Jun 03

Stock option delta – 7 min screencast

by David Harper, CFA, FRM, CIPM

This brief screencast illustrates the option delta (one of the Greeks along with vega, gamma, rho, theta). Note the following:

Delta of a European-style call option = N(d1). Delta of put = N(d1) â€“ 1. Note that delta is embedded inside the Black-Scholes-Merton OPM.
Delta informs an instantaneous hedge. In this example, delta of 0.61 means we can hedge a long position in 61 shares with a short position (we "write") in 100 call options.

But note: the delta hedge is only a linear approximation that holds under the current delta. There are actually two aspects to this:

As a linear approximation, it won't capture larger non-linear movements (we could introduce gamma to help with this)
As the stock price moves, delta changes. We need to (dynamically) re-balance in order to maintain delta neutrality.

Screencast: