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John C. Cox developed mathematical methods for option pricing and risk-neutral pricing. With Stephen A. Ross and Mark Rubinstein, he introduced the Cox--Ross--Rubinstein model, whose binomial price tree gives a particularly transparent example of a replicating portfolio.^[ref]

At each node, the two possible next-step payments determine the holdings in a stock and a riskless asset. Repeating this calculation by backward induction values the final payment through the tree. For an American option, the calculation also compares continuation value with the value of immediate exercise. This turns the distinction between European and American exercise rules into a concrete computational decision.^[ref]

Institutional profile: mitsloan.mit.edu/faculty/directory/john-c-cox

Mark Rubinstein worked on option pricing, including the Cox--Ross--Rubinstein model developed with John C. Cox and Stephen A. Ross. Their 1979 paper constructs an accessible discrete-time model in which successive up and down moves form a binomial price tree. Replicating a contingent payment with traded assets determines its value under the model's no-arbitrage assumptions.^[ref]

The construction makes the relation between hedging and valuation explicit. Its risk-neutral probabilities are weights consistent with the model's prices, rather than predictions of the actual frequency of an upward market move. Refining the time steps also connects the discrete model to the Black-Scholes model.^[ref]

By John C. Cox, Stephen A. Ross, Mark Rubinstein.

Author manuscript: bpb-us-w2.wpmucdn.com/u.osu.edu/dist/7/36891/files/2017/07/CRR79-1yy8av8.pdf

The inspected cover states March1979, revised July1979, and publication under the same title in Journal of Financial Economics in September1979. The original article is Journal of Financial Economics7(3),229–263; DOI doi.org/10.1016/0304-405X(79)90015-1 . Later reprints are listed separately on the manuscript cover and do not change the original publication date.

Cited passages: Section3, manuscript pp.4–11, binomial setup, unrestricted borrowing/lending and short sales, no-arbitrage inequality, replicating hedge and discounted risk-neutral expectation; Section5, manuscript pp.17 onward, small-step limiting cases. Our topic notation uses uppercase U,D,R for undiscounted multipliers, reserving u,d for the discounted ones.

Stephen A. Ross developed arbitrage pricing theory, which relates expected asset returns to exposures to common sources of risk under assumptions limiting arbitrage. His mathematical approach asks how restrictions on feasible trading strategies constrain prices, rather than starting solely from an individual investor's preferences.^[ref]

With John C. Cox and Mark Rubinstein, he also developed the Cox--Ross--Rubinstein model for option pricing. The binomial price tree separates the possible stock-price paths from the valuation rule: a replicating portfolio and no-arbitrage produce risk-neutral pricing even when the actual up-move probability is not specified.^[ref]