Hawgdriver

April 29th 2007, 03:33 AM

Can anyone explain why the BS formula uses (r - d + 1/2 sigma ^2) instead of (r - d - 1/2 sigma^2) ?

McDonald's text for MFE includes a development of this topic, but it is VERY confusing about this point.

For example, on page 599 he uses the expression

'Prob( St < K ) = N (-d2) <-- 18.24

where d2 is the standard Black-Scholes argument (see equation (12.1)) with the risk-free rate, r, replace with the actual expected return on the stock, a <alpha>.'

<note: in the text, the d has a hat>

However, the equation that McDonald references is NOT the d2 in the BS formula, which has "+ .5 sigma ^2", it has the "- .5 sigma ^2" term.

On page 604, the "+ .5 sigma ^2" term seems to magically appear just prior to explicit treatment of BS formula.

Please help, I'm confused! The only thing I can figure is that the BS formula decides alpha = r + sigma^2 , but ???

I don't think chap 18 is on the syllabus, but this certainly underlies MFE material.

McDonald's text for MFE includes a development of this topic, but it is VERY confusing about this point.

For example, on page 599 he uses the expression

'Prob( St < K ) = N (-d2) <-- 18.24

where d2 is the standard Black-Scholes argument (see equation (12.1)) with the risk-free rate, r, replace with the actual expected return on the stock, a <alpha>.'

<note: in the text, the d has a hat>

However, the equation that McDonald references is NOT the d2 in the BS formula, which has "+ .5 sigma ^2", it has the "- .5 sigma ^2" term.

On page 604, the "+ .5 sigma ^2" term seems to magically appear just prior to explicit treatment of BS formula.

Please help, I'm confused! The only thing I can figure is that the BS formula decides alpha = r + sigma^2 , but ???

I don't think chap 18 is on the syllabus, but this certainly underlies MFE material.