[Quantlib-dev] [ quantlib-Bugs-3417114 ] BS call option price lower than intrinsic value

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Bugs item #3417114, was opened at 2011-10-02 15:52
Message generated for change (Comment added) made by lballabio
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Category: None
Group: None
>Status: Closed
>Resolution: Invalid
Priority: 5
Private: No
Submitted By: R Y (fancidev)
Assigned to: Nobody/Anonymous (nobody)
Summary: BS call option price lower than intrinsic value

Initial Comment:
Compile and run the following program in Visual Studio 2010 produces the bug.

#include <iostream>
#include <ql/pricingengines/blackformula.hpp>

using namespace QuantLib;

static void TestBlackScholesBound()
{
	double F = 1.35;
	double K = 0.39;
	double stdev = 0.12;
	double c = blackFormula(Option::Call, K, F, stdev);
	if (c < (F - K))
	{
		std::cerr << "Error: Option price = " << c << ", Lower Bound = "
			<< (F - K) << std::endl;
	}
}

int main()
{
	TestBlackScholesBound();
	system("PAUSE");
}


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>Comment By: Luigi Ballabio (lballabio)
Date: 2011-10-03 12:16

Message:
That also happens with g++ on Linux, but it's only caused by floating-point
precision issues. If you print out the values with more precision, you'll
find:

Option price = 0.95999999999999996447
Lower Bound = 0.9600000000000000755

due to the fact that you can't store 0.96, nor 1.35, nor 0.39 in a
floating-point number exactly.  Also, if you write the check as:

if (c < 0.96)

instead of
if (c < (F - K))

the test passes.

That's not something we can fix on the library side, and adding a check
might just cause false positives.

----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=112740&aid=3417114&group_id=12740