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/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.volatility.surface;
import java.util.Map;
import org.apache.commons.lang.Validate;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import com.opengamma.analytics.financial.model.option.definition.OptionDefinition;
import com.opengamma.analytics.financial.model.option.definition.StandardOptionDataBundle;
import com.opengamma.analytics.financial.model.option.pricing.OptionPricingException;
import com.opengamma.analytics.financial.model.option.pricing.analytic.AnalyticOptionModel;
import com.opengamma.analytics.financial.model.option.pricing.analytic.BlackScholesMertonModel;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.rootfinding.SingleRootFinder;
import com.opengamma.analytics.math.surface.ConstantDoublesSurface;
import com.opengamma.util.ArgumentChecker;
import com.opengamma.util.tuple.DoublesPair;
/**
*
*/
public class BlackScholesMertonImpliedVolatilitySurfaceModel implements VolatilitySurfaceModel<Map<OptionDefinition, Double>, StandardOptionDataBundle> {
private static final Logger s_logger = LoggerFactory.getLogger(BlackScholesMertonImpliedVolatilitySurfaceModel.class);
private final AnalyticOptionModel<OptionDefinition, StandardOptionDataBundle> _bsm = new BlackScholesMertonModel();
private SingleRootFinder<StandardOptionDataBundle, Double> _rootFinder;
@Override
public VolatilitySurface getSurface(final Map<OptionDefinition, Double> optionPrices, final StandardOptionDataBundle optionDataBundle) {
Validate.notNull(optionPrices);
ArgumentChecker.notEmpty(optionPrices, "option prices");
Validate.notNull(optionDataBundle);
if (optionPrices.size() > 1) {
s_logger.info("Option price map had more than one entry: using the first pair to imply volatility");
}
final Map.Entry<OptionDefinition, Double> entry = optionPrices.entrySet().iterator().next();
final Double price = entry.getValue();
final Function1D<StandardOptionDataBundle, Double> pricingFunction = _bsm.getPricingFunction(entry.getKey());
_rootFinder = new MyBisectionSingleRootFinder(optionDataBundle, price);
return _rootFinder.getRoot(pricingFunction, optionDataBundle.withVolatilitySurface(new VolatilitySurface(ConstantDoublesSurface.from(0))),
optionDataBundle.withVolatilitySurface(new VolatilitySurface(ConstantDoublesSurface.from(10)))).getVolatilitySurface();
}
private static class MyBisectionSingleRootFinder implements SingleRootFinder<StandardOptionDataBundle, Double> {
private final StandardOptionDataBundle _data;
private final double _price;
private final DoublesPair _origin = DoublesPair.of(0., 0.);
private static final double ACCURACY = 1e-12;
private static final int MAX_ATTEMPTS = 10000;
public MyBisectionSingleRootFinder(final StandardOptionDataBundle data, final double price) {
_data = data;
_price = price;
}
@Override
public StandardOptionDataBundle getRoot(final Function1D<StandardOptionDataBundle, Double> function, final StandardOptionDataBundle... volData) {
final StandardOptionDataBundle lowVolData = volData[0];
final StandardOptionDataBundle highVolData = volData[1];
final Double lowPrice = function.evaluate(lowVolData) - _price;
if (Math.abs(lowPrice) < ACCURACY) {
return lowVolData;
}
Double highPrice = function.evaluate(highVolData) - _price;
if (Math.abs(highPrice) < ACCURACY) {
return highVolData;
}
final double highVol = highVolData.getVolatilitySurface().getVolatility(_origin);
final double lowVol = lowVolData.getVolatilitySurface().getVolatility(_origin);
double dVol, midVol, rootVol;
if (lowPrice < 0) {
dVol = highVol - lowVol;
rootVol = lowVol;
} else {
dVol = lowVol - highVol;
rootVol = highVol;
}
StandardOptionDataBundle midVolData;
for (int i = 0; i < MAX_ATTEMPTS; i++) {
dVol *= 0.5;
midVol = rootVol + dVol;
midVolData = _data.withVolatilitySurface(new VolatilitySurface(ConstantDoublesSurface.from((midVol))));
highPrice = function.evaluate(midVolData) - _price;
if (highPrice <= 0) {
rootVol = midVol;
}
if (Math.abs(dVol) < ACCURACY) {
return _data.withVolatilitySurface(new VolatilitySurface(ConstantDoublesSurface.from((midVol))));
}
}
throw new OptionPricingException("Could not find volatility in " + MAX_ATTEMPTS + " attempts");
}
}
}