Derivatives covers forward contracts, futures, options, and swaps. The topic focuses on the characteristics, pricing, and valuation of these instruments, as well as their use in risk management strategies.
A forward contract is a private agreement to buy or sell an asset at a specified price on a future date. Forwards are customized, traded OTC, and carry counterparty risk. Futures contracts are standardized, exchange-traded versions with daily settlement (marking to market) that eliminates counterparty risk through the clearinghouse. The forward price is determined by the cost of carry: F₀ = S₀ × (1+r)ᵀ for assets with no income, adjusted for storage costs or income.
An option gives the holder the right, but not the obligation, to buy (call) or sell (put) an underlying asset at a specified strike price. Call option payoff at expiration: max(0, S-X). Put option payoff: max(0, X-S). Option value = Intrinsic value + Time value. In-the-money: call when S>X, put when X>S. Key factors affecting option prices: underlying price, strike price, time to expiration, volatility, risk-free rate, and dividends.
Put-call parity establishes a relationship between European call and put options with the same strike price and expiration: C + PV(X) = P + S. This means a protective put (stock + put) has the same payoff as a fiduciary call (call + bond with face value X). If put-call parity is violated, arbitrage opportunities exist. This relationship only holds exactly for European options.
A swap is an agreement to exchange a series of cash flows. The most common is an interest rate swap, where one party pays a fixed rate and receives a floating rate (or vice versa). The notional principal is not exchanged. A plain vanilla interest rate swap can be viewed as a series of forward rate agreements (FRAs) or as exchanging a fixed-rate bond for a floating-rate bond. Currency swaps involve exchanging cash flows in different currencies, with the notional principal exchanged at inception and maturity.
Common option strategies include: Covered call — own stock + sell call (generates income, limits upside); Protective put — own stock + buy put (provides downside protection); Bull spread — buy call at lower strike + sell call at higher strike (limited profit and loss); Bear spread — buy put at higher strike + sell put at lower strike. Straddle — buy call + buy put at same strike (profits from high volatility). Collar — own stock + buy put + sell call (limits both upside and downside).
Forward price equals spot price compounded at the risk-free rate.
At expiration, call holder receives the greater of zero or stock price minus strike.
At expiration, put holder receives the greater of zero or strike minus stock price.
Fundamental relationship between European call, put, bond, and stock prices.
Total option premium consists of intrinsic value (in-the-money amount) plus time value.
The fundamental relationship between European call and put option prices.