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Cuchulainn
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### Re: Silly questions

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

Last edited by Cuchulainn on April 19th, 2019, 1:17 pm, edited 2 times in total.
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Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik

Cuchulainn
Topic Author
Posts: 60865
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Silly questions

Stressed data

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Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik

Cuchulainn
Topic Author
Posts: 60865
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Silly questions

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.
http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik

Cuchulainn
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Posts: 60865
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Silly questions

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.
Last edited by Cuchulainn on January 27th, 2020, 2:56 pm, edited 1 time in total.
http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik

Cuchulainn
Topic Author
Posts: 60865
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Silly questions

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 $\frac{\partial^2 V}{\partial x \partial y}$
http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik

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