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Hi Jim,

For perspective sake, I view this as kicking some ideas around and some resulting brainstorming. From my perspective, I have learned that through all these models we must ask ourselves, does this pass the smell test, or simply, does this make sense economically? Otherwise the cognitive dissonance ringing in my head is too much :)

First let me point out that their is some arithmetic issues with the original calculation of B_so:

The original model's B_so was 3.2192 -> which I propose is not correct:

B_so = 1.3105 * (77.44/38.57) * .9335 = 2.456

Now applying the smell test what if the stock price jumped to $100 and we use the original model to recalculate B_so?

B_so = 1.3105 * (96.30 / 38.57) * .955 = 3.125

This passes the smell test. As the stock price goes up the effective cost of issuing the options is greater. The call option effectively is worth 72.83 with this data.

Using your revised or "real" model lets take the same position that the stock price jumped to $100.

Plugging all the data into the Black-Scholes-Merton model to get a new value of the call and delta. Using this new data for B_so:

B_so = 1.3105 * (96.30/72.83) * .9550 = 1.655

The new B_so is actually lower than the B_so of 1.7222 when the stock was at 81.13. That doesn't smell right to me. I could me mistaken (always a safe hedge) but as the stock price goes up the cost of financing also goes up.

The original model might not be right - heck if I know - but the original model makes more sense to me. What I do know is that because the stock options strike price is fixed and the exercise price is not and can effectively go to infinity (don't we wish) the cost of issuing equity in such a case would also go to infinity. So I guess I never had an issue with the original wonkiness.

Whatcha think?

Matthew
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