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by Billy7
March 27th, 2018, 12:59 pm
Forum: General Forum
Topic: Local Stochastic Volatility - Lorenzo Bergomi
Replies: 20
Views: 2543

Re: Local Stochastic Volatility - Lorenzo Bergomi

Heston for FX and equity, SABR for IR, 95% of the market. Some people try uncertain volatility or Schöbel/Zhu, Heston for IR is becoming more and more popular but it doesn't change the big picture. And there are quite serious flaws in Heston  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2902...
by Billy7
March 22nd, 2018, 1:18 pm
Forum: General Forum
Topic: Local Stochastic Volatility - Lorenzo Bergomi
Replies: 20
Views: 2543

Re: Local Stochastic Volatility - Lorenzo Bergomi

I was wondering, did anyone try to calibrate such a mixed LSV model  Probably everyone did. LSV is around 90% of the market for various SV models. It seems to me that the question is more specific, Quantuplet is asking if people have tried to apply this toy model from this book (which I don't have)...
by Billy7
March 8th, 2018, 2:19 pm
Forum: Numerical Methods Forum
Topic: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.
Replies: 231
Views: 15134

Re: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.

One alternative from Gil Strang (Strang-Marchuk splitting) is to split according to the PDE components  A1: Pure elliptic part + convection A2: Mixed derivatives Separately, these are easy, haven't tried it. What do you think? Yes, but that's what the ADI variants are doing (CS, HV), plus split A1 ...
by Billy7
March 7th, 2018, 10:37 pm
Forum: Numerical Methods Forum
Topic: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.
Replies: 231
Views: 15134

Re: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.

Oh, should've guessed... Well yes, since the original ADI is for rho=0 (no mixed derivatives), is unconditionally stable, so I was just wondering how it failed exactly. Well if it is to be tried for Heston (or other SV models) as you suggested then one should know what to do with the mixed derivativ...
by Billy7
March 7th, 2018, 6:44 pm
Forum: Numerical Methods Forum
Topic: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.
Replies: 231
Views: 15134

Re: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.

A while  collaborated with Alex Levin on a HW2-type PDE (no correlation); Long story short,   unable to get ADI to work and we went for Marchuck's 1-2-2-1 dimensional splitting method. Maybe someone at some stage could try it for Heston. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.505....
by Billy7
March 6th, 2018, 10:07 pm
Forum: Numerical Methods Forum
Topic: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.
Replies: 231
Views: 15134

Re: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.

How would ADI be used in this (HW2D) case? I see no structural difference from the SV PDE's, so the same way as in the paper, or the papers referenced therein I guess. Not difficult I think. For the spatial discretization one can use whatever they like, the one proposed by Samarski for example. Reg...
by Billy7
March 6th, 2018, 7:00 pm
Forum: Numerical Methods Forum
Topic: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.
Replies: 231
Views: 15134

Re: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.

I am trying to view these kinds of PDE/FDM from several viewpoints and to trigger discussions, e.g. the ADI with bells and whistles is fine but not easy for FDM noobies. For example, how easy would ADI be for _non_ Heston-style, e.g 2 factor Hull White Bermudan callable bond, to take a random examp...
by Billy7
March 5th, 2018, 4:34 pm
Forum: Numerical Methods Forum
Topic: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.
Replies: 231
Views: 15134

Re: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.

I reckon a yuge number of manhours went into that paper. Well done :) This could be a great baseline for other ADI and FDM peoples. To reproduce the results by others you could provide the input data in XML so it can be read by any language.  A general remark on ADI (not my favourite for several re...
by Billy7
January 22nd, 2018, 11:48 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 830
Views: 72446

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Sounds like a simple extension, don't you want to try it and see how it works? If I had spent so much time researching a method, I'd be looking forward to show people what it can do.
by Billy7
January 21st, 2018, 9:09 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 830
Views: 72446

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Well, that's more info but I still don't know if that's for continuous monitoring or discrete. Can the method do both easily? For example in Monte Carlo you cannot directly find the continuous monitored price (as far as I know), but you can run one with say 50 averaging dates, then one with 100 and ...
by Billy7
January 21st, 2018, 7:11 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 830
Views: 72446

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Well, if I were you I would try to sell it like this: Go into the trouble of optimizing simple examples like that and then say: "My method calculates the price of an Asian option in 10ms, whereas a PDE method takes 200ms, MC takes 1 sec, a tree takes 100 ms for the same accuracy."  And do it as Cuch...
by Billy7
January 21st, 2018, 4:36 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 830
Views: 72446

Re: Breakthrough in the theory of stochastic differential equations and their simulation

I could give an "exact" solution to this, if I understood the inputs. Is it supposed to be continuous averaging, or discrete with 120, or 1200 averaging fixings? Either way both prices above seem approximately correct. The question is how long does it take.
by Billy7
January 20th, 2018, 4:48 pm
Forum: Numerical Methods Forum
Topic: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.
Replies: 231
Views: 15134

Re: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.

I've seen a people use GARCH for the underlying (in a risk setting), Heston for the implied ..but then when doing MC (for VaR analysis on portfolios with derivatives) the Heston calibration to implied vol scenarios was eventually dropped because of speed issues. I've seen that Yianis' PDE method is...
by Billy7
January 20th, 2018, 12:14 am
Forum: Numerical Methods Forum
Topic: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.
Replies: 231
Views: 15134

Re: PDE methods for optimal quantizers of stochastic processes ? An example with Heston PDE.

Thanks outrun, it was quite a bit of work all right! But mostly fun and working with Alan was a pleasure too :)
by Billy7
December 21st, 2017, 2:16 pm
Forum: Programming and Software Forum
Topic: Using Quantlib
Replies: 181
Views: 16170

Re: Using Quantlib

Duh...I just realised I had read the above as " Don't know why Boost uses  it   ", without the "because". That's what happens when you do 3-4 things at the same time. I still don't understand why you are wondering about QL having it in experimental (probably because they haven't had time to test it ...
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