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by JohnLeM
November 2nd, 2016, 12:45 pm
Forum: Numerical Methods Forum
Topic: Heston - Reference Prices
Replies: 37
Views: 33938

Re: Heston - Reference Prices

@yeahmoon, thanks, I forgot to have a look to Quantlib. Indeed, it provides a lot of material concerning Heston, including a PDE engine. That should be enough for my purposes : benchmarking my PDE engine against a cassical PDE engine for forward start option under Heston.
by JohnLeM
October 27th, 2016, 11:14 am
Forum: Numerical Methods Forum
Topic: Heston - Reference Prices
Replies: 37
Views: 33938

Re: Heston - Reference Prices

Hello,

This thread is quite helpful for benchmarking tests for Heston models thanks !

I have a similar concern but for forward start options : is there a paper or source that provides Forward start options prices under Heston that have been computed to high precision for a range of strikes ?
by JohnLeM
October 19th, 2016, 10:35 am
Forum: Numerical Methods Forum
Topic: Convex numerical schemes ?
Replies: 37
Views: 12787

Re: Convex numerical schemes ?

Cuchulain,
Hi. Oops, i am just reading your answer, messing up with the new forum design. Thank you very much for your answer, I will read all this.
by JohnLeM
October 5th, 2016, 6:07 am
Forum: Numerical Methods Forum
Topic: Convex numerical schemes ?
Replies: 37
Views: 12787

Re: Convex numerical schemes ?

Cuchulainn, Hello. Concerning this monotonicity topic, I am testing a suggestion from G. Derveaux that seems to work so far. T he idea is the following :  y ou want to solve a linear equation having parabolic and hyperbolic (convection) terms. 1) You can always kill the convection term through a cha...
by JohnLeM
July 5th, 2016, 1:58 pm
Forum: Numerical Methods Forum
Topic: Numerical results concerning the curse of dimensionality
Replies: 8
Views: 2283

Numerical results concerning the curse of dimensionality

Cuchulainn hello.I agree with you, open science is a better and more efficient one. However I can't open it more, sorry.
by JohnLeM
July 3rd, 2016, 8:55 pm
Forum: Numerical Methods Forum
Topic: Numerical results concerning the curse of dimensionality
Replies: 8
Views: 2283

Numerical results concerning the curse of dimensionality

<t>Hello again.(4) is phrasing the problem. It is somehow stating two problems :- We are not given the Kolmogorov operator.- Even if we knew this operator, the problem is stated with a big number of risk sources, and numerical PDE methods are unable to compute due to the Curse of Dimensionality (CoD...
by JohnLeM
July 3rd, 2016, 6:10 pm
Forum: Numerical Methods Forum
Topic: Numerical results concerning the curse of dimensionality
Replies: 8
Views: 2283

Numerical results concerning the curse of dimensionality

<r>QuoteOriginally posted by: CuchulainnI read the paper but I find it hard to see how the curse has been exorcised.Maybe a second, scoped version is needed with let's say a 3d FP PDE and then from A to Z. With PDE complexity is exponential, so I don't see how to get round that problem.Cuchulainn, h...
by JohnLeM
June 27th, 2016, 8:01 am
Forum: Numerical Methods Forum
Topic: Convex numerical schemes ?
Replies: 37
Views: 12787

Convex numerical schemes ?

<t>Cuchulainn,Hello.It is a quite interesting suggestion from god father Lions...I've taken a read over Roelof Sheppard thesis. His work (although very technical), as well as your work on fitted schemes and all others included references of course, are suggesting that there is a general construction...
by JohnLeM
June 26th, 2016, 1:54 pm
Forum: Numerical Methods Forum
Topic: Convex numerical schemes ?
Replies: 37
Views: 12787

Convex numerical schemes ?

I google it at datasim :) Roelof Sheppard. Is this correct ?
by JohnLeM
June 25th, 2016, 5:56 pm
Forum: Numerical Methods Forum
Topic: Convex numerical schemes ?
Replies: 37
Views: 12787

Convex numerical schemes ?

<t>Cuchulainn,Thx again for the paper. Indeed, I did not find out these references before, and it is closely related to my problem. As far as I understand, the problem here came from incorporating convection in a parabolic equation. In equation (40) of your paper, when the condition [$]\mu \ge \frac...
by JohnLeM
June 25th, 2016, 12:38 pm
Forum: Numerical Methods Forum
Topic: Convex numerical schemes ?
Replies: 37
Views: 12787

Convex numerical schemes ?

Yep, you got it all, it is linked to Perron-Frobenius theorem. I am having a look to your paper, thx a lot.
by JohnLeM
June 25th, 2016, 8:58 am
Forum: Numerical Methods Forum
Topic: Convex numerical schemes ?
Replies: 37
Views: 12787

Convex numerical schemes ?

<t>I am encountering some issues with numerical schemes, typically Crank Nicolson ones, that seems to be linked with a lack of convexity, and is probably related to some threads in this site : for instance negative probability, Instabilities. Surely others. It is not very clear to me how to formulat...
by JohnLeM
June 23rd, 2016, 9:33 am
Forum: Numerical Methods Forum
Topic: Numerical results concerning the curse of dimensionality
Replies: 8
Views: 2283

Numerical results concerning the curse of dimensionality

oops.. thanks for the fix Cuchulainn
by JohnLeM
June 23rd, 2016, 6:36 am
Forum: Numerical Methods Forum
Topic: Numerical results concerning the curse of dimensionality
Replies: 8
Views: 2283

Numerical results concerning the curse of dimensionality

...are accessible here or here.[edit :] link submitted arxiv paper Any comments welcomed from this site. These are first results, small, but research time, big .
by JohnLeM
November 16th, 2011, 1:51 pm
Forum: Numerical Methods Forum
Topic: Weighted Monte Carlo (Avellaneda)
Replies: 19
Views: 201293

Weighted Monte Carlo (Avellaneda)

<t>QuoteOriginally posted by: TrillimanI have used this technique for pricing exotic commodity instruments. It works quite well, but as you can imagine, is pretty slow. So, it is best to just use it for instruments that are very difficult to price. It is better than local vol since you need make no ...