Mark Rubinstein

Overview

Mark Rubinstein (1944–2019) was a financial economist at UC Berkeley's Haas School of Business. He made foundational contributions to option pricing theory, particularly showing that the Black-Scholes formula holds in discrete time under risk aversion (Rubinstein 1976), and later developed implied binomial trees as a nonparametric approach to recovering risk-neutral probabilities from option prices across strikes (Rubinstein 1994).

Key Contributions / Features

• Rubinstein (1976): Derived the Black-Scholes option pricing formula in discrete time with risk-averse CPRA investors using a stochastic discount factor framework. Key results: $Y_t = R_{Mt}^{-b}$ under CPRA; bivariate lognormality of $(S_t, Y_t)$ is sufficient for Black-Scholes; the log-CAPM $\ln E(r_i) = \ln r_F + b \cdot \text{Cov}(\ln r_i, \ln r_M)$; and the Stein–Rubinstein lemma $\text{Cov}(x, g(y)) = E[g'(y)]\text{Cov}(x, y)$. See Rubinstein (1976).
• Rubinstein (1987): Pedagogical survey for JEP's inaugural issue covering forward pricing, put-call parity, the Black-Scholes delta interpretation, the binomial method (attributed to Sharpe / Cox-Ross-Rubinstein 1979), risk-neutral pricing, four classes of Black-Scholes deviations, index futures anomalies, and portfolio insurance. Traces Black-Scholes to Arrow (1964). See Rubinstein (1987).
• Rubinstein (1994): Introduced implied binomial trees — a nonparametric lattice calibrated to observed option prices across strikes — extending Black-Scholes to accommodate the empirical volatility smile.

Related

• Black-Scholes Option Pricing
• Stochastic Discount Factor
• Contingent Claim Model Error