A linear derivative is one whose payoff is a linear function of the underlying asset price — no optionality, no convexity. Forward and futures contracts pay (at settlement) exactly the difference between the contract price and the prevailing market price. Swap contracts exchange streams of cash flows whose present values are linear in the underlying rate or price. Contracts for difference (CFDs) are cash-settled forwards.
This topic covers all linear derivative families. It builds in three layers:
First, mechanics. Forwards and futures differ in settlement (terminal vs. daily), venue (OTC vs. exchange), and credit structure (bilateral risk vs. clearing house). Understanding these differences is prerequisite to using either instrument correctly.
Second, pricing. The cost-of-carry model gives a unified formula for the no-arbitrage futures/forward price of any investment asset. The key insight, introduced already in the FX topic, is that two strategies reaching the same terminal cash flow must cost the same today — deviation creates riskless profit.
Third, risk management. Duration hedging with bond futures, minimum-variance hedging with commodity and equity futures, and DV01-based interest rate hedging are the most widely used applications of linear derivatives in institutional finance.
By the end of this topic you should be able to:
- distinguish forwards from futures mechanically and explain why futures have a basis risk that forwards do not;
- derive the cost-of-carry formula for forward prices and apply it to assets with no income, known income, known yield, currencies, and commodities;
- compute the minimum-variance hedge ratio and the required number of contracts to hedge an equity or commodity position;
- value an interest rate swap as a pair of bonds and as a series of FRAs;
- compute the par swap rate that gives a new swap zero initial value;
- describe currency swaps, equity swaps, and CFDs and place them in the delta-one family.
In this lesson
- Contents
- The big picture
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