Bicubic vs. Bilinear interpolation for volatility surface

[Max-118]

Hi,

I am using QuantLib-0.8.1 on cygwin platform.
I have written a simple C++ program to construct volatility surface using Bilinear (default method) and Bicubic interpolation.
However, the result from Bicubic method is unsatisfactory, while Bilinear method works fine.

Here is the way how I set up BlackVarianceSurface class:

    boost::shared_ptr<BlackVarianceSurface> bVarSurface(
            new BlackVarianceSurface(settlementDate, dates,
                                     strikes, vols, dayCounter));

    // change interpolation method to Bicubic
    bVarSurface->setInterpolation<Bicubic>();

    Handle<BlackVolTermStructure> blackSurface(bVarSurface);

Say, for the following simple data set:

strike   1M     3M
90        0.29   0.27
95        0.26   0.25

For Bilinear, blackSurface->blackVol(1/12, 90, true) returns 0.29, which is correct.
However, for Bicubic, blackSurface->blackVol(1/12, 90, true) returns 0, which is definitely wrong.

Does this suggest that Bicubic interpolation is broken for volatility surface? Or any mistake in my coding?

Thanks in advance!

Best regards,
Max

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[Luigi Ballabio]

On Wed, 2007-10-03 at 23:33 +0800, Max wrote:

> I have written a simple C++ program to construct volatility surface
> using Bilinear (default method) and Bicubic interpolation.
> However, the result from Bicubic method is unsatisfactory, while
> Bilinear method works fine.
>
> Say, for the following simple data set:
>
> strike   1M     3M
> 90        0.29   0.27
> 95        0.26   0.25
>
> For Bilinear, blackSurface->blackVol(1/12, 90, true) returns 0.29,
> which is correct.
> However, for Bicubic, blackSurface->blackVol(1/12, 90, true) returns
> 0, which is definitely wrong.

Max,
        I can't reproduce the problem---meaning that for your data, I get an
error when I try to switch to bicubic (it requires at least a 3x3
matrix.)  Maybe you're catching the error and returning 0? May you try
extending the matrix with an additional row and column?

Also, careful with the argument you're passing. 1/12 is an integer
division whose result is 0. You want to write 1.0/12 instead.

Later,
        Luigi

--

Vin: It's like this fellow I knew in El Paso. One day, he just took
all his clothes off and jumped in a mess of cactus. I asked him that
same question, "Why?"
Calvera: And?
Vin: He said, "It seemed like a good idea at the time."
-- The Magnificent Seven



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[Max-118]

Hi  Luigi,

By following your hints, I still face the same issue with BiCubic interpolation.

Here is how I build and run the test program (appended bellow) when BiCubic is set by the line "bVarSurface->setInterpolation<Bicubic>();" :

$ g++ -g -O2 -Wall -I/usr/local/include/ql -I/usr/include/boost-1_33_1/ -L/usr/local/lib TestVolSurface.cpp -lQuantlib -o TestVolSurface
$ ./TestVolSurfacel.exe
Minimum strike = 90
Maximum strike = 100
Implied Vol (1M, 90) = 0

---------------------------------------------------------------------------------------------------------------------------------------------
#include <iostream>
#include <ql/quantlib.hpp>

using namespace QuantLib;

int main(int argc, char **argv) {

    Date todaysDate(3, Oct, 2007);
    Date settlementDate(3, Oct, 2007);
    Settings::instance().evaluationDate() = todaysDate;

    DayCounter dayCounter = Actual365Fixed();

    std::vector<Date> dates(3);
    dates[0] = settlementDate + 1*Months;
    dates[1] = settlementDate + 3*Months;
    dates[2] = settlementDate + 6*Months;

    std::vector<Real> strikes(3);
    strikes[0] = 90;
    strikes[1] = 95;
    strikes[2] = 100;

    Matrix vols(3, 3);

    vols[0][0] = 0.293; vols[0][1] = 0.277; vols[0][2] = 0.263;
    vols[1][0] = 0.256; vols[1][1] = 0.257; vols[1][2] = 0.249;
    vols[2][0] = 0.220; vols[2][1] = 0.240; vols[2][2] = 0.237;

    boost::shared_ptr<BlackVarianceSurface> bVarSurface(
            new BlackVarianceSurface(settlementDate, dates,
                                     strikes, vols, dayCounter));

    // change interpolation method to Bicubic
    bVarSurface->setInterpolation<Bicubic>();

    Handle<BlackVolTermStructure> blackSurface(bVarSurface);

    std::cout << "Minimum strike = " << blackSurface->minStrike()  << std::endl;
    std::cout << "Maximum strike = " << blackSurface->maxStrike()  << std::endl;
    std::cout << "Implied Vol = " << blackSurface->blackVol(1.0/12, 90, true)  << std::endl;
}
---------------------------------------------------------------------------------------------------------------------------------------------

Do you get the same result as I do?

Thanks

Best regards,
Max

On 10/4/07, Luigi Ballabio <[hidden email]> wrote:

On Wed, 2007-10-03 at 23:33 +0800, Max wrote:
> I have written a simple C++ program to construct volatility surface

> using Bilinear (default method) and Bicubic interpolation.
> However, the result from Bicubic method is unsatisfactory, while
> Bilinear method works fine.
>
> Say, for the following simple data set:
>
> strike   1M     3M
> 90        0.29   0.27
> 95        0.26   0.25
>
> For Bilinear, blackSurface->blackVol(1/12, 90, true) returns 0.29,
> which is correct.
> However, for Bicubic, blackSurface->blackVol(1/12, 90, true) returns
> 0, which is definitely wrong.

Max,
        I can't reproduce the problem---meaning that for your data, I get an
error when I try to switch to bicubic (it requires at least a 3x3
matrix.)  Maybe you're catching the error and returning 0? May you try
extending the matrix with an additional row and column?

Also, careful with the argument you're passing. 1/12 is an integer
division whose result is 0. You want to write 1.0/12 instead.

Later,
        Luigi

--

Vin: It's like this fellow I knew in El Paso. One day, he just took
all his clothes off and jumped in a mess of cactus. I asked him that
same question, "Why?"
Calvera: And?
Vin: He said, "It seemed like a good idea at the time."
-- The Magnificent Seven

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[Luigi Ballabio]

On Thu, 2007-10-04 at 00:35 +0800, Max wrote:
> By following your hints, I still face the same issue with BiCubic
> interpolation.

Hi Max,
        I've reproduced your problem. The good news is that the code currently
in Subversion works---I haven't checked in depth, but I suspect that the
reason is the change logged at
<http://quantlib.svn.sourceforge.net/viewvc/quantlib/trunk/QuantLib/ql/math/interpolations/cubicspline.hpp?r1=11481&r2=12381>.
May you try applying it and see if it fixes the problem?

Luigi


--

Newton's Law of Gravitation:
What goes up must come down. But don't expect it to come down
where you can find it. Murphy's Law applies to Newton's.



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[Max-118]

On 10/4/07, Luigi Ballabio <[hidden email]> wrote:

On Thu, 2007-10-04 at 00:35 +0800, Max wrote:
> By following your hints, I still face the same issue with BiCubic
> interpolation.

Hi Max,
        I've reproduced your problem. The good news is that the code currently
in Subversion works---I haven't checked in depth, but I suspect that the
reason is the change logged at
< http://quantlib.svn.sourceforge.net/viewvc/quantlib/trunk/QuantLib/ql/math/interpolations/cubicspline.hpp?r1=11481&r2=12381>.
May you try applying it and see if it fixes the problem?

Hi Luigi,

Now the interpolated numbers are looking good after applying the fix.
And I will try to further verify it with matlab.

A side question, I didn't see "configure" script in the Subversion code, so how can I build the code?

Thanks a lot!

Best regards,
Max 

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[Luigi Ballabio]

On Thu, 2007-10-04 at 23:56 +0800, Max wrote:
> Now the interpolated numbers are looking good after applying the fix.
> And I will try to further verify it with matlab.
>
> A side question, I didn't see "configure" script in the Subversion
> code, so how can I build the code?

Run autogen.sh first.  To do that, you'll need recent (ideally, the
latest) versions of autoconf, automake, and libtool.

Luigi


--

The young man knows the rules, but the old man knows the exceptions.
-- O. W. Holmes



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