Overview
Derivatives are contracts whose value is derived from an underlying asset, rate, or index. The Level I curriculum covers the four main instrument types — forwards, futures, options, and swaps — focusing on payoff structures, pricing, and risk management applications. Questions mix conceptual understanding with payoff calculations.
Forwards and Futures
A forward contract is a bilateral agreement to buy or sell an asset at a specified price (forward price) on a future date. No cash changes hands at initiation; settlement occurs at expiration. Forward contracts are traded OTC and expose both counterparties to credit risk.
Futures contracts are standardized forwards traded on exchanges. Daily mark-to-market and margin requirements (initial margin, maintenance margin) almost eliminate credit risk but introduce basis risk. A margin call is triggered when the account balance falls below the maintenance margin.
The no-arbitrage forward price for a non-dividend-paying asset: F₀ = S₀ × (1+r)ᵀ, where S₀ is the spot price and r is the risk-free rate for the period T.
Options
An option gives the buyer the right, but not the obligation, to buy (call) or sell (put) an underlying asset at the strike price K before or at expiration.
Payoffs at expiration:
- Long call: max(ST − K, 0)
- Long put: max(K − ST, 0)
- Short call: −max(ST − K, 0)
- Short put: −max(K − ST, 0)
Put-call parity (for European options): C − P = S₀ − K/(1+r)ᵀ. Violations create arbitrage opportunities.
Option value components:
- Intrinsic value: The immediate exercise value — max(S − K, 0) for a call
- Time value: The option premium above intrinsic value, reflecting the possibility of future favorable moves
Options prices increase with volatility, time to expiration, and (for calls) the underlying price.
Swaps
A swap is an agreement to exchange cash flows based on different underlying references. In a plain-vanilla interest rate swap, one party pays a fixed rate and receives a floating rate (LIBOR/SOFR) on the same notional principal. Swaps are used to convert fixed-rate liabilities to floating, or vice versa.
Currency swaps exchange cash flows denominated in different currencies. Equity swaps exchange a return tied to an equity index for a fixed or floating rate.