Binomial Trees - page 22 from Notes - European put option

[LL]

Hi David,

1. Page 22 of notes:
I am not getting 0.93 or 12.42 in my calculations.
Not sure am I missing something ?
Can you please explain how did you calculate these ?



2. U and D calculation in excel sheet - tab 2 (European put)
To make myself clear on above, when I used the excel, I was not getting U and D calculations similar to yours. The inputs are similar to the above question. Then why is U and D different here ?



Thanks and Regards
LL

 

[Aleksander Hansen]

How are you solving for U?
exp(sigma * sqrt[T]) = exp(0.3) = 1.349859

 

[LL]

Hi Alek,

yep, I am also getting 1.349.
My question for snapshot 1 - I am not getting 0.93 and 12.42 (as highlighted in red)
My question for snapshot 2 - As your calculation, I am also getting 1.349. But why is excel showing 1.2 for U and 0.8 for D.

Thanks and Regards
LL

 

[David Harper CFA FRM]

Hi LL,

1. Can you view this? https://www.dropbox.com/s/xyxdhtv6oe7x3fi/0505_eurobinomial.xlsx
Those blue cells represent the "backward induction" to get the DISCOUNTED EXPECTED VALUE, eg,
0.93 = [51%*0 + 49%*$2.00]*exp(-5%*1.0 years); i.e., the weighted average of the two forward option values (0 and $2), then discounted at risk free rate.

2. Only because it is the more basic approach, it does follow Hull, it hard codes u = +20% and d = -20% and therefore does NOT use the volatility input and is symmetrical. It's akin to treating the prices as normal. But it's "better" to use volatility and let u = exp(sigma*SQRT[T]) and d=1/u, which DOES use volatility, is not symmetrical, and informs the binomial with the same lognormal price assumption in the BSM. (GARP has used both, fwiw, in exam ... but they will definitely tell you) ... you are not wrong to replace the "arbitrary" u and d with u and d that instead match volatility.

Thanks,

 

[Aleksander Hansen]

I would offer to have a look at your spreadsheet, however I'm only Tier 2 so it would be unethical and probably violate David's copyright, so I will have to defer this one to him.

The answer must involve the formula though.
Sorry I couldn't be of more help on this one.

 

[Aleksander Hansen]

Never mind.. He was already on it.

 

[LL]

Gawwd ! After solving so much on these, I made a very stupid mistake !
for 1, I was multiplying $2 with value of U (instead of lambda(u)) !! Such a stupid mistake that was !

 

[David Harper CFA FRM]

Alek - not that you need to feel obligated to help but, since you've already given so much help to others, we will enable your Tier 3 access. Please, it's the LEAST i can do, accept as a small token of my gratitude for your participation. The first XLS just follows Hull with an u = 1.2 and d = 0.8, and therefore does not use the volatility input and is not lognormal. I want to say it's more like an assumption of arithmetic returns are normal but there's not really even normality in it (although it still recombines). Thanks,

 

[LL]

Alek, good job !! Keep it up !
I have seen your replies on other posts too !! You are very helpful

 

[Aleksander Hansen]

Wow David,
Thanks a lot - I really appreciate that!

A general observation, which to me is a bit surprising, is that only a handful of members try to answer questions on the forum. I would expect people who know the answers to help others out, and in that way build a network which can quickly give answers to questions.

This is the case for two other (unrelated to the FRM) forums I am a member of. Indeed, people will go to great lengths to try to help one another out or attack a problem jointly.

The benefit of this, beyond the obvious answers and help is that:
1) A great way to check if you know a concept, or to better understand it is to try to explain/teach it to someone.
2) it would, in this case, probably allow you, at the early stage of the exam cycle, to focus on producing PQs, spreadsheets, study notes and videos, thus enabling their production and publication earlier in the cycle - something which everyone clearly benefits from!
3) at this point in the cycle, more experienced members could help answering more trivial questions and so forth so that you would have more time to focus on critical concepts and non-trivial problems/answers.

And this is by no means an exhaustive list.

I would thus encourage members to participate more actively - especially those who are more experienced, or have already completed level 1. It takes a few minutes to answer a question. Even if you are not 100% certain of the answer you can still provide guidance and qualify your answer. If you happen to be wrong, so what? David would quickly correct it.

This extends to a work-situation as well. In a hedge fund or investment bank for example, don't think you can get away with never contributing. It is a collaborative effort. Those who think otherwise are asked to, "exit the company," to quote one investment bank.

 

[Suzanne Evans]

Alek - not that you need to feel obligated to help but, since you've already given so much help to others, we will enable your Tier 3 access. Please, it's the LEAST i can do, accept as a small token of my gratitude for your participation. The first XLS just follows Hull with an u = 1.2 and d = 0.8, and therefore does not use the volatility input and is not lognormal. I want to say it's more like an assumption of arithmetic returns are normal but there's not really even normality in it (although it still recombines). Thanks,

Hi Alek,

Your access has been upgraded!

Thanks for your participation and assistance in the forum. It is greatly appreciated.

Thanks,
Suzanne Evans