Derivatives

Résumé

Derivatives are instruments whose value derives from an underlying asset, rate, or index. The topic distinguishes forward commitments, which obligate both parties, from contingent claims, which grant a right. Forward commitments include forwards (customized, over-the-counter), futures (standardized, exchange-traded, marked to market daily through a clearinghouse), and swaps (a series of exchanges of cash flows equivalent to a portfolio of forwards). Contingent claims are options: a call gives the right to buy and a put the right to sell at a strike price, with European options exercisable only at expiration and American options exercisable any time. Derivative markets serve risk transfer, price discovery, and cost or operational efficiency, though they carry counterparty and leverage risks. Pricing and valuation rest on arbitrage and replication: the no-arbitrage forward price equals the cost of carrying the underlying to delivery, adjusting for income and carrying costs. The value of a forward changes as the spot price and time evolve. Option pricing recognizes intrinsic value and time value, factors affecting option value (underlying price, strike, time, volatility, risk-free rate, and cash flows on the underlying), and the one-period and two-period binomial models using risk-neutral probabilities. Put-call parity links the prices of European calls, puts, the underlying, and a risk-free bond, while put-call-forward parity uses the forward price. Understanding payoffs, boundary conditions, and the replication of positions allows analysts to value derivatives and to construct hedges and synthetic positions.