CFA Level I · CFA Level I Exam

Forward Commitment and Contingent Claim Features and Instruments: formula sheet

Full chapter guide

Key formulas

Forward commitment: Obligation for BOTH parties; payoff can be positive or negative for each; Forwards, futures and swaps. Forwards and swaps are typically priced at zero value at initiation, so no premium is paid. Futures require margin, which is a performance bond, not a premium.
Contingent claim: Buyer: right, pays premium. Seller: obligation, receives premium; Options and credit derivatives. Buyer's loss is limited to the premium; the payoff is asymmetric.
Exchange-traded vs OTC: Exchange: standardized, cleared, low counterparty risk. OTC: customized, private, higher counterparty risk; Customization is the main benefit of OTC; the clearinghouse guarantee is the main benefit of exchange trading.
Long vs short: Long = buyer of the underlying or option; short = seller; For options, 'long' means holding the right; 'short' means holding the obligation.
Long forward payoff at expiry: Payoff to long = ST − K; ST is the spot price at expiry, K is the agreed forward price. The long gains if the spot price ends above K.
Short forward payoff at expiry: Payoff to short = K − ST; Zero-sum: the short's payoff is the negative of the long's. Multiply by contract size and number of contracts.
Daily futures gain or loss: Gain (long) = (Settlement price today − Settlement price yesterday) × contract size × number of contracts; Short gets the opposite sign. On day 1, use the trade price as the prior reference price.
Margin account balance: New balance = Previous balance + daily gain − daily loss (± deposits or withdrawals); Compare with maintenance margin each day.
Margin call amount: Deposit = Initial margin − Current balance; Applies only when balance is below maintenance margin. Under the standard CFA convention you restore to initial margin, not to maintenance. Exact rules vary by exchange and broker.
Futures value after settlement: Value of futures contract = 0 immediately after daily settlement; Because gains and losses are paid each day, the contract is reset to zero value. A forward keeps accumulated value until expiry.
Net payment, interest rate swap: Net = (Fixed rate − Floating rate) × Notional × (days ÷ day-count basis); Positive means the fixed-rate payer pays. Negative means the fixed-rate payer receives.
Periodic fixed payment: Fixed payment = Fixed rate × Notional × period fraction; For quarterly payments use 1/4 of the annual rate. Use the day-count given in the question.
Floating payment timing: Payment at date t uses the rate set at date t − 1; Set in advance, paid in arrears.
Equity swap, equity leg: Equity payment = Notional × Equity return over the period; A negative return means the equity payer receives that amount from the counterparty.
Swap as forwards: Swap ≈ series of forward contracts at one fixed rate, with initial value 0; Individual forward legs can have non-zero values, but the total at initiation is zero.
Long call payoff at expiration: Payoff = max(0, S_T − X); S_T is the underlying price at expiration. The payoff cannot be negative for the buyer.
Long call profit: Profit = max(0, S_T − X) − c₀; c₀ is the call premium paid. Breakeven price = X + c₀.
Short call payoff and profit: Payoff = −max(0, S_T − X); Profit = c₀ − max(0, S_T − X); Maximum gain is the premium. Loss is unlimited. Breakeven = X + c₀.
Long put payoff at expiration: Payoff = max(0, X − S_T); Exercise only if the underlying price is below the strike.
Long put profit: Profit = max(0, X − S_T) − p₀; p₀ is the put premium paid. Breakeven price = X − p₀. Maximum profit = X − p₀.
Short put payoff and profit: Payoff = −max(0, X − S_T); Profit = p₀ − max(0, X − S_T); Maximum gain is the premium. Maximum loss = X − p₀. Breakeven = X − p₀.
Moneyness: Call ITM if S > X; Put ITM if S < X; ATM if S = X; Out of the money is the opposite of in the money.
Cash settlement payout: Payout = Notional × (1 − Recovery rate); Equivalently Notional × loss given default. Paid by seller to buyer after a credit event.
Loss given default: LGD = 1 − Recovery rate; Recovery rate is the fraction of face value recovered.
Annual CDS premium: Premium = CDS spread × Notional; Paid by the protection buyer, usually quarterly. Divide by the number of payments per year for each payment.
Approximate change in CDS market value: ΔValue ≈ ΔSpread × Risky duration × Notional; Approximation. Risky duration is the CDS's own duration, the sensitivity of the PV of its premium annuity (not a bond's duration). Value rises for the buyer when the spread widens, and falls for the seller.
Approximate CDS spread: Spread ≈ Probability of default × LGD; Rough annual relationship used for intuition, not an exact pricing formula.
Caplet payoff (per period): Notional × max(0, reference rate − cap strike) × (days ÷ 360 or period fraction); The rate is set at the start of the period (in advance) and the payoff is made at the end (in arrears). This is the usual convention for caps and floors.
Floorlet payoff (per period): Notional × max(0, floor strike − reference rate) × period fraction; Gains when rates fall below the strike.
Collar: Long cap + short floor (borrower); long floor + short cap (lender); Premium on the short option offsets the cost of the long option.
Payer swaption: Right to pay fixed, receive floating at the exercise rate; Gains when market swap fixed rate rises above the exercise rate.
Receiver swaption: Right to receive fixed, pay floating at the exercise rate; Gains when market swap fixed rate falls below the exercise rate.
Callable bond value: Callable = option-free bond value − call option value; Issuer owns the call.
Putable bond value: Putable = option-free bond value + put option value; Investor owns the put.
Convertible bond value: Convertible = straight bond value + conversion option value; Conversion value = share price × conversion ratio. Value is at least the higher of straight value and conversion value.

Quick revision

Forward commitments (forwards, futures, swaps) bind both parties; contingent claims give one party a right.
A forward or futures contract has a payoff that is linear in the underlying price; the long gains when the price rises and the short gains when it falls.
Forwards are customised and traded over the counter; futures are standardised, exchange-traded and cleared, with daily settlement.
A plain vanilla swap exchanges fixed payments for floating payments on a notional amount, usually netted.
Call payoff at expiry for the buyer = max(0, S − X); put payoff = max(0, X − S).
Option profit for the buyer = payoff − premium; the buyer's maximum loss is the premium.
Option sellers receive the premium and face the opposite payoff of the buyer; a short call has unlimited loss potential.
A call is in the money when S > X; a put is in the money when S < X.
A credit default swap: the protection buyer pays periodic premiums and receives compensation if the credit event occurs.
A cap is a series of interest rate calls; a floor is a series of interest rate puts.
A swaption is an option to enter a swap; a convertible bond lets the holder exchange the bond for shares.

Common mistakes

Calling a swap a contingent claim because it has several payments Fix: A swap is a series of forward commitments. Both sides are obligated, so it is a forward commitment.
Thinking an option seller has a right Fix: Only the buyer holds the right. The seller (writer) holds the obligation and keeps the premium.
Restoring the margin to the maintenance level after a margin call. Fix: Maintenance is only the trigger. The deposit brings the balance back up to the initial margin.
Giving the short the same sign as the long. Fix: Forwards and futures are zero-sum. The short's payoff is K − ST, the exact opposite.
Using the floating rate at the payment date instead of the rate set at the start of the period Fix: Floating is set in advance and paid in arrears. Use the previous reset rate.
Exchanging the notional in an interest rate swap Fix: In a plain vanilla interest rate swap, the notional is never exchanged. In currency swaps it is usual, though not always required.
Reporting payoff when the question asks for profit, or the reverse. Fix: Underline the word in the question. Profit always includes the premium; payoff never does.
Treating a put as in the money when S > X. Fix: A put is in the money when the underlying is below the strike. Ask whether selling at X beats selling in the market.
Thinking the protection seller pays the premium. Fix: The buyer pays the premium and the seller receives it. The seller pays only after a credit event.
Using the recovery rate as the payout fraction. Fix: The seller pays the loss, so payout is notional × (1 − recovery rate).

Exam tips

Every question has three options. Use the obligation-versus-right test to eliminate two quickly.
Expect classification questions: forwards, futures and swaps go in one bucket; options and credit derivatives in the other.
Read who holds the position. 'Buyer of a call' and 'writer of a call' have opposite rights and duties.
Look for keywords such as standardized, clearinghouse and customized to settle market-type questions.
No penalty for a wrong answer, so never leave a question blank.
Always confirm long or short before you do any arithmetic. The sign is the most common trap.
For margin calls, check whether the question asks for the deposit amount or the new balance. Restore to initial margin, not maintenance.
Feature questions often test credit risk, liquidity and customization. Link forward to OTC, customized, higher credit risk and futures to exchange, standardized, clearinghouse.