/** Test the nu = 0 edge case */
@Test
public void testVolatilityAdjointNu0() {
double eps = 1e-5;
double tol = 1e-6;
SabrFormulaData data = DATA.withNu(0.0);
testVolatilityAdjoint(F, CALL_ATM, data, eps, tol);
testVolatilityAdjoint(F, CALL_ITM, data, eps, 2e-4);
testVolatilityAdjoint(F, CALL_OTM, data, eps, 5e-5);
}
@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");
}
