CFA Level I Exam · Derivative Instrument and Derivative Market Features
Contingent Claims: Options and Credit Derivatives Explained
Updated 7 October 2026 · Fact-checked
A contingent claim is a derivative whose payoff depends on a future event, such as the underlying price ending above or below a strike. Options give the buyer a right and the seller an obligation. A credit default swap pays out if a credit event occurs. Payoff is the exercise value; profit is payoff minus premium.
Understand Contingent Claims: Options, Credit Derivatives
A contingent claim pays off only if something happens. With a forward, both sides must perform. With a contingent claim, one side holds a right and the other side holds an obligation.
An option gives the buyer (long) the right, but not the duty, to trade the underlying at a fixed exercise price (strike). A call is the right to buy. A put is the right to sell. The buyer pays a premium to the seller (writer) up front. The seller keeps the premium and must perform if the buyer exercises.
A European option can be exercised only at expiration. An American option can be exercised at any time up to expiration. The buyer's loss is limited to the premium. The call buyer's gain is unlimited, since the price can rise without limit. The put buyer's gain is capped because the underlying price cannot fall below zero. The seller's results are the mirror image: the gain is capped at the premium, and the loss can be large.
A credit default swap (CDS) is a contingent claim on credit quality. The protection buyer pays a periodic premium (the CDS spread, often quoted as a coupon). The protection seller pays compensation if a credit event occurs, such as bankruptcy or failure to pay, on the reference entity's debt. The buyer is like an owner of a put on the bond. The seller is like someone who has written insurance and earns the premium. The payout is usually the loss on the reference obligation, which is the notional times (1 − recovery rate).
Keep one distinction clear. A contingent claim is a one-sided right. A forward commitment is a two-sided obligation. The option buyer pays a premium for this one-sided right. The forward has no upfront premium.
Key formulas to remember
- Call payoff at expiration (buyer)
- max(0, S_T − X)
- S_T is the underlying price at expiration, X is the strike. Never negative.
- Put payoff at expiration (buyer)
- max(0, X − S_T)
- Never negative for the buyer.
- Buyer profit
- Profit = Payoff − Premium
- Ignores financing cost and transaction costs unless the question includes them.
- Seller (writer) profit
- Profit = Premium − Payoff
- Seller's profit is the exact negative of the buyer's.
- Breakeven price
- Call: X + premium. Put: X − premium
- The same for buyer and seller.
- Maximum loss and gain
- Long call: loss = premium, gain unlimited. Long put: loss = premium, gain = X − premium. Short call: gain = premium, loss unlimited. Short put: gain = premium, loss = X − premium
- Put gain/loss assumes the underlying can fall to zero.
- Moneyness
- Call in the money if S > X; put in the money if S < X; at the money if S = X
- Out of the money has zero exercise value now.
- CDS payout on credit event
- Payout = Notional × (1 − Recovery rate)
- Equals loss given default on the notional covered.
How to solve Contingent Claims: Options, Credit Derivatives questions
Use this routine for any question on option payoffs, profit or CDS.
- 1Identify the contract: call or put, and whether the person is the buyer (long) or seller (short).
- 2Write down the strike X, the premium and the expiration price S_T (or the credit event details).
- 3Compute the buyer's payoff with max(0, S_T − X) for a call or max(0, X − S_T) for a put.
- 4Subtract the premium to get the buyer's profit. For the seller, flip the sign of the buyer's profit.
- 5Check the limits: the buyer can lose only the premium; the seller's gain is only the premium.
- 6For breakeven, add the premium to X for a call or subtract it from X for a put.
- 7For a CDS, decide who pays the spread (protection buyer) and compute the payout as notional × (1 − recovery) if a credit event occurs.
Quickest way: Sketch and test the two cases
When to use it: Use this when the question is conceptual or when you must eliminate options fast.
- Ask: is the option in the money at expiration? If not, the buyer's payoff is 0 and the buyer's profit is minus the premium.
- If it is in the money, payoff is the distance between S_T and X.
- Take off the premium for the buyer profit. The seller is the opposite.
- Remember the shape: long call rises right of X; long put rises left of X.
- Eliminate any option that gives the buyer a loss bigger than the premium, or the seller a gain bigger than the premium.
Common mistakes in Contingent Claims: Options, Credit Derivatives
Treating the buyer's payoff as negative when the option expires worthless.
Students mix up payoff and profit.
Fix: Payoff is never below zero for the buyer. The loss shows up only after subtracting the premium.
Forgetting the premium when asked for profit.
Payoff is calculated first and the question stops feeling finished.
Fix: Read whether the question asks for payoff or profit. Profit always includes the premium.
Calling a put's breakeven X + premium.
The call formula is applied by habit.
Fix: A put gains as the price falls, so breakeven is X − premium.
Saying the put buyer has unlimited gain.
Students copy the call logic.
Fix: The underlying cannot go below zero, so the maximum put gain is X minus the premium.
Confusing who pays the CDS premium.
The word 'protection' is mistaken for a payer of compensation.
Fix: The protection buyer pays the spread and receives compensation on a credit event. The protection seller receives the spread and pays.
Assuming a CDS pays the full notional.
Recovery on the bond is ignored.
Fix: The payout reflects the loss: notional × (1 − recovery rate).
Worked examples
Example 1
An investor buys a European call on a share with strike $50 for a premium of $3. At expiration the share trades at $58. What are the buyer's payoff, the buyer's profit and the seller's profit?
Show the solution
- Buyer payoff = max(0, 58 − 50) = $8.
- Buyer profit = 8 − 3 = $5.
- Seller profit = 3 − 8 = −$5.
- Check: the seller's result is the negative of the buyer's.
Answer: Buyer payoff $8, buyer profit $5, seller profit −$5.
Example 2
A protection buyer holds a CDS with a notional of €10,000,000 on a bond issuer. The issuer defaults and the bond's recovery rate is 40%. What does the protection seller pay, ignoring accrued premium?
Show the solution
- Loss given default = 1 − 0.40 = 0.60.
- Payout = 10,000,000 × 0.60 = €6,000,000.
- The protection seller pays this to the protection buyer.
Answer: €6,000,000 paid by the protection seller to the protection buyer.
Exam tips
- Read whether the question asks for payoff, profit or breakeven. They are different numbers.
- Identify the person's side first. Buyer and seller results are exact opposites.
- For a three-option question, remove first the answer that breaks the premium limit on gain or loss.
- In CDS items, find who pays the spread: the protection buyer.
- Questions on contingent claims versus forward commitments often hinge on the word 'right' versus 'obligation'.
Practice questions from Derivative Instrument and Derivative Market Features
- A trader enters an over-the-counter forward contract with a bank, and later the forward's value to the trader is positive. The trader's main…
- Compared with a transaction in the underlying asset, a derivative contract most likely has which of the following features?
- A trader writes a European call with a strike of 80 for a premium of 5 and simultaneously buys a European put on the same underlying with a …
- An investor entered a long forward contract to buy an asset at 100. At a later date, the forward price for the same maturity is 108. Ignorin…
- A party that has entered a long forward contract on a currency is most likely exposed to credit risk when the forward contract has:
Contingent Claims: Options, Credit Derivatives in other exams
The same ground in other exams, if you are preparing for more than one or want another angle on it.
Contingent Claims: Options, Credit Derivatives: frequently asked questions
What is a contingent claim in derivatives?
It is a derivative whose payoff depends on a specified future event, such as the underlying price relative to a strike. Options are the main example. Credit default swaps are also treated as contingent claims because they pay out only after a credit event.
How do you calculate profit for an option buyer and seller?
Find the buyer's payoff at expiration, then subtract the premium for the buyer's profit. The seller's profit is the premium minus that payoff, which is exactly the opposite of the buyer's profit.
What is the difference between a call and a put payoff?
A call pays max(0, S_T − X), so it gains when the price rises above the strike. A put pays max(0, X − S_T), so it gains when the price falls below the strike.
Who pays whom in a credit default swap?
The protection buyer pays a periodic premium to the protection seller. If a credit event happens, the protection seller compensates the buyer for the loss on the reference obligation.