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by Alan
May 20th, 2019, 9:33 pm
Forum: Numerical Methods Forum
Topic: One-liner questions of a numerical kind
Replies: 22
Views: 738

Re: One-liner questions of a numerical kind

Well, for a put option, theta does not have the same sign at all points. My bad (something in the cornflakes) Looking at diagram  theta = -dP/dt is not always negative? It can be positive? Sure: r > 0 (European option, no divs) and small enough stock price [$]S_0[$].  Then, [$]P \sim K e^{-r (T-t)}...
by Alan
May 20th, 2019, 4:36 pm
Forum: Numerical Methods Forum
Topic: One-liner questions of a numerical kind
Replies: 22
Views: 738

Re: One-liner questions of a numerical kind

Well, for a put option, theta does not have the same sign at all points.
by Alan
May 17th, 2019, 11:37 pm
Forum: Trading Forum
Topic: End of bitcoin?
Replies: 778
Views: 63205

Re: End of bitcoin?

… Speculative transactions accounted for roughly 60 to 80 percent of all transactions on the blockchain, according to Chainalysis, a start-up that does analysis of the blockchain for big companies and governments. Most of those transactions are Bitcoins moving between cryptocurrency exchanges aroun...
by Alan
May 17th, 2019, 1:42 pm
Forum: Trading Forum
Topic: End of bitcoin?
Replies: 778
Views: 63205

Re: End of bitcoin?

Interesting read in today's WSJ (paywall): Lack of Banking Options a Big Problem for Crypto Businesses Bitfinex’s loss of access to $850 million in customer funds after using a Panama-based processing firm highlights a persistent issue for crypto companies. An extended excerpt: "... Crypto exchanges...
by Alan
May 14th, 2019, 3:19 pm
Forum: Student Forum
Topic: Is it possible to "complexify" SDEs?
Replies: 20
Views: 774

Re: Is it possible to "complexify" SDEs?

My read is that Daniel is experimenting with alternative ways to compute vega. It started with the Complex Step Differentiation Method -- hence the complex-valued SDEs. Then it seemed to morph into seeking a real-valued SDE or SDE pair to solve. Beyond that, I don't know and will leave to him ...
by Alan
May 13th, 2019, 6:51 pm
Forum: Student Forum
Topic: Is it possible to "complexify" SDEs?
Replies: 20
Views: 774

Re: Is it possible to "complexify" SDEs?

But vega is the derivative of a value function, so you have to start with the SDE for that.
by Alan
May 13th, 2019, 5:43 pm
Forum: Student Forum
Topic: Is it possible to "complexify" SDEs?
Replies: 20
Views: 774

Re: Is it possible to "complexify" SDEs?

Sorry -- you've lost me.
by Alan
May 12th, 2019, 5:50 pm
Forum: Economics Forum
Topic: Debt to GDP ratio
Replies: 2
Views: 176

Re: Debt to GDP ratio

First part seems well-answered at  Quora .  Re the negative yield, at least according to  Reuters , it is partly a stable situation because apparently foreigners can earn a decent premium over comparable US Tsy's with little perceived risk due to the answer to the first part. As for the usual argume...
by Alan
May 12th, 2019, 5:31 pm
Forum: Off Topic
Topic: A Music Game II for 2009
Replies: 2838
Views: 296173

Re: A Music Game II for 2009

One Step Beyond (Prince Buster -- 1964)

I didn't realize, or knew and forgot, that 'Madness' got their band name from another Prince Buster hit.

Also, reminds of this:
by Alan
May 11th, 2019, 11:27 pm
Forum: Off Topic
Topic: News from Outer Space
Replies: 1179
Views: 127492

Re: News from Outer Space

I can see a lot of cats' eyes glowing in the dark :-)

Yes, we have cats within galaxies and cats with galaxies:
by Alan
May 11th, 2019, 9:49 pm
Forum: Off Topic
Topic: News from Outer Space
Replies: 1179
Views: 127492

Re: News from Outer Space

Image

New Hubble shot of an ancient galaxy cluster. Is it just me, or does anyone else see a giant galactic dollar sign? (clearer if you click on the photo to enlarge).

Source: NASA
by Alan
May 11th, 2019, 4:04 pm
Forum: Student Forum
Topic: Is it possible to "complexify" SDEs?
Replies: 20
Views: 774

Re: Is it possible to "complexify" SDEs?

I think it's OK. If the SDE process variable is [$]X_t[$] and the parameter [$]\sigma[$], then better notation would be to write [$]X^{\sigma}_t[$] everywhere it appears in the SDE, so you are sure to differentiate those terms as well as the explicit appearances of [$]\sigma[$]. The end result shoul...
by Alan
May 10th, 2019, 6:32 pm
Forum: Student Forum
Topic: Is it possible to "complexify" SDEs?
Replies: 20
Views: 774

Re: Is it possible to "complexify" SDEs?

Seems fine to me, including the last part. 
by Alan
May 10th, 2019, 5:52 pm
Forum: Student Forum
Topic: Is it possible to "complexify" SDEs?
Replies: 20
Views: 774

Re: Is it possible to "complexify" SDEs?

 I don't see any issue in differentiating.

Also, take [$]a = -1/2[$] and [$]\sigma = i[$] and you're back to my example ([$]X_t = Z_t[$]).

[$]dZ_t = -\frac{1}{2} Z_t \, dt + i \, Z_t \, dW_t[$]  (BM on a circle: [$]Z_t \in \mathbb{C}[$]).
by Alan
May 10th, 2019, 5:13 pm
Forum: Student Forum
Topic: Is it possible to "complexify" SDEs?
Replies: 20
Views: 774

Re: Is it possible to "complexify" SDEs?

A well-behaved example might be "Brownian motion on a circle", [$]Z_t = e^{i B_t}[$] discussed in Oksendahl's SDE book. Here [$]B_t[$] is standard linear BM. This generates a complex-valued SDE but, by taking real and imaginary parts, you get a pair of innocuous real SDEs.  To visualize the paths, j...
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