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by ferdelo
December 6th, 2017, 9:30 am
Forum: Trading Forum
Topic: SABR: One parametrization to rule the world .. ?
Replies: 3
Views: 4735

Re: SABR: One parametrization to rule the world .. ?

i am afraid i will keep sleeping not so well... 

thank you anyway...
by ferdelo
December 5th, 2017, 7:13 am
Forum: Trading Forum
Topic: SABR: One parametrization to rule the world .. ?
Replies: 3
Views: 4735

SABR: One parametrization to rule the world .. ?

I have two questions that prevent me from sleeping well... If someone could help me .. :(  1. I was wondering whether traders use the same smile model (parametrization)  to price vanillas (EUR cash swaptions) and CMS. When they contribute to Totem at end of month, do they use the same parametrizatio...
by ferdelo
January 20th, 2017, 8:03 am
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10621

Re: Cheyette Unstability in PDE

Thank you very much for posting the results..!!! they look pretty good. Just to make sure, the approximation you use for [$]\bar{y}_t[$] is the variance of [$]x_t[$] (the one where the local vol is killed), right?

Thx again ..!
by ferdelo
January 13th, 2017, 5:29 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10621

Re: Cheyette Unstability in PDE

I have solved the PDE: [$]  \partial_t V + \left( \bar{y}_t - 2 \chi x_t \right)\partial_x V + \frac{1}{2}\sigma(t, x)^2  \partial_{xx}V - r_t V = 0[$]  Where [$] \bar{y}_t  = \frac{\alpha^2}{2 \chi} \left(1- e^{-2 \chi t} \right)[$] in case of constant parameters. Parameteres: [$]\alpha = 70  [$]bp...
by ferdelo
January 12th, 2017, 5:34 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10621

Re: Cheyette Unstability in PDE

Thanks again Cuchulain ..! I just tried what VivienB proposed (project onto 1D PDE by freezing y_t to its mean) and i don't get good values for long maturities and medium to high volatilities. Perhaps i should modify [$] \bar{y}_t[$] so as to be fit to the interest rate term structure by solving the...
by ferdelo
January 10th, 2017, 1:27 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10621

Re: Cheyette Unstability in PDE

Cuchulain thank you very much again for your reply (and sincerity :) ) 1. Ghost Points : I would say that the scheme (i described) remains the same without need of the ghost point: In the case of the 2-point upwind scheme, By defining the grid u_k for all k = 0, ..N; defining the diff operator for k...
by ferdelo
January 9th, 2017, 10:50 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10621

Re: Cheyette Unstability in PDE

Thanks Cuchulain and Lapsilago for your replies..!! I have written with some detail the discretization i made to solve the problem (as Cuchulain said, it is the local vol model proposed by Andreasen in "Turbo charging .." ).(perhaps there is something i misunderstood... ) @Lapsilago: The code is wri...
by ferdelo
January 8th, 2017, 8:35 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10621

Re: Cheyette Unstability in PDE

Cuchulainn, thanks for your quick reply. When i said "upwind scheme" i meant upwind/downwind scheme. The penta-diagonal system is because i discretize the first order derivative (in one of the implementatios) in y-direction with a 5 point scheme so a I have to solve a pentadiagonal system when i sol...
by ferdelo
January 8th, 2017, 7:00 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10621

Cheyette Unstability in PDE

I have implemented the Cheyette model (with linear local volatiltiy) in PDE by the finite difference Method. I use standard ADI methods (in the test i am talking about i use the Craig Sneyd one). I shallow describe what i do in bullet points: Domain for X an Y : I solve a system of diff equations to...
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