I’m sorry. I don’t. I’m very mild mannered. At the same time, I do think the standard paradigm is a pretty reasonable starting point, into which one can try to insert various kinds of real world complications. Like transaction costs and other problems that prevent even simple claims from being perfe...

So you want to postulate a model with totally unreasonable parameters, making no sense whatsoever, and then use the existence of said model to argue that the modeling framework is wrong? Isn’t that a bit like saying that a car, driving at a speed of 99% of the speed of light, is very implausible, an...

Sorry, I interrupted myself. By the time our continental colleagues got to NFLVR, I lost a bit of enthusiasm, but I like this little note by Freddy and Wally: https://www.ams.org/notices/200405/what-is.pdf Aside from the fact that they manage to repeatedly say Cox-Ingersoll-Ross when they meant Cox-...

Please, can we call it “a replicating portfolio”? As I was typing that, the word tallywhacker came to mind, for reasons that should be obvious.

Maybe we should focus less on him and more on the ordinary Russians who are committing war crimes and other atrocities by the tens of thousands.

Yes, but, as far as we can tell, not specificly motivated by the Jan 6 sedition case. That being said, evidence found under a lawful warrant motivated by an investigation into crime A can happily be used in the prosecution of case B, C, D, etc. So this could still lead to his hanging. Wishful thinki...

8 turns out to be the magic “number” to determine the possible “shapes”.

No. Why would you even ask that? Surely there must be other stupid questions to be asked today!

I’d like to blame Marsden for his unconventional use of [$] \mu [$], but that’s probably not fair. With a negative drift, my first property will not hold, though, since then the process will tend to go zero in all relevant senses.

I should have written If  0.5σ 2  > r - μ > 0  then  S t  = e μt + σW(t)   has the property that  lim t→∞ E [ S t  - e rt ]  = ∞  but  lim t→∞ ( S t  - e rt )  < 0  almost surely. Bearish, your " lim t→∞ S t   = 0 " is wrong, which is probably what is causing the confusion. I don't know i...

I’m pretty sure I wrote what I meant to write. Your statements are true, too, but I saw no particular reason to bring the money market account into play. We can set [$] r = 0 [$] and we’ll all be happy.

I mean, you could do that, and the result would be very different. Or you could raise the whole thing to the power of 17, and it would also be different. And, likewise, probably not in an interesting way.

The standard martingale theory approach to model replication, pricing, etc. always comes with a bounded time horizon, to avoid problems of this sort. The law of large numbers prevents non-trivially different measures from being equivalent in the limit as time goes to infinity. Another version of yo...

To be honest, I just eyeballed the implied vol at that strike in the low 20’s and figured the skew was going to work against you. I did not actually do the real calculation, although I don’t think that should be too hard. And then, yes, I think it is appropriate to apply a haircut of sorts to accoun...

Local Domino's pizza fills for bankrupcy

Aww - it couldn’t have happened to nicer people! Unlike Italy, the people behind Dominos are indeed trash.