Skip to content

IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model

In the Cox-Ross-Rubinstein (CRR) calibration of a binomial tree to a share whose returns have volatility sigma, with time step h, which pair of up and down factors is used?

The CRR calibration uses u = exp(sigma times the square root of h) and d = 1/u. This makes the tree recombine and matches the log-return variance sigma squared times h, because variance scales with time, so volatility scales with the square root of time.

  1. Au = exp(sigma*sqrt(h)) and d = 1/uCorrect
  2. Bu = 1 + sigma*h and d = 1 - sigma*h
  3. Cu = exp(sigma*h) and d = exp(-sigma*h)
  4. Du = exp(r*h) and d = exp(-r*h)
  5. u = 1 + sigma and d = 1 - sigma

Explanation

The CRR tree sets u = exp(sigma*sqrt(h)) and d = 1/u so that the tree recombines and its variance per step matches sigma squared times h. Using sigma*h instead of sigma*sqrt(h) scales volatility wrongly because variance grows linearly with time, not the square of time.

Did you get it right without looking?

One question tells you little. A timed set on Binomial option-pricing model shows your real accuracy, how long you take and where you lose marks.

Practise Binomial option-pricing modelFree diagnostic mock

More Binomial option-pricing model questions