real and serious exposure. What the writer does not carry is credit exposure to the buyer, because there is no future payment from the buyer that could fail to arrive. A risk report that shows an option writer with zero counterparty exposure is not saying the position is safe. It is saying the danger comes from the market rather than from the person on the other side.
Measuring current exposure
Bank A buys a one-year over the counter call option from Bank B and pays a premium of $2 million at inception. Six months later the option is worth $5 million. Compare the credit exposures with those on a forward between the same two banks.
- Option, A’s exposure to B: max(5, 0) = $5 million. Bank B could fail owing Bank A that amount.
- Option, B’s exposure to A: max(−5, 0) = $0. Bank A owes nothing under any outcome.
- Suppose the market reverses and the option falls to $0.3 million. A’s exposure becomes $0.3 million and B’s is still $0.
- Forward worth +$5 million to A: A’s exposure is $5 million and B’s is $0, the same picture as the option.
- Forward worth −$3 million to A: A’s exposure is now $0 and B’s exposure to A is $3 million. The exposure has changed hands.
Answer: the option’s exposure never reaches step five. Bank B’s exposure to Bank A is zero at inception, at every point in the life of the trade, and at expiry. For credit purposes an option writer is not taking counterparty risk at all, which is why a bank will write options to counterparties it would not enter a swap with.
One clarification is worth adding because it is a common confusion. The premium itself is not credit exposure to the buyer once paid, and it is not a loss the buyer can suffer twice. If the writer defaults, the buyer loses the current value of the option, and the premium is a sunk payment that is already reflected in that value having been acquired at all. Exposure is measured on the mark to market position, not on what was paid for it.
Potential future exposure, and the shapes it takes
Current exposure is what would be lost today. It says nothing about what might be lost in a year, and a counterparty is more likely to default later than immediately. So the measure that matters for limits and capital is potential future exposure: the exposure at some future date, at a stated confidence level.
Two forces drive that profile in opposite directions. Diffusion pushes exposure up over time, because the underlying has longer to move and the range of possible values widens. Amortisation pulls it down, because as payments are made there is progressively less contract left to be exposed on. Which force dominates, and when, gives each instrument its characteristic shape.
| Instrument | Shape over time | Why |
|---|---|---|
| Forward, single payment at maturity | Rises throughout, roughly with the square root of time | Diffusion only. Nothing amortises before maturity |
| Interest rate swap | Humped, peaking around a third to halfway through the life, then falling to zero | Diffusion wins early, amortisation wins later as remaining payments run out |
| Purchased option, one-sided | Rises with time, and never negative | Diffusion only, with a floor at zero |
| Written option | Zero throughout | The writer has no claim on the buyer after the premium |
The practical use of the profile is limit setting. A counterparty limit is normally set against potential future exposure at a high confidence level rather than against current exposure, because a limit that only reflects today’s mark to market would permit a trade whose exposure is small now and very large in a year. Reading the profile also tells a credit officer where in the life of a trade the institution is most exposed, which is what a break clause or a collateral threshold has to be positioned around.
Related measures follow from the same profile. Expected exposure is the average exposure at a given future date rather than a high percentile of it, and expected positive exposure is the time-weighted average of expected exposure across the life. Basel’s effective expected positive exposure adjusts that further, by preventing the measure from falling as short-dated trades roll off, which stops a portfolio of rolling short trades from appearing safer than it is.
Putting a price on it: CVA
Exposure is a quantity. What a bank actually needs is a price, because the counterparty risk on a derivative has to be charged for and reported. That price is the credit valuation adjustment.
CVA ≈ LGD × Σt EE(t) × PD(t) × DF(t)
summing across time buckets, where EE is expected exposure, PD is the marginal default probability in the bucket and DF is the discount factor. This form assumes exposure and default are independent
A three-year option position has expected exposure of $4 million at the end of year one, $6 million at the end of year two and $3 million at the end of year three. The counterparty’s marginal default probabilities are 1.0%, 1.2% and 1.5%. Loss given default is 60% and the discount factors are 0.96, 0.92 and 0.88.
- Year 1: 4 × 0.010 × 0.96 = 0.03840.
- Year 2: 6 × 0.012 × 0.92 = 0.06624.
- Year 3: 3 × 0.015 × 0.88 = 0.03960.
- Sum = 0.14424, in millions.
- CVA = 0.60 × 0.14424 = $0.0865 million, that is about $86,500.
Answer: roughly $86,500 against a peak expected exposure of $6 million. CVA is small relative to the exposure because it is the exposure multiplied by a small default probability and a recovery haircut. It is not small relative to the margin on the trade, which is why a desk that quotes without charging CVA is systematically underpricing its riskier counterparties.
The mirror of CVA is the debit valuation adjustment, which values the possibility that the bank itself defaults on what it owes. For a written option, where the bank has no exposure to the buyer, there is no CVA to charge, and the position carries DVA instead. The asymmetry of the payoff shows up directly in which adjustment applies.
Wrong-way risk
The CVA formula above assumes exposure and default probability are independent. Where they are not, the adjustment understates the risk and can do so severely.
Wrong-way risk is the case where exposure rises exactly as the counterparty becomes more likely to fail. Specific wrong-way risk arises from a direct link, such as buying a put on a company’s shares from a bank whose own fortunes are tied to that company, or buying credit protection on a sovereign from a bank domiciled in it. In both cases the event that makes the option valuable is the event that impairs the writer.
General wrong-way risk is looser and comes from shared macroeconomic drivers: a currency option bought from a counterparty whose funding depends on the same currency, for example. There is no contractual link, only a correlation that shows up under stress.
An option’s exposure is one-sided, so there is no offsetting position to fall back on when the correlation turns against you. On a swap, a move that increases your exposure to the counterparty at least means the trade is in your favour, and previous periods may have had the exposure the other way. On a purchased option there is no other side of the trade to net against, and the whole position is the exposure. Right-way risk exists too, and it is simply rarer, since counterparties are not usually selected for it.
What actually reduces the exposure
Four mechanisms are used in practice, and they address different parts of the problem.
| Mechanism | What it does | What it does not do |
|---|---|---|
| Close-out netting | Reduces many trades with one counterparty to a single net amount on default | Nothing, where the trades are all one way, which is common for an option-only relationship |
| Collateral under a credit support annex | Posts margin against the current mark to market, reducing exposure toward the threshold and minimum transfer amount | Remove the gap risk between margin calls, or the liquidity demand a call creates |
| Central clearing | Replaces the bilateral counterparty with a clearing house, backed by initial margin, variation margin and a default fund | Apply to bespoke contracts that cannot be cleared, and it concentrates risk in the clearing house |
| Break clauses and downgrade triggers | Allow termination if the counterparty’s credit deteriorates past a defined point | Help if the deterioration is sudden, and triggers can accelerate a counterparty’s distress |
The netting row deserves attention, because it is where an option-heavy relationship differs from a swap relationship. Netting works by offsetting positions of opposite sign. If every trade with a counterparty is a purchased option, every position has positive or zero value and there is nothing to offset, so the netting agreement provides no benefit at all. That is a structural consequence of the one-sidedness, and it is why option exposures often need collateral rather than netting to be brought down.
What changes on an exchange
Everything above describes over the counter options. A listed option is a different credit proposition.
The clearing house becomes the counterparty to both sides, so the buyer’s exposure is to the clearing house rather than to whoever wrote the contract, and the identity of the writer stops mattering. Writers post initial margin and are marked to market daily, and the clearing house holds a default fund contributed by its members. Counterparty credit risk on the individual writer is effectively removed.
What replaces it is worth being clear about rather than treating as zero. The exposure has been transferred to the clearing house, which is a highly collateralised institution but a single one, and a very large one. The residual risks are concentration in that institution and the liquidity risk of meeting margin calls, which is a different risk from credit but has ended positions before now.
One convention is worth checking before applying any of this to a specific contract. The analysis above assumes the premium is paid in full at inception, which is the standard equity and over the counter arrangement. Some listed options, particularly options on futures in certain markets, are instead margined in the futures style, with no upfront premium and daily variation margin on both sides. Under that convention the buyer does have an obligation, the value can run against them, and the clean one-way asymmetry does not hold. The asymmetry is a consequence of how the premium is settled, not an inherent property of the word option.
The reliable question here is which party has credit exposure on an option and why. The answer is the buyer, for the whole life, because current exposure is the maximum of value and zero and an option’s value to its holder is never negative. Follow that through to the consequences: no CVA for the writer, no benefit from netting in a one-way book, and wrong-way risk with nothing to offset it.
The short version
- Current exposure is the maximum of the mark to market value and zero, so only a positive position creates credit exposure.
- A purchased option can never have negative value to its holder, so the buyer carries all the exposure and the writer carries none.
- Forwards and swaps are two-way: exposure changes hands as the market moves.
- Exposure profiles differ by instrument: forwards rise throughout, swaps hump and fall, purchased options rise with a floor at zero.
- CVA prices the exposure as loss given default times the sum of expected exposure, default probability and discount factor across time.
- Netting gives no benefit in a one-way option book, because there are no negative positions to offset, so collateral does the work instead.
Frequently Asked Questions
Who bears the credit risk on an option?
The buyer, entirely. Current exposure is the maximum of the position’s value and zero, and a purchased option’s value to its holder is never negative, since the holder is never obliged to do anything. So the buyer is exposed to the writer for the whole life of the contract and the writer has no exposure to the buyer once the premium has been paid.
How is this different from a forward or a swap?
Those are two-way. Their value can be positive or negative to either party depending on where the market has gone, so the credit exposure changes hands over the life of the trade. An option never crosses zero, so the exposure sits permanently with one side and never moves.
What shape does potential future exposure take?
It depends on which of two forces dominates. Diffusion pushes exposure up as the underlying has longer to move; amortisation pulls it down as payments are made and less contract remains. A forward rises throughout, roughly with the square root of time. An interest rate swap humps, peaking around a third to halfway through its life. A purchased option rises with a floor at zero, and a written option is flat at zero.
What is CVA?
The credit valuation adjustment, which is the market value of counterparty credit risk on a derivative. Under an assumption that exposure and default are independent, it is loss given default multiplied by the sum across time of expected exposure, the marginal default probability for that period and the discount factor. It is what turns an exposure quantity into a price a desk can charge.
What is wrong-way risk?
The case where exposure increases exactly as the counterparty becomes more likely to default, which breaks the independence assumption inside the CVA formula and causes it to understate the risk. Buying a put on a company from a bank tied to that company is a specific example; a shared macroeconomic driver with no contractual link is a general one.
Does netting help with option exposures?
Usually very little. Netting works by offsetting positions of opposite sign, and every purchased option has positive or zero value. A book made up entirely of purchased options with one counterparty has nothing to offset, so the netting agreement provides no reduction. Collateral, or clearing, is what brings those exposures down.
Loading comments...
Add your Thoughts: