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### Re: Silly questions

Posted: **April 19th, 2019, 1:04 pm**

by **Cuchulainn**

Update: Turn BS PDE into a parabolic PDE system and _then_ discretis (in contrast to discretising BS PDE and then trying to recover the Greeks by jumping

through hoops and messing).
QED

### Re: Silly questions

Posted: **April 19th, 2019, 1:14 pm**

by **Cuchulainn**

Stressed data

### Re: Silly questions

Posted: **January 2nd, 2020, 1:31 pm**

by **Cuchulainn**

Actually, in finance we write x = log S, S = exp(x) and use them in calculations as if there is no relationship between them. They look like constants.

BUT they are functions!

S = f(x) == exp(x)

x = g(S) == log(S)

Transformations are functions, not numbers.

### Re: Silly questions

Posted: **January 8th, 2020, 5:48 pm**

by **Cuchulainn**

Paul (and maybe others as well!) knows the answer to this one:

1. Consider a continuous Asian PDE[$](S,A)[$]

2. Take {Float, Fixed}{Put, Call} Strike payoff

3. Arithmetic average [$]A[$] defined on [$](0,1)[$] after scaling,

Hypothesis 1 is that any numerical BC on [$]A=0[$] and [$]A=1[$] have no bearing on the solution in the interior of the domain (e.g. Anchor PDE as we discussed), i.e. no source information coming from the [$]A[$] boundaries.

And the same conclusions should hold for Cheyette model (Hypothesis 2).

Justify this. Or disprove.

### Re: Silly questions

Posted: **January 27th, 2020, 2:47 pm**

by **Cuchulainn**

Here's another one regarding elliptic PDEs that can be transformed to

*canonical form* (aka get rid of them pesky mixed derivatives that people so unhappy but still an area of active experimentation).

https://en.wikipedia.org/wiki/Elliptic_partial_differential_equation
Some remarks/questions:

1. It works and is easy once you get the hang of it.

2. What would be the rationale for using it?

3. What would be/are the reasons for not using it?

4. Has anyone published the method for 2-factor pdes with mixed derivatives like Heston, BS, CB?

// There are about 20 million ways to approximate [$]\frac{\partial^2 V}{\partial x \partial y} [$]

### Re: Silly questions

Posted: **February 12th, 2020, 10:02 pm**

by **Cuchulainn**

Some guy on LI claims for integer [$]n[$]

[$]\frac {dn!}{dn} = n[$]

Vote

1. True

2. False

### Re: Silly questions

Posted: **February 12th, 2020, 10:38 pm**

by **Paul**

Via gamma fn, looks messy!

### Re: Silly questions

Posted: **February 13th, 2020, 1:23 am**

by **Alan**

Via gamma fn, looks messy!

That works.

Since [$]\frac{d}{dz} \log \Gamma[z] = \psi(z)[$], the Digamma function (A&S, 6.3.1), then

[$] \frac{dn!}{dn} = \psi(n+1) \, n![$], where of course [$]n![$] is interpreted everywhere as [$]\Gamma(n+1)[$].

### Re: Silly questions

Posted: **February 13th, 2020, 1:28 am**

by **Paul**

That looks a bit circular to me!

### Re: Silly questions

Posted: **February 13th, 2020, 1:30 am**

by **Alan**

I think it's just recognizing a "named function".

So, take n=6

In Mathematica, what I posted evaluates to [$]1764 - 720 \, \gamma \approx 1348.4[$], using Euler's constant [$]\gamma[$].

Since [$]1348.4 \not= 6[$] that answer's Daniel's question. If it was truly circular, I don't think one could get a numerical result.

### Re: Silly questions

Posted: **February 13th, 2020, 2:03 am**

by **Paul**

The named function just happens to be the answer!

Exam question 1: Find the solution of ...

Answer: Define [$]\mbox{Lewis}_1[$] as the answer to question 1. Trivially and wlog the answer to question 1 is [$]\mbox{Lewis}_1[$].

Exam question 2: Etc.

!!!

### Re: Silly questions

Posted: **February 13th, 2020, 2:04 am**

by **Paul**

But we do now know that the answer to Cuch's question is no!

### Re: Silly questions

Posted: **February 13th, 2020, 5:34 am**

by **Alan**

The named function just happens to be the answer!

Exam question 1: Find the solution of ...

Answer: Define [$]\mbox{Lewis}_1[$] as the answer to question 1. Trivially and wlog the answer to question 1 is [$]\mbox{Lewis}_1[$].

Exam question 2: Etc.

!!!

Well, I'm glad the thread title is called "Silly questions". That way, I feel free to belabor the issue.

The more careful analogy to the question would be:

Q1. Some guy claims that "function expression blah blah (x)" = 3 x. True or False?

Answer: "function expression blah blah (x)" is actually a named special function, called the Lewis function. Like all special functions, it's well-studied. It is known that Lewis(x) does not equal 3 x. In fact, at x=3, 3 x = 9, and Lewis(3) = 1036, which I get from Mathematica, which has it built-in.

### Re: Silly questions

Posted: **February 13th, 2020, 5:48 am**

by **Paul**

Well, if we are going to be so literal, then since the original post did not want an answer but a vote I am going to vote yes!! This is maths 21st century style!

### Re: Silly questions

Posted: **February 13th, 2020, 5:52 am**

by **Alan**

I demand a recount! Anyway, it's not even 6am -- don't you people sleep?