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Argument is an intellectual process. Contradiction is just the automatic gainsaying of anything the other person says.In that case everything I write must be highly relevant, because you pick on every single sentence. WHY, OH WHY?! Yawn...
Don't worry, these are my last few weeks here
No they don't.Some people just like to argue
RebumpHere's a way to 'recover' [$]\frac{1}{2}\sigma^2 T[$] from first principles.
. Starting from the BS [$]Pde(S,t)[$] define the [$]Pde(x, \tau)[$] by new variables [$] x = log(S), t = T - 2\tau/\sigma^2[$].
. After some arithmetic we get a Cauchy initial value problem for a 1d heat equation defined by
[$]\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} [$]
with [$]-\infty \lt x \lt \infty[$]
[$]0 \lt \tau \le[$] [$]\frac{1}{2}\sigma^2 T[$]
This IVP has an analytical solution and if you work it out you can retrieve the famous BS equation.
So, [$]\frac{1}{2}\sigma^2 T[$] is a dimensionless time.
Haha!No they don't.Some people just like to argue
P.S. I didn't know they made faucets at Caltech. I thought it was MIT's province.
For me, this one does it. BTW the liberal arts types were really like that in the 70s.Haha!No they don't.Some people just like to argue
P.S. I didn't know they made faucets at Caltech. I thought it was MIT's province.
Anyway, the Caltech mention is one of the reasons I remember that scene!
No it doesn't. We agree on the meaning of the word 'meaning'.To summarize this thread, as Bill Clinton famously almost said:
"It depends on what the meaning of the word ‘meaning’ is.”
See it as a bit of fun at the weekend. It's not easy being couped up with the wife and kids 24/7 when you'r trying to get ideas.
www.youtube.com/watch?v=2Cv2vM4dgpM
Seriously, I actually converted BS PDE to heat equation when I was waiting for my tea to arrive (my butler is not so fast) just to see what came out of the woodwork. It might have some mileage and be even better than FDM in this case (we get an integral involving payoff and transition density). We can also do FDM for heat equation.
And of course, Caltech, and not MIT is leader in faucet design.
I always knew that applied mathematicians like that sort of stuff but it is useful. Once you know why.
But this was not the question raised by my OP, which was about the semantics of sigma root t, i.e. its meaning. The fact my question has so consistently been misunderstood kind of answers my question.I don't post a ton, but I believe this is a waste of most of these guys' time. You require too much prerequisite information. This should really be moved to the 'Student Forum' where it will be appropriately ignored as it has been covered by many texts already. For stock options, start with a Bachelier (normal) model, do simple price diffs, and then find out why you don't want that. Then move to logReturns where when you take the log(Px) then the diffs are actually log returns with some nice features dLogPx = (log(Px_1) - log(Px_0)) = log(Px_1/Px_0) . Doing this stuff over time, etc.... As was said earlier. Kindergarten stuff. Maybe I'd give it 8th grade, but I'm American. So everywhere else it may be like 4th grade
Not sure - there were many intermediate steps missing, and the proposition to be proved was not clear.BTW did I get the correct answer with my PDE solution?
