Jun 05

One step binomial – 7 min screencast

by David Harper, CFA, FRM, CIPM

Here is a review of John Hull's example in Chapter 11 (11.1). Aside from stock price (S), strike price (K or X), riskless rate and term, there are three key variables:

(u) is the size of the up jump. This can be matched with volatility (i.e., solved for given volatility) but it is a user input. If it changes, the option value changes; e.g., higher volatility implies both a higher (u) and a lower (u). In short, option value is sensitive to (u) and (d)
(d) is the size of the up jump
(p) is the probability of an up jump (or up step). It does not enter into the approach illustrated here. The riskless portfolio consists of long a fractional share and short a call option. The option value is solved under that assumption and (p) does not enter into the valuation. Hence, Hull says the expected return of the stock is "irrelevant."

Screencast: