Cox, Ross, & Rubinstein

[Mark Banford-Lawrence]

Cox, Ross, & Rubinstein

[Anonymous]

I have noticed in the sample questions from here, the formaula used is different to what is seen on the net. For a jump up the solution from here comes to be EXP(Vol * SQRT(1/t), but on Wikipedia its EXP(Vol*SQRT(t)

Can someone please clarify if they have seen this or know which is correct?

Thanks

MB

[Anonymous]

MB,

Thank you for the question. The ‘up’ and ‘down’ parameters for constructing binomial trees using Coss, Ross and Rubenstein are indeed what you note – ie u= exp(? ?dt) and d=1/u.

To be sure, it is NOT sqrt(1/t). It can only be SQRT(t)

As for the question, I believe the one you are referring to requires 4 steps, ie there are 4 equal periods to consider in a year, and each ‘step’ is 1/4 years. Therefore t = 0.25 (from 1/4). So when the answer says u = exp(20% x ?1/4); the 1/4 does not represent 1/t but t. All we are doing really is converting the volatility to the same time period as that for a single step in the tree.

But if I am mistaken and it is another question you are referring to, please let me know.

Mukul Pareek

[Anonymous]

Thanks for this…do you know where i can find how to calculate the value of the option at each node?

[Anonymous]

MBanford,

To calculate the value of the tree at each node, you will need to build the tree. The calculations are too involved to explain here – and quite honestly they are best understood if you actually build a tree by hand (or in Excel). You start the tree by populating the prices from the left to the right – each ‘up’ and ‘down’ price being just the product of the up/down factor above with the price on the prior node. Once this is done for the entire tree, you then need to work backwards for the option price from the last step in the tree all the way to the first. On the last step, the value of the option is the max of the option payoff or zero, and for the steps prior, it is the max of
– exercising the option at the given spot price at that node, or
– PV of the [p*option value at the next up step]+[(1-p)*option value at the next down step]

I doubt if the above will make sense unless you build a tree yourself. Try rebuilding in Excel the tree illustrated in the handbook in Figure II.G.11 in the last chapter.

[Author]

Posts