Re: LocalvolSurface.cpp

Posted by MH_quant on
URL: http://quantlib.414.s1.nabble.com/LocalvolSurface-cpp-tp12806p12810.html


Hallo Klaus,

I ran my tests with both. BiLinear and BiCubic intrapolation. I encountered
the instability issues with both.

You are right that the problems appear far ITM and OTM. But I cant really
figure out why, since I set up a constant extrapolation for both, Strike and
Maturity in my BlackVarianceSurface.

I attached the cpp file that I use for my tests as well as a small jpg of
the surface that is included in my test cases.

I hope this gives you all the information you need and you can give me some
feedback on my test cases.

Thank you also for the link. To me it seem like if we want to use the dupire
formula efficient, stable and productive, we wont get around implementing
some fancy optimization-splines and smoothing algorithm.

I am looking forward to hear back from you.

Greetings,
Michael



-----Original Message-----
From: Klaus Spanderen [mailto:[hidden email]]
Sent: Sonntag, 26. April 2009 22:01
To: [hidden email]
Cc: Michael Heckl
Subject: Re: [Quantlib-dev] LocalvolSurface.cpp

>
> It happens at different strikes and moneyness under some conditions that
> the d2wdy2 blows up and becomes something like -4231,12
>

Which interpolation scheme do you use for the volatility surface. The
standard
interpolation is linear in the variance which very often leads to problems
with the second derivative. Therefore I've used BicubicSplineInterpolation

    volTS->setInterpolation<Bicubic>();

 
Does this happen only for deep ITM or OTM paths? (Is this a extrapolation
problem for very large (very small) spots?) At least for "extrem"
extrapolations" I found simillar problems and "solved" it be setting
negative
variances to zero.

Can I get access to the parameters of your test-surface?

> But would that probably
> make the dupire formula useless to us?

People your using e.g. splines together with an optimization technique like
in

Reconstructing The Unknown Local Volatility Function, Thomas F. Coleman,
Yuying Li, ARUN VERMA,
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.6202

to solve the instability. But a lot of code is needed to implemented
this;-(.
For the time being I think we should give Nando's approach a try and use the

first and second derivatives taken from the interpolation method


regards
 Klaus

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