discretization of binomial lattice

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Dan
Posts: 25
Joined: Mon Oct 24, 2011 4:00 pm

discretization of binomial lattice

Postby Dan » Sat Oct 29, 2011 10:27 am

Dear Carol,

i dont have a strong background in maths. So i made sure that i go through volume 1 slowly in order to grasp the tools that are going to be so essential in the understanding of later volumes. So far I have reached numerical methods and dont have that long a distance before finishing the chapter. I look forward to the chapter on portfolio theory and dont anticipate major wrestling with maths there. But in the numerical methods, on page 214, i dont quite follow the second half of the page. I understand the big picture, which is to prove that the particular set of parameters of binomial lattice satisfy a couple of particular conditions. But i dont follow the steps. I wonder if you could shed some light or provide some assistance? Many thanks, professor Carol! I look forward to your reply!

Dan

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: discretization of binomial lattice

Postby coalexander » Sun Oct 30, 2011 1:12 pm

Glad to help Dan, if I can. I took a look at the page and the proof is complete, in that I state exactly what I am doing at every step, so I am not sure exactly what extra help I can give. perhaps you could point out to me excatly where you get lost -- eg do you follow the first step, the 2nd order Taylor approximation? If so, do you follow the expression of (I.5.39) in the JR param case? etc. Lets see where you get lost first and then try to help, Carol

Dan
Posts: 25
Joined: Mon Oct 24, 2011 4:00 pm

Re: discretization of binomial lattice

Postby Dan » Mon Oct 31, 2011 4:41 am

Hi, thanks Carol!

What i dont follow is how we get the two equations by plugging the taylor approximation into conditions I.5.39 and I.5.40? Also I dont understand why it says at the bottom of the page that I.5.42 is the solution to I.5.43 and I.5.44, becauase after all, isnt the proof about proving that I.5.42 satisfy the conditions of I.5.39 and I.5.40, so i'm a little confused.

Much appreciation, Dan

Dan
Posts: 25
Joined: Mon Oct 24, 2011 4:00 pm

Re: discretization of binomial lattice

Postby Dan » Wed Nov 09, 2011 1:34 pm

Hi Carol, I am still looking forward to hearing from you. Thank you very much! Dan.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: discretization of binomial lattice

Postby coalexander » Wed Nov 09, 2011 10:40 pm

Hi Dan, not sure why but I didn't get the notification of your last post - have seen it now and will reply on Friday (today and tom. very busy) Carol

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: discretization of binomial lattice

Postby coalexander » Thu Nov 10, 2011 10:35 am

Ok Dan

The steps are outlined in text -- so not sure about the problem -- but can you follow this?
Step 1: Since u = exp(m+delta) and d = exp(m-delta) and p = 0.5 we have
pu + (1-p)d = exp(m) (1 + delta^2/2)

Step 2: Put this as r.h.s of (I.5.39) then take logs and use approx. ln(1+x) = x for small x (here x = delat^2/2)…this gives (I.5.43)

....can you see your way through other steps now?

Dan
Posts: 25
Joined: Mon Oct 24, 2011 4:00 pm

Re: discretization of binomial lattice

Postby Dan » Sun Nov 13, 2011 2:02 pm

Hi Professor Carol, thank you so much for the enlightenment! `:D` I worked it out now. Cheers, Dan

Dan
Posts: 25
Joined: Mon Oct 24, 2011 4:00 pm

Re: discretization of binomial lattice

Postby Dan » Sun Dec 30, 2012 3:22 pm

Hi Carol,

Thanks so much for the material on Volatility.

Could you please check the very last line on page 214 of vol. 1? I think it should read "I.5.42 is the solution to I.5.39 and I.5.40."

Cheers,

Dan

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: discretization of binomial lattice

Postby coalexander » Mon Dec 31, 2012 12:07 pm

Hi Dan

Thanks for spotting this, but the last line on page 214 is fine as it is. I.5.43 is an expression equivalent to I.5.39 and I.5.44 is equivalent to I.5.40.

Happy new year! Carol


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