Hi,
I am trying to work around the problem of zero dividend time by using a
small, say 1e-4, dividend time and has run into a problem of another kind.
If the number of asset steps is bigger than the number of time steps the
solver doesn't work right. Below are reulsts of pricing an option using
timeSteps of 40 and various assetSteps: 20, 40, 60. You can see that for
assetSteps=60 the results are completely wrong.
assetSteps=20 price=2.16968 delta=0.51742 vega=7.7254
assetSteps=40 price=2.16968 delta=0.517419 vega=7.72562
assetSteps=60 price=4.75005 delta=-4.39606 vega=131.91
Does anyone have an explanation for this phenomenon and/or suggestions for a
work around?
Thanks, Vadim
P.S. This is how to reproduce the results
#include <ql/quantlib.hpp>
using namespace std;
using namespace QuantLib;
using namespace QuantLib::Pricers;
int main() {
const unsigned timeSteps = 40;
vector<unsigned> assetStepsA;
assetStepsA.push_back(20);
assetStepsA.push_back(40);
assetStepsA.push_back(60);
vector<double> dividendA, dividendTimeA;
dividendA.push_back(0.025);
dividendTimeA.push_back(1e-4);
double under=54.625;
double strike=55;
double dividendYield=0;
double interestRate=0.052706;
double expirationTime=0.126027;
double sigma=0.282922;
for (unsigned i=0; i<assetStepsA.size(); i++) {
const unsigned assetSteps = assetStepsA[i];
FdDividendAmericanOption opt(Option::Call, under,
strike,
dividendYield, interestRate,
expirationTime, sigma,
dividendA, dividendTimeA,
timeSteps, assetSteps);
cout << "assetSteps=" << assetSteps
<< " price=" << opt.value()
<< " delta=" << opt.delta()
<< " vega=" << opt.vega()
<< '\n';
}
return 0;
}
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