Black-Scholes is a continuous-time limit of the binomial model

Evidence

The Black-Scholes-Merton model is a limit case of the Cox-RossRubinstein model. If the time periods become infinitely many and infinitesimally small, a “multiplicative” binomial process like that in figure E. becomes the Black-Scholes-Merton log-normal random walk in continuous time, but other stochastic processes can also be modeled using the Cos-Ross-Rubinstein approach. — Donald MacKenzie, An Engine, Not a Camera, 1289

Categorization

• DEFINE: Establishes the mathematical relationship between the discrete binomial model and the continuous-time Black-Scholes-Merton model.
• XREF: connects to: Continuous-time models give sharper results and drop quadratic utility. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 594; The binomial model reduces option pricing to a stock that only rises or falls — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1274; Pre-Black-Scholes option models relied on unmeasurable parameters — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95