Moments and transition probability of Trinomial Tree
I just switched from using WP-Latex to MathJax since Chrome is soon going to have built-in support for MathJax and it is easier to recover the tex codes for the reader.
To test out the functionality, I wanted to write down some equations befitting to the occasion. I scraped through my notes to see if there was anything interesting and worth posting. I stumbled upon Trinomial Tree ( \ddagger ). Now it is not that common and haven’t seen much usage of Trinomial Tree outside finance (One of the ways for Options Pricing), nonetheless I thought it would be interesting to refresh these formulas, you never know when you might need them again.
Trinomial Tree, a special case of binomial tree where instead of two we have three branches, lets call them Up ( u ) , Middle ( m ) and Down (d ) . Transition of each step could then be defined as —
with probability
with probability
with probability
For simplicity sake let’s consider that transition magnitude is same on each side, i.e
then the transition probability is given by
from above equations we can derive the **moments **as given below,
Phelim Boyle in 1986.
An excellent 23 slide background on Trinomial including other forms besides Boyle’s.