The binomial model reduces option pricing to a stock that only rises or falls

Evidence

A simple numerical example (based on Sharpe 1978, pp. 366-373) captures important features of option pricing in a model that is extremely straightforward but nevertheless possesses essential aspects of more complex models. The setting in the model is “binomial”: in any given time period, the price of a stock can only do two things, rise by a set amount or fall by a set amount. (To make the model more realistic, we would have to examine the path of a stock price over many such periods, as in the Cox-Ross-Rubinstein model discussed below, but the main points emerge when considering a single period.) In the model it is assumed that investors can both lend and borrow at the riskless rate of interest of, let us say, 5 percent a year that the stock pays no dividends and can be sold short without penalty, and that buying or selling stock or options incurs no transaction costs. — Donald MacKenzie, An Engine, Not a Camera, 1274

Categorization

• DEFINE: Introduces the binomial option-pricing setup with its simplifying assumptions — foundational for the more complex Cox-Ross-Rubinstein model.
• XREF: connects to: The dynamic hedge ratio at the core of option pricing resisted analytic solution. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 577; Black-Scholes is a continuous-time limit of the binomial model — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1289; Option prices equal the expected payoff discounted at the riskless rate — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1284

Broader Connections

• Black-Scholes is a continuous-time limit of the binomial model #qualifies (0.90) — Donald MacKenzie, An Engine, Not a Camera, 1289
• Option prices equal the expected payoff discounted at the riskless rate #expands (0.85) — Donald MacKenzie, An Engine, Not a Camera, 1284