The option delta determines the hedge ratio of stock to warrants.

Evidence

Black and Scholes could see how a zero-beta portfolio would have to be constructed. If the stock price x changed by the small amount Ax, the warrant or option price w would alter by Ax multiplied by aw/ax, the partial derivative of w with respect to x and thus the rate at which the warrant or option price changes as the stock price changes. (This partial derivative-” delta,” as it was to become known to the option traders discussed in chapter 6 would vary with time and with stock-price changes, but would be calculable if w could be expressed as a differentiable function of x and of the other parameters of the problem.) So the necessary hedge was to short-sell a quantity aw/ax of stock for every warrant held. That was in a sense the same conclusion Thorp and Kassouf had arrived at: aw/ax is their hedging ratio, expressed in their case as the slope of the empirically derived curves of warrant price plotted against stock price as in figure 5.1. — Donald MacKenzie, An Engine, Not a Camera, 579

Categorization

• DEFINE: Introduces the option delta term that will recur in later chapters about traders.