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Author: jimgillies Big gold star, 5000 posts Feste Award Winner! Old School Fool CAPS All Star Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 14423  
Subject: MMM - Options Strategy - Binomial Date: 9/7/2005 9:01 PM
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Hello Fools,

This post is to build on some of the critque received from my prior thread on MMM as a synthetic long.


http://boards.fool.com/Message.asp?mid=22974198&sort=whole


In that thread, TheNajdorfDefens suggested a binomial pricing model for the option components making up the synthetic long. TMFMillerTime put a floor on MMM's stock of $60 (a value admitted plucked from the ether, but as good an estimate as any).

So I decided to try to price these options as such. However, that is not something that can be presented effectvely in a TMF post. So I've made my spreadsheet available at the following link.


http://fast.filespace.org/jimgillies/MMM_Binomial.xls


Some assumptions/notes on the models - particularly areas where I'm not terribly happy with the results:

Assumptions:

* Flat yield curve
* I used the inputs from my original write-up (Stock price = $70.86, Call price of $8.50, Put
price of $9.40, time to expiry = 2.3808, risk-free rate of 3.80%), even though things have
marginally changed. If the model is good, we can go back and edit later.
* Risk-free rates expressed as continuously compounding.
* Not sure I've handled dividends correctly. At each node (1 through 10, ignoring our first node),
I've deducted FV(Dividends) from the calculated expected stock price. I'm not sure this is correct,
although I'm having difficulty articulating why. Fresh eyes?
* Red text indicates that value of the option is greater from the payoff from early exercise, although
the difference in the model is very little (a few cents at each node) - might be a rounding error.

I think it's the dividend thing that bugs me the most. So, those with binomial construction experience, please speak up

The spreadsheet includes four 'sheets'.

The first is a basic call sheet - price calculated out as $8.45, as opposed to the quoted price of $8.50.

The second sheet is the call calculation again, this time with the stock price floor set at $60 as suggested. The option value calculates out as $25.74. (Quite like that result!)

The third sheet is the basic put sheet - tree reduces to a put price of 10.04 as opposed to the quoted price of $9.40.

The fourth sheet is the put calculation again, this time with the stock price floor set to $60. The option value calculated out at $6.64.

Critique, and suggestions for tweaking - particularly on how I could refine the dividend - is greatly appreciated.

Cheers,

Jim
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