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bearish
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Re: Who understands Black Scholes Boundary Conditions, really

October 31st, 2018, 11:23 pm

Umm - without reading it closely, it looks oddly like early 70's binomial methods, which were also mercifully free of the need of any spatial boundaries.
 
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Cuchulainn
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Re: Who understands Black Scholes Boundary Conditions, really

November 1st, 2018, 2:48 pm

"Das ist nicht nur nicht richtig; es ist nicht einmal falsch!"
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FaridMoussaoui
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Re: Who understands Black Scholes Boundary Conditions, really

November 1st, 2018, 5:03 pm

So they use a Dirichlet BC at x = 0 and they do not use any BC at the far field boundary.
and they wrote "Instead, we reduce grid points by one in every time step" ???????

Here a screenshot of that part of the paper:

Image
 
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Cuchulainn
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Re: Who understands Black Scholes Boundary Conditions, really

November 2nd, 2018, 8:09 am

So they use a Dirichlet BC at x = 0 and they do not use any BC at the far field boundary.
and they wrote "Instead, we reduce grid points by one in every time step" ???????

Here a screenshot of that part of the paper:

Image
Scheme (3) is explicit Euler on non-uniform meshes. This went out of fashion after Richardson's famous article (1910?).
The authors claim 2nd order convergence in the last sentence of section 3.. And it is slow, very slow in general.
I'll leave further comments to FaridMoussaoui :)

// This is a parabolic PDE  and not a hyperbolic PDE so I think this approach is doomed.

For a double barrier option the method cannot work. You need to use _all_ of both boundaries.
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Cuchulainn
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Re: Who understands Black Scholes Boundary Conditions, really

March 30th, 2021, 6:13 pm

Way back in 2014 we 3 wrote an article on Asian PDE(S,A) on transformed domain (0,1)X(0,1). I do by Fichera. OK.
We all agreed (me, P and A) that no continuous BC are needed.

https://onlinelibrary.wiley.com/doi/epd ... wilm.10366

Some folk truncate S and A. So, A is now in (0, Amax). By Fichera they say no BC needed at A = 0 but at A = Amax a BC is needed and they search for some kind of BC by taking the analytical solution of the PDE.

My claim is that this is wrong on several levels... the 'truncated PDE' gets a BC even though the original PDE does not.

bit of a fallacy here.. "truncated PDE don't have BC". Otherwise it is guesswork.

I can test my claim by modifying the Anchor code.
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JohnLeM
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Re: Who understands Black Scholes Boundary Conditions, really

March 30th, 2021, 8:34 pm

Umm - without reading it closely, it looks oddly like early 70's binomial methods, which were also mercifully free of the need of any spatial boundaries.
I can't read this article but it is possible to get rid of boundary conditions. As Bearish said, x-nomial trees do it. I am also doing it with kernel methods.
 
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Cuchulainn
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Re: Who understands Black Scholes Boundary Conditions, really

March 30th, 2021, 9:46 pm

Umm - without reading it closely, it looks oddly like early 70's binomial methods, which were also mercifully free of the need of any spatial boundaries.
I can't read this article but it is possible to get rid of boundary conditions. As Bearish said, x-nomial trees do it. I am also doing it with kernel methods.
No. I'm talking about Asian options using FDM, not trees nor your meshless method. You are not even close.
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Cuchulainn
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Re: Who understands Black Scholes Boundary Conditions, really

March 31st, 2021, 11:49 am

Umm - without reading it closely, it looks oddly like early 70's binomial methods, which were also mercifully free of the need of any spatial boundaries.
I can't read this article but it is possible to get rid of boundary conditions. As Bearish said, x-nomial trees do it. I am also doing it with kernel methods.
OK. let's cut to the chase.
Can the Cheyette (Asian) be solved using lattices (ugh!) or meshless??
viewtopic.php?f=34&t=100474&sid=7af69b4 ... d64aee6f78
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