6
$\begingroup$

I'm trying to confirm my understanding of the 2 models. It is my understanding that the black-scholes is a special case of a binomial model with infinite steps.

Does this mean that if I were to start with a Binomial model with 1 step and increase steps towards infinity I would approach the same value concluded by the black-scholes?

If so does this mean I could use the implied volatility from Black-scholes formula derived from the market price of an option with the rest of the values (r, t, K, S, σ(IV) ) and approach the same market price from the black-scholes as # of steps approaches infinity? Would this only be the case for a European call with more disagreement on the value of American options with early exercise?

Thanks!

$\endgroup$
  • $\begingroup$ After some more research... I found this article that shows the connections between the two models.. epublications.bond.edu.au/cgi/… that shows that prices do converge as N Periods increases. Also they provide all the Excel formulas to recreate their work if anyone is interested. $\endgroup$ – Andromeda Apr 18 '14 at 8:07
  • 3
    $\begingroup$ Make it an answer and score some points ;) $\endgroup$ – Bob Jansen Apr 18 '14 at 9:56
6
$\begingroup$

As anticlimactic as this may be, I'm going to answer my own question here..

I found this article that shows the connections between the two models..

http://epublications.bond.edu.au/cgi/viewcontent.cgi?article=1126&context=ejsie (mirror) that shows

that prices do converge as N Periods increases. Also they provide all the Excel formulas to recreate their work if anyones interested.

$\endgroup$
2
$\begingroup$

FYI, the binomial distribution converges to normal as n goes to infinity, which is a nice way of thinking about the relationship between BS and the binomial tree models.

see here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.