Derivatives: Forwards, Futures, Options, and Swaps
The mechanics, pricing, and risk characteristics of the four major derivative types — the building blocks of modern risk management.
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Cash Versus Derivatives Exposure
Different instruments change exposure shape, funding needs, and margin risk even when the directional view looks similar.
Why it matters
The exam often asks which instrument delivers exposure most efficiently once leverage, margin, and optionality are considered.
Derivatives: Forwards, Futures, Options, and Swaps
Forward Contracts
A forward contract is a private agreement between two parties to buy or sell an asset at a specified price on a future date.
Key Features
- OTC (over-the-counter) — customized, no exchange
- No daily settlement — profit/loss realized at maturity
- Counterparty risk — the losing party may default
- No upfront cost (ignoring credit requirements)
Pricing — Cost of Carry Model
The forward price for a non-dividend-paying asset:
F₀ = S₀ × e^(rT)
For an asset with continuous dividend yield q:
F₀ = S₀ × e^((r−q)T)
Where Sâ‚€ = spot price, r = risk-free rate, T = time to maturity.
Payoff at Maturity
- Long forward (buyer): S_T − F₀
- Short forward (seller): F₀ − S_T
Futures Contracts
Futures are standardized forward contracts traded on organized exchanges.
Key Differences from Forwards
| Feature | Forwards | Futures |
|---|---|---|
| Trading venue | OTC | Exchange |
| Standardization | Customized | Standardized |
| Counterparty risk | Yes (bilateral) | Cleared by CCP |
| Settlement | At maturity | Daily (mark-to-market) |
| Liquidity | General |
...
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