R27.P1.T4.Hull_Ch13_15_19:Topic: BINOMIAL_TREE_OPTION_PRICING

[gargi.adhikari]

In reference to R27.P1.T4.Hull_Ch13_15_19:Topic: BINOMIAL_TREE_OPTION_PRICING :-
Hi,
I just wanted to clarify something on this topic in the example illustrated below:-
Here , the Volatility is a given input = 30 %
Time = 1 yr
So, then the Magnitude of Up Jump , u should be solved to be = e ^ [ Volatility * SQRT( Time) ] = e^ [ .3 * 1] = 1.345
But, instead the Magnitude of Up Jump , u: seems to be a Given input = 1.2 instead of 1.345..

Note : I do see in the new/latest notes for this example that Volatility is not given and so the Magnitude of Up Jump , u is a given input = 1.2

Much gratitude for a clarification on this.

 

[David Harper CFA FRM]

Hi @gargi.adhikari I think you are still using the previous study note? Please note we published a revision, which includes improved graphics. See the same example below (it becomes Hull Ex 13.8 in the latest). Notice that you are are correct: in the above (Hull Example 12.8) the provided volatility is not used, which is better explained below. I hope that clarifies, thanks!

 

[brian.field]

Incidentally, the application of u = exp(sigma*root(h)), etc. is only true for Cox-Ross-Rubenstein trees (and for forward trees applied to futures I think).

It is not necessarily the case, as this question illustrates, that u = exp(sigma*root(h)). As additional examples, consider lognormal trees where u = exp(r - delta -.5*sigma^2)*h + sigma*root(h), etc.

 

[gargi.adhikari]

@David Harper CFA FRM Thanks so much for the clarification ..just wanted to make sure...
@brian.field Thanks for the additional example