Derivatives
Derivatives tests the four building blocks: forwards, futures, options and swaps. You need to know what each obliges or entitles a party to do, how the payoff is computed, and the no-arbitrage relationships that link derivatives to the underlying.
Contracts and payoffs
- A forward commits both parties to trade at a fixed price; its value at initiation is zero, and it gains value to one side as the spot price moves.
- Futures are standardised, exchange-traded and marked to market daily, which introduces daily cash-flow variation that forwards lack.
- A long call pays max(0, S - X) at expiry; a long put pays max(0, X - S). The buyer pays a premium, the writer receives it. Profit = payoff - premium paid.
- An interest rate swap exchanges fixed for floating payments on a notional principal; the notional is not exchanged.
No-arbitrage relationships
- Put-call parity for European options on a non-dividend-paying stock: C - P = S - PV(X).
- The lower bound on a European call is max(0, S - PV(X)); on a European put it is max(0, PV(X) - S).
Worked example
A stock trades at 100. A one-year European call and put have a strike of 100, the risk-free rate is 5%, and the put premium is 5. PV(X) = 100 / 1.05 = 95.24. From parity: C = S - PV(X) + P = 100 - 95.24 + 5 = 9.76. If the call were quoted at 8.00, it is underpriced: buy the call, sell the put, sell the stock, and invest the proceeds at the risk-free rate to lock in the 1.76 difference.
Traps that cost marks
- Confusing payoff with profit by omitting the premium.
- Applying parity to American options, where early exercise breaks the equality into a band.
- Forgetting that futures gains and losses are settled daily, so the terminal value differs from a forward's.
- Assuming a forward's value is its price; the initial value is zero, not the forward price.