Wilmott Forums - Methods for Volatility Surface Interpolation

Forum Navigation:

new topic

FORUMS > Technical Forum

< refresh >

Topic Title: Methods for Volatility Surface Interpolation
Created On Tue Dec 27, 05 03:10 PM

Topic View:

BobJefferson
Member

Posts: 44
Joined: Sep 2005

Tue Dec 27, 05 03:10 PM

Does anyone has any suggestions, bibliography, papers, anything else related with vols surface interpol?

Regards

Bob

Quote

Top

Bottom

doreilly
Senior Member

Posts: 728
Joined: Feb 2005

Tue Dec 27, 05 03:41 PM

Quote
Originally posted by: BobJefferson
Does anyone has any suggestions, bibliography, papers, anything else related with vols surface interpol?

Regards

Bob

In Market Models Carol Alexander uses "cubic spline interpolation" from "Numerical Recipes in C", which obviously has an overview and some code. The latter that is, not the former.

Posts: 188
Joined: Sep 2004

Wed Dec 28, 05 05:31 AM

yes.. spline interpolation is a method that is used in practice.

Posts: 129
Joined: Jul 2002

Mon Jan 02, 06 04:28 PM

If you have a t least three reliable prices for an expiry, you can use the method explained in the paper at the following address. It has some more financial rationale than a spline interpolation.

http://www.fabiomercurio.it/consistentfxsmile.pdf

Quote

Top

Bottom

doublebarrier2000
Senior Member

Posts: 219
Joined: Jul 2002

Thu Jan 05, 06 12:15 PM

Hi. The QuantLib open source software has some excellent volatility interpolation functions that can be implemented in excel.

From memory, the function qlBlackVol will interpolate vols making sure that the surface is arbitrage free

download the excel add-in package here

Quote

Top

Bottom

doreilly
Senior Member

Posts: 728
Joined: Feb 2005

Thu Jan 05, 06 01:36 PM

Quote
Originally posted by: doublebarrier2000
Hi. The QuantLib open source software has some excellent volatility interpolation functions that can be implemented in excel.

From memory, the function qlBlackVol will interpolate vols making sure that the surface is arbitrage free

download the excel add-in package here

oop's db, the link is a little unsaansitaave, I presume you meant this link

Edited: Thu Jan 05, 06 at 01:36 PM by doreilly

Posts: 190
Joined: Jan 2002

Thu Jan 05, 06 02:34 PM

Here is a paper by Matthias Fengler:

http://141.20.100.9/papers/pdf/SFB649DP2005-019.pdf

Quote

Top

Bottom

jschnaz
Junior Member

Posts: 11
Joined: Jul 2002

Mon Jan 09, 06 01:20 PM

Be very careful with geometric interpolation methods (such as cubic spline) : they tend to generate weird implied distributions. Be careful also about what happens at the wings.

Quote

Top

Bottom

doreilly
Senior Member

Posts: 728
Joined: Feb 2005

Mon Jan 09, 06 01:32 PM

Quote
Originally posted by: jschnaz
Be very careful with geometric interpolation methods (such as cubic spline) : they tend to generate weird implied distributions. Be careful also about what happens at the wings.

bluetrin
Senior Member

Posts: 231
Joined: Sep 2005

Mon Jan 09, 06 01:44 PM

Quote
Originally posted by: doreilly
Quote
Originally posted by: jschnaz
Be very careful with geometric interpolation methods (such as cubic spline) : they tend to generate weird implied distributions. Be careful also about what happens at the wings.

care to elaborate ?

Because the differentials of the curve are computed to fit the points and to make the curve differentiable, you can have kind of border effects when one point move: it will also change the shape of the curve on the adjacent points.

So when the data is not very accurate you can have strange shapes (especially on a market move) which can also change very quickly (when the prices update).

And if you try to extrapolate the curve after your last point, the shape is only dependant of what your algorithm found as differential to fit the last points and most implementations will just continue the curve in a kind of straight line. (meaning that you get huge variations when the last point move)

Quote

Top

Bottom

jschnaz
Junior Member

Posts: 11
Joined: Jul 2002

Mon Jan 09, 06 03:32 PM

Well yes with any polynomial method you have a border effect in that the whole curve moves when a single point is shifted. This is not too bad though.

But more important is that the distribution implied from the vol surface depends on the 2nd derivative of the option price with respect to the strike. Obviously this function incorporate your interpolation function, whose 2nd derviative therefore comes to play. Any local irregularity of this function gets magnified and this can result in very conunterintuitive, if not directly arbitrable, distribution curves. Even with a standard cubic spline applied to real mkt data for a very liquid asset you will find cases where your density function actually decreases at some points ...

So you may actually be better off not interpolating at all ... and instead price vanillas off the same model you use for exotics (or maybe use it to generate more points on your smile grids).

Posts: 26
Joined: May 2003

Wed Jan 11, 06 09:29 PM

Check out the paper by Nabil Kahale "An arbitrage-free interpolation of volatilities" published in 2004 Risk.

Posts: 47
Joined: Mar 2002

Thu Jan 12, 06 03:13 PM

Eric Reiner, "The Characteristic Curve Approach to Arbitrage-Free Time Interpolation of Volatility", ICBI Global Derivatives Conference, 2004

Quote

Top

Bottom

pschwen
Junior Member

Posts: 20
Joined: Jul 2002

Sat Jan 21, 06 07:45 AM

>Eric Reiner, "The Characteristic Curve Approach to Arbitrage-Free Time Interpolation of Volatility", ICBI >Global Derivatives Conference, 2004

does anyone have this presentation?

Posts: 132
Joined: Jul 2006

Tue Apr 03, 07 08:00 AM

Quote
Originally posted by: jrquant1
Check out the paper by Nabil Kahale "An arbitrage-free interpolation of volatilities" published in 2004 Risk.

anyone tried out this one? I just read through the introduction. It sounds very promising