Pedagogical survey of derivative assets analysis for a general economics audience, published in Journal of Economic Perspectives 1(2): 73–93 at the journal's founding. Covers forward/futures pricing, put-call parity, the Black-Scholes formula and its delta interpretation, the Cox-Ross-Rubinstein binomial method, risk-neutral pricing, four classes of Black-Scholes deviations, index futures anomalies, portfolio insurance, and an appendix cataloguing ~30 applications of derivative assets analysis across futures, options, corporate securities, government bonds, financial institutions, and real assets.
Key Claims
Forward pricing: Fair forward price is F=(S−D)rt where D is present value of dividends through delivery. Any linear payoff function can be replicated by a static buy-and-hold position in the underlying assets and a riskless bond; the valuation formula follows from the value-additivity theorem alone.
Put-call parity: max(0,K−S∗)=max(0,S∗−K)−S∗+K implies P=C−(S−D)+Kr−t. Puts are manufactured from calls ("option conversion relationship"); this allows the entire derivative assets valuation problem to be reduced to valuing a single call.
Black-Scholes delta interpretation: N(x) is the number of index units held in the replicating portfolio; −Kr−tN(x−σt) is the riskless borrowing. Unlike linear payoffs, the replicating strategy is dynamic because N(x) depends on the concurrent stock price and time remaining.
Binomial procedure (Cox-Ross-Rubinstein 1979): If over each discrete interval the underlying asset can only move up or down by known percentages, a two-asset portfolio (index + cash) exactly replicates the option each period. In the limit as intervals shrink, this converges to Black-Scholes. Widely used by practitioners for American options (early exercise handled by replacing the holding value with the exercise value when advantageous).
Risk-neutral pricing (Cox-Ross 1976): Since investor preferences don't enter the replication argument, one may assume risk neutrality and compute C=EQ[max(0,S∗−K)]/rt under lognormal S∗. This yields Black-Scholes exactly and can be used whenever a replicating strategy exists.
Four deviations from Black-Scholes: (1) price jumps → short-maturity Out-of-the-Money (OTM) calls overpriced relative to At-the-Money (ATM); (2) price-dependent volatility → moneyness skew; (3) interest-rate-dependent volatility; (4) stochastic volatility with mean reversion. Only (1) had consistent empirical support as of 1987; all four became more salient after the October 1987 crash.
Index futures anomalies: S&P 500 futures persistently deviated from theory in both directions (underpriced May–June 1982 and Sep 1986; overpriced Sep–Dec 1984). Rubinstein attributes this to insufficient arbitrage capital — an early limits-to-arbitrage observation.
Arrow (1964) connection: Black-Scholes is a special case of Arrow's sequential-markets result: with only two traded assets (stock + bond), continuous rebalancing can replicate any derivative on the stock, substituting for a complete set of state-contingent forward markets.
"Derivative assets analysis enjoys an unusual status; it is a recently developed, relatively complex tool of economic analysis, faithful to the core of economic theory, and widely used to make real-life decisions."
"I am forced to the conclusion that even today the growth in index futures trading continues to outstrip the amounts of capital that are available for arbitrage."
My Take
A well-crafted 1987 snapshot written for JEP's inaugural issue. The Arrow (1964) historical connection — tracing Black-Scholes to the 1952/1964 sequential-markets result — is genuinely illuminating. The comprehensive appendix of applications remains a useful taxonomy. The paper's assumption that Black-Scholes is empirically adequate became untenable within months: the October 1987 crash produced the persistent post-crash volatility skew that has characterized equity index options ever since. For this wiki, the main value is as a companion to Rubinstein (1976), adding the binomial method, put-call parity, portfolio insurance, and the Arrow historical link to the Black-Scholes concept page. No new concepts warranted; all content folds into existing pages.