Instead of arbitrarily selecting the up (u) and down (d) jumps in the binomial, we can "match them to a volatility input assumption, σ. The correct values are given by u = exp[σ*sqrt(Δt)] and d = 1/u; notice that the exponent is just apply the Square Root Rule (SRR) of scaling the per annum volatility to the correct period volatility; in this example, a 30.0% per annum volatility translated into 30.0% * sqrt(0.25) = 15.0% three-month volatility. When we use these assumptions, we implicitly assume that the geometric (aka, continuous) returns are normally distributed which is tantamount to assuming the prices are lognormally distributed, and this version of the binomial (aka, Cox Ross Rubinstein) converges on the classic Black-Scholes-Merton (BSM) as the number of steps increases.
David's XLS is here: https://trtl.bz/2Ri5R7r
David's XLS is here: https://trtl.bz/2Ri5R7r
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