Learning Module 2
Forward Commitment and Contingent Claim Features and Instruments
Key Outcomes Summary & Practice Problems
What you must be able to do
Curriculum Year: 2026
Define forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives and compare their basic characteristics.
Determine the value at expiration and profit from a long or a short position in a call or put option.
Contrast forward commitments with contingent claims.
1 · Forwards
A forward contract is an OTC firm commitment in which the buyer agrees to purchase the underlying from the seller at a future date for a pre-agreed forward price, F0(T).
No upfront payment is exchanged at t = 0; the payoff equals the profit because there is no premium.
Symmetric (linear) payoff — a defining feature of all firm commitments (forwards, futures, swaps).
Forward buyer = long position, gains as ST rises; forward seller = short position, gains as ST falls.
Daily gain/loss = [ft(T) − ft−1(T)] × contract size
Margin call needed = Initial margin − Current balance (if balance < maintenance margin)
2 · Futures
Futures = standardized forward contracts (size, dates, underlying) traded on an exchange with daily settlement — the key structural difference from forwards.
Mark-to-market (MTM) / daily settlement — the clearinghouse settles gains/losses each day at the end-of-day settlement price.
Initial margin — required deposit at trade inception (per contract); maintenance margin — minimum balance that must be maintained; falling below it triggers a margin call (deposit of variation margin to restore the balance to the initial margin).
If a counterparty cannot meet a margin call, the position is closed out; the clearinghouse guarantees performance via an insurance fund.
At maturity: cash or physical settlement based on open interest; a position can also be closed early via an offsetting trade.
Forward vs. futures: both settle to the same cumulative amount at maturity, but futures settle through daily MTM cash flows rather than one lump sum — a (usually small) time-value-of-money difference exists between the two.
Buyer payoff/profit = ST − F0(T)
Seller payoff/profit = F0(T) − ST
3 · Swaps
A swap is a firm commitment to exchange a series of cash flows in the future — usually one floating leg (resets via a market reference rate, MRR) and one fixed leg.
Fixed-rate payer (= floating-rate receiver) vs. floating-rate payer (= fixed-rate receiver).
Notional principal is typically not exchanged — used only to calculate interest cash flows; payments are usually netted.
Swap value at inception ≈ 0 (no upfront exchange); as rates/market conditions change, the swap develops a positive MTM for one side and an equal, offsetting negative MTM for the other.
Swaps can be viewed as a series of forward contracts (one per settlement date).
Net payment to fixed-rate receiver = (Fixed rate − MRR) × Notional × Period
If MRR > fixed rate → floating-rate payer owes the net amount
4 · Options
An option is a contingent claim: the buyer has the right, but not the obligation, to transact; the seller is obligated to perform if exercised.
Call option = right to buy at the exercise price (X); put option = right to sell at X.
European options exercise only at maturity; American options exercise any time up to maturity (the labels refer to exercise timing, not geography).
Option buyer's payoff is always ≥ 0 — asymmetric (non-linear) payoff, a defining feature of contingent claims.
Moneyness: call is in-the-money if St > X (intrinsic value = St − X); out-of-the-money / at-the-money options have zero intrinsic value (price = time value only).
Option seller has no counterparty credit risk to the buyer once the premium is received; the buyer bears counterparty risk equal to the option's potential payoff.
Payoff = max(0, ST − X)
Profit (buyer) = max(0, ST − X) − c0
Profit (seller) = c0 − max(0, ST − X)
Payoff = max(0, X − ST)
Profit (buyer) = max(0, X − ST) − p0
Profit (seller) = p0 − max(0, X − ST)
Position | Max Gain | Max Loss |
|---|---|---|
Long call | Unlimited | Premium paid (c0) |
Short call | Premium received (c0) | Unlimited |
Long put | X − p0 (underlying → 0) | Premium paid (p0) |
Short put | Premium received (p0) | X − p0 (underlying → 0) |
5 · Credit Derivatives
Credit default swap (CDS) — the most common credit derivative; based on the default risk of a single issuer or an index of issuers.
CDS trades on a credit spread, which depends on the probability of default (POD) and loss given default (LGD). Higher spread (more distress risk) → lower cash bond price.
CDS contracts are technically contingent claims but share features of firm commitments: the protection buyer pays a fixed periodic spread; the protection seller receives it and must make a contingent payment ≈ LGD × notional if a credit event occurs.
CDS MTM change ≈ Δ CDS spread × notional × effective duration of the CDS (between credit events).
A protection seller's position is economically similar to a long position in the reference issuer's cash bond — receiving spread income in exchange for default risk.
6 · Forward Commitments vs. Contingent Claims — Comparing Payoffs
Both a long forward and a long call (with X = F0(T)) gain as ST rises, but the forward's gain/loss is symmetric while the call's loss is capped at the premium.
A long forward and a short put (with X = F0(T)) both resemble a long position in the underlying on the upside; the short put's upside is capped at the premium received.
Long call ≈ long underlying position with downside protection, paid for via premium. Short put ≈ long underlying exposure, with upside given up in exchange for receiving premium.
Forward vs. Option Profit (X = F0(T)) | Relationship |
|---|---|
ST − F0(T) > −c0 | Forward profit exceeds long call profit |
ST − F0(T) = −c0 | Forward profit equals long call profit |
ST − F0(T) < −c0 | Long call profit exceeds forward profit |