private void testVolatilityAdjoint(
double forward,
EuropeanVanillaOption optionData,
SabrFormulaData sabrData,
double eps,
double tol) {
double volatility =
FUNCTION.getVolatility(
forward, optionData.getStrike(), optionData.getTimeToExpiry(), sabrData);
double[] volatilityAdjoint =
toArray(
FUNCTION.getVolatilityAdjoint(
forward, optionData.getStrike(), optionData.getTimeToExpiry(), sabrData));
assertEquals(volatility, volatilityAdjoint[0], tol);
assertEqualsRelTol(
"Forward Sensitivity" + sabrData.toString(),
fdSensitivity(optionData, forward, sabrData, SabrParameter.Forward, eps),
volatilityAdjoint[1],
tol);
assertEqualsRelTol(
"Strike Sensitivity" + sabrData.toString(),
fdSensitivity(optionData, forward, sabrData, SabrParameter.Strike, eps),
volatilityAdjoint[2],
tol);
assertEqualsRelTol(
"Alpha Sensitivity" + sabrData.toString(),
fdSensitivity(optionData, forward, sabrData, SabrParameter.Alpha, eps),
volatilityAdjoint[3],
tol);
assertEqualsRelTol(
"Beta Sensitivity" + sabrData.toString(),
fdSensitivity(optionData, forward, sabrData, SabrParameter.Beta, eps),
volatilityAdjoint[4],
tol);
assertEqualsRelTol(
"Rho Sensitivity" + sabrData.toString(),
fdSensitivity(optionData, forward, sabrData, SabrParameter.Rho, eps),
volatilityAdjoint[5],
tol);
assertEqualsRelTol(
"Nu Sensitivity" + sabrData.toString(),
fdSensitivity(optionData, forward, sabrData, SabrParameter.Nu, eps),
volatilityAdjoint[6],
tol);
}
private void volatilityAdjoint2ForInstrument(
EuropeanVanillaOption option, double tolerance1, double tolerance2) {
// vol
double volatility =
FUNCTION.getVolatility(F, option.getStrike(), option.getTimeToExpiry(), DATA);
double[] volatilityAdjoint =
toArray(
FUNCTION.getVolatilityAdjoint(F, option.getStrike(), option.getTimeToExpiry(), DATA));
double[] volD = new double[6];
double[][] volD2 = new double[2][2];
double vol =
FUNCTION.getVolatilityAdjoint2(
F, option.getStrike(), option.getTimeToExpiry(), DATA, volD, volD2);
assertEquals(volatility, vol, tolerance1);
// Derivative
for (int loopder = 0; loopder < 6; loopder++) {
assertEquals(volatilityAdjoint[loopder + 1], volD[loopder], tolerance1);
}
// Derivative forward-forward
double deltaF = 0.000001;
double volatilityFP =
FUNCTION.getVolatility(F + deltaF, option.getStrike(), option.getTimeToExpiry(), DATA);
double volatilityFM =
FUNCTION.getVolatility(F - deltaF, option.getStrike(), option.getTimeToExpiry(), DATA);
double derivativeFF_FD = (volatilityFP + volatilityFM - 2 * volatility) / (deltaF * deltaF);
assertEquals(derivativeFF_FD, volD2[0][0], tolerance2);
// Derivative strike-strike
double deltaK = 0.000001;
double volatilityKP =
FUNCTION.getVolatility(F, option.getStrike() + deltaK, option.getTimeToExpiry(), DATA);
double volatilityKM =
FUNCTION.getVolatility(F, option.getStrike() - deltaK, option.getTimeToExpiry(), DATA);
double derivativeKK_FD = (volatilityKP + volatilityKM - 2 * volatility) / (deltaK * deltaK);
assertEquals(derivativeKK_FD, volD2[1][1], tolerance2);
// Derivative strike-forward
double volatilityFPKP =
FUNCTION.getVolatility(
F + deltaF, option.getStrike() + deltaK, option.getTimeToExpiry(), DATA);
double derivativeFK_FD =
(volatilityFPKP + volatility - volatilityFP - volatilityKP) / (deltaF * deltaK);
assertEquals(derivativeFK_FD, volD2[0][1], tolerance2);
assertEquals(volD2[0][1], volD2[1][0], 1E-6);
}
@SuppressWarnings("null")
private double fdSensitivity(
EuropeanVanillaOption optionData,
double forward,
SabrFormulaData sabrData,
SabrParameter param,
double delta) {
Function<SabrFormulaData, Double> funcC = null;
Function<SabrFormulaData, Double> funcB = null;
Function<SabrFormulaData, Double> funcA = null;
SabrFormulaData dataC = null;
SabrFormulaData dataB = sabrData;
SabrFormulaData dataA = null;
Function<SabrFormulaData, Double> func = getVolatilityFunction(optionData, forward);
FiniteDifferenceType fdType = null;
switch (param) {
case Strike:
double strike = optionData.getStrike();
if (strike >= delta) {
fdType = FiniteDifferenceType.CENTRAL;
funcA = getVolatilityFunction(withStrike(optionData, strike - delta), forward);
funcC = getVolatilityFunction(withStrike(optionData, strike + delta), forward);
} else {
fdType = FiniteDifferenceType.FORWARD;
funcA = func;
funcB = getVolatilityFunction(withStrike(optionData, strike + delta), forward);
funcC = getVolatilityFunction(withStrike(optionData, strike + 2 * delta), forward);
}
dataC = sabrData;
dataB = sabrData;
dataA = sabrData;
break;
case Forward:
if (forward > delta) {
fdType = FiniteDifferenceType.CENTRAL;
funcA = getVolatilityFunction(optionData, forward - delta);
funcC = getVolatilityFunction(optionData, forward + delta);
} else {
fdType = FiniteDifferenceType.FORWARD;
funcA = func;
funcB = getVolatilityFunction(optionData, forward + delta);
funcC = getVolatilityFunction(optionData, forward + 2 * delta);
}
dataC = sabrData;
dataB = sabrData;
dataA = sabrData;
break;
case Alpha:
double a = sabrData.getAlpha();
if (a >= delta) {
fdType = FiniteDifferenceType.CENTRAL;
dataA = sabrData.withAlpha(a - delta);
dataC = sabrData.withAlpha(a + delta);
} else {
fdType = FiniteDifferenceType.FORWARD;
dataA = sabrData;
dataB = sabrData.withAlpha(a + delta);
dataC = sabrData.withAlpha(a + 2 * delta);
}
funcC = func;
funcB = func;
funcA = func;
break;
case Beta:
double b = sabrData.getBeta();
if (b >= delta) {
fdType = FiniteDifferenceType.CENTRAL;
dataA = sabrData.withBeta(b - delta);
dataC = sabrData.withBeta(b + delta);
} else {
fdType = FiniteDifferenceType.FORWARD;
dataA = sabrData;
dataB = sabrData.withBeta(b + delta);
dataC = sabrData.withBeta(b + 2 * delta);
}
funcC = func;
funcB = func;
funcA = func;
break;
case Nu:
double n = sabrData.getNu();
if (n >= delta) {
fdType = FiniteDifferenceType.CENTRAL;
dataA = sabrData.withNu(n - delta);
dataC = sabrData.withNu(n + delta);
} else {
fdType = FiniteDifferenceType.FORWARD;
dataA = sabrData;
dataB = sabrData.withNu(n + delta);
dataC = sabrData.withNu(n + 2 * delta);
}
funcC = func;
funcB = func;
funcA = func;
break;
case Rho:
double r = sabrData.getRho();
if ((r + 1) < delta) {
fdType = FiniteDifferenceType.FORWARD;
dataA = sabrData;
dataB = sabrData.withRho(r + delta);
dataC = sabrData.withRho(r + 2 * delta);
} else if ((1 - r) < delta) {
fdType = FiniteDifferenceType.BACKWARD;
dataA = sabrData.withRho(r - 2 * delta);
dataB = sabrData.withRho(r - delta);
dataC = sabrData;
} else {
fdType = FiniteDifferenceType.CENTRAL;
dataC = sabrData.withRho(r + delta);
dataA = sabrData.withRho(r - delta);
}
funcC = func;
funcB = func;
funcA = func;
break;
default:
throw new MathException("enum not found");
}
if (fdType != null) {
switch (fdType) {
case FORWARD:
return (-1.5 * funcA.apply(dataA) + 2.0 * funcB.apply(dataB) - 0.5 * funcC.apply(dataC))
/ delta;
case BACKWARD:
return (0.5 * funcA.apply(dataA) - 2.0 * funcB.apply(dataB) + 1.5 * funcC.apply(dataC))
/ delta;
case CENTRAL:
return (funcC.apply(dataC) - funcA.apply(dataA)) / 2.0 / delta;
default:
throw new MathException("enum not found");
}
}
throw new MathException("enum not found");
}
