private static readonly VolatilityFunctionProvider <SabrFormulaData>[] FUNCTIONS = new VolatilityFunctionProvider[] { FUNC_HAGAN }; // other volatility functions to be added
/// <summary>
/// Testing C2 continuity.
/// </summary>
//JAVA TO C# CONVERTER TODO TASK: Most Java annotations will not have direct .NET equivalent attributes:
//ORIGINAL LINE: @Test public void smoothnessTest()
public virtual void smoothnessTest()
{
foreach (VolatilityFunctionProvider <SabrFormulaData> func in FUNCTIONS)
{
SabrExtrapolationRightFunction extrapolation = SabrExtrapolationRightFunction.of(FORWARD, SABR_DATA, CUT_OFF_STRIKE, TIME_TO_EXPIRY, MU, func);
foreach (PutCall isCall in new PutCall[] { PutCall.CALL, PutCall.PUT })
{
double priceBase = extrapolation.price(CUT_OFF_STRIKE, isCall);
double priceUp = extrapolation.price(CUT_OFF_STRIKE + EPS, isCall);
double priceDw = extrapolation.price(CUT_OFF_STRIKE - EPS, isCall);
assertEquals(priceBase, priceUp, EPS);
assertEquals(priceBase, priceDw, EPS);
double priceUpUp = extrapolation.price(CUT_OFF_STRIKE + 2.0 * EPS, isCall);
double priceDwDw = extrapolation.price(CUT_OFF_STRIKE - 2.0 * EPS, isCall);
double firstUp = (-0.5 * priceUpUp + 2.0 * priceUp - 1.5 * priceBase) / EPS;
double firstDw = (-2.0 * priceDw + 0.5 * priceDwDw + 1.5 * priceBase) / EPS;
assertEquals(firstDw, firstUp, EPS);
// The second derivative values are poorly connected due to finite difference approximation
double firstUpUp = 0.5 * (priceUpUp - priceBase) / EPS;
double firstDwDw = 0.5 * (priceBase - priceDwDw) / EPS;
double secondUp = (firstUpUp - firstUp) / EPS;
double secondDw = (firstDw - firstDwDw) / EPS;
double secondRef = 0.5 * (firstUpUp - firstDwDw) / EPS;
assertEquals(secondRef, secondUp, secondRef * 0.15);
assertEquals(secondRef, secondDw, secondRef * 0.15);
}
}
}
/// <summary>
/// Test small forward.
/// </summary>
//JAVA TO C# CONVERTER TODO TASK: Most Java annotations will not have direct .NET equivalent attributes:
//ORIGINAL LINE: @Test public void smallForwardTest()
public virtual void smallForwardTest()
{
double smallForward = 0.1e-6;
double smallCutoff = 0.9e-6;
foreach (VolatilityFunctionProvider <SabrFormulaData> func in FUNCTIONS)
{
SabrExtrapolationRightFunction right = SabrExtrapolationRightFunction.of(smallForward, SABR_DATA, smallCutoff, TIME_TO_EXPIRY, MU, func);
foreach (PutCall isCall in new PutCall[] { PutCall.CALL, PutCall.PUT })
{
double priceBase = right.price(smallCutoff, isCall);
double priceUp = right.price(smallCutoff + EPS * 0.1, isCall);
double priceDw = right.price(smallCutoff - EPS * 0.1, isCall);
assertEquals(priceBase, priceUp, EPS * 10.0);
assertEquals(priceBase, priceDw, EPS * 10.0);
}
}
}
/// <summary>
/// Tests the price derivative with respect to forward for options in SABR model with extrapolation.
/// </summary>
public virtual void priceDerivativeForwardPut()
{
SabrExtrapolationRightFunction func = SabrExtrapolationRightFunction.of(FORWARD, SABR_DATA, CUT_OFF_STRIKE, TIME_TO_EXPIRY, MU, SabrHaganVolatilityFunctionProvider.DEFAULT);
double strikeIn = 0.08;
double strikeAt = CUT_OFF_STRIKE;
double strikeOut = 0.12;
EuropeanVanillaOption optionIn = EuropeanVanillaOption.of(strikeIn, TIME_TO_EXPIRY, PutCall.PUT);
EuropeanVanillaOption optionAt = EuropeanVanillaOption.of(strikeAt, TIME_TO_EXPIRY, PutCall.PUT);
EuropeanVanillaOption optionOut = EuropeanVanillaOption.of(strikeOut, TIME_TO_EXPIRY, PutCall.PUT);
double shiftF = 0.000001;
SabrFormulaData sabrDataFP = SabrFormulaData.of(ALPHA, BETA, RHO, NU);
SabrExtrapolationRightFunction sabrExtrapolationFP = SabrExtrapolationRightFunction.of(FORWARD + shiftF, TIME_TO_EXPIRY, sabrDataFP, CUT_OFF_STRIKE, MU);
// Below cut-off strike
double priceIn = func.price(optionIn.Strike, optionIn.PutCall);
double priceInFP = sabrExtrapolationFP.price(optionIn.Strike, optionIn.PutCall);
double priceInDF = func.priceDerivativeForward(optionIn.Strike, optionIn.PutCall);
double priceInDFExpected = (priceInFP - priceIn) / shiftF;
assertEquals(priceInDFExpected, priceInDF, 1E-5);
// At cut-off strike
double priceAt = func.price(optionAt.Strike, optionAt.PutCall);
double priceAtFP = sabrExtrapolationFP.price(optionAt.Strike, optionAt.PutCall);
double priceAtDF = func.priceDerivativeForward(optionAt.Strike, optionAt.PutCall);
double priceAtDFExpected = (priceAtFP - priceAt) / shiftF;
assertEquals(priceAtDFExpected, priceAtDF, 1E-6);
// Above cut-off strike
double priceOut = func.price(optionOut.Strike, optionOut.PutCall);
double priceOutFP = sabrExtrapolationFP.price(optionOut.Strike, optionOut.PutCall);
double priceOutDF = func.priceDerivativeForward(optionOut.Strike, optionOut.PutCall);
double priceOutDFExpected = (priceOutFP - priceOut) / shiftF;
assertEquals(priceOutDFExpected, priceOutDF, 1E-5);
double[] abc = func.Parameter;
double[] abcDF = func.ParameterDerivativeForward;
double[] abcFP = sabrExtrapolationFP.Parameter;
double[] abcDFExpected = new double[3];
for (int loopparam = 0; loopparam < 3; loopparam++)
{
abcDFExpected[loopparam] = (abcFP[loopparam] - abc[loopparam]) / shiftF;
assertEquals(1.0, abcDFExpected[loopparam] / abcDF[loopparam], 5E-2);
}
}
/// <summary>
/// Extrapolator is not calibrated in this case, then the gap may be produced at the cutoff.
/// </summary>
//JAVA TO C# CONVERTER TODO TASK: Most Java annotations will not have direct .NET equivalent attributes:
//ORIGINAL LINE: @Test public void smallExpiryTest()
public virtual void smallExpiryTest()
{
double smallExpiry = 0.5e-6;
foreach (VolatilityFunctionProvider <SabrFormulaData> func in FUNCTIONS)
{
SabrExtrapolationRightFunction right = SabrExtrapolationRightFunction.of(FORWARD * 0.01, SABR_DATA, CUT_OFF_STRIKE, smallExpiry, MU, func);
foreach (PutCall isCall in new PutCall[] { PutCall.CALL, PutCall.PUT })
{
double priceBase = right.price(CUT_OFF_STRIKE, isCall);
double priceUp = right.price(CUT_OFF_STRIKE + EPS * 0.1, isCall);
double priceDw = right.price(CUT_OFF_STRIKE - EPS * 0.1, isCall);
assertEquals(priceBase, priceUp, EPS);
assertEquals(priceBase, priceDw, EPS);
assertEquals(right.Parameter[0], -1.0E4, 1.e-12);
assertEquals(right.Parameter[1], 0.0, 1.e-12);
assertEquals(right.Parameter[2], 0.0, 1.e-12);
}
}
}
/// <summary>
/// Tests the price for options in SABR model with extrapolation.
/// </summary>
public virtual void priceCloseToExpiry()
{
double[] timeToExpiry = new double[] { 1.0 / 365, 0.0 }; // One day and on expiry day.
double strikeIn = 0.08;
double strikeAt = CUT_OFF_STRIKE;
double strikeOut = 0.12;
for (int loopexp = 0; loopexp < timeToExpiry.Length; loopexp++)
{
SabrExtrapolationRightFunction sabrExtra = SabrExtrapolationRightFunction.of(FORWARD, timeToExpiry[loopexp], SABR_DATA, CUT_OFF_STRIKE, MU);
double volatilityIn = SABR_FUNCTION.volatility(FORWARD, strikeIn, timeToExpiry[loopexp], SABR_DATA);
double priceExpectedIn = BlackFormulaRepository.price(FORWARD, strikeIn, timeToExpiry[loopexp], volatilityIn, true);
double priceIn = sabrExtra.price(strikeIn, PutCall.CALL);
assertEquals(priceExpectedIn, priceIn, TOLERANCE_PRICE);
double volatilityAt = SABR_FUNCTION.volatility(FORWARD, strikeAt, timeToExpiry[loopexp], SABR_DATA);
double priceExpectedAt = BlackFormulaRepository.price(FORWARD, strikeAt, timeToExpiry[loopexp], volatilityAt, true);
double priceAt = sabrExtra.price(strikeAt, PutCall.CALL);
assertEquals(priceExpectedAt, priceAt, TOLERANCE_PRICE);
double priceOut = sabrExtra.price(strikeOut, PutCall.CALL);
double priceExpectedOut = 0.0; // From previous run
assertEquals(priceExpectedOut, priceOut, TOLERANCE_PRICE);
}
}
/// <summary>
/// Tests the price for options in SABR model with extrapolation.
/// </summary>
public virtual void price()
{
double strikeIn = 0.08;
double strikeAt = CUT_OFF_STRIKE;
double strikeOut = 0.12;
double volatilityIn = SABR_FUNCTION.volatility(FORWARD, strikeIn, TIME_TO_EXPIRY, SABR_DATA);
double priceExpectedIn = BlackFormulaRepository.price(FORWARD, strikeIn, TIME_TO_EXPIRY, volatilityIn, true);
double priceIn = SABR_EXTRAPOLATION.price(strikeIn, PutCall.CALL);
assertEquals(priceExpectedIn, priceIn, TOLERANCE_PRICE);
double volatilityAt = SABR_FUNCTION.volatility(FORWARD, strikeAt, TIME_TO_EXPIRY, SABR_DATA);
double priceExpectedAt = BlackFormulaRepository.price(FORWARD, strikeAt, TIME_TO_EXPIRY, volatilityAt, true);
double priceAt = SABR_EXTRAPOLATION.price(strikeAt, PutCall.CALL);
assertEquals(priceExpectedAt, priceAt, TOLERANCE_PRICE);
double priceOut = SABR_EXTRAPOLATION.price(strikeOut, PutCall.CALL);
double priceExpectedOut = 5.427104E-5; // From previous run
assertEquals(priceExpectedOut, priceOut, TOLERANCE_PRICE);
}
/// <summary>
/// Tests the price derivative with respect to forward for options in SABR model with extrapolation. Other data.
/// </summary>
public virtual void priceDerivativeSABR2()
{
double alpha = 0.06;
double beta = 0.5;
double rho = 0.0;
double nu = 0.3;
double cutOff = 0.10;
double mu = 2.5;
double strike = 0.15;
double t = 2.366105247;
EuropeanVanillaOption option = EuropeanVanillaOption.of(strike, t, PutCall.CALL);
SabrFormulaData sabrData = SabrFormulaData.of(alpha, beta, rho, nu);
double forward = 0.0404500579038675;
SabrExtrapolationRightFunction sabrExtrapolation = SabrExtrapolationRightFunction.of(forward, t, sabrData, cutOff, mu);
double shift = 0.000001;
SabrFormulaData sabrDataAP = SabrFormulaData.of(alpha + shift, beta, rho, nu);
SabrFormulaData sabrDataBP = SabrFormulaData.of(alpha, beta + shift, rho, nu);
SabrFormulaData sabrDataRP = SabrFormulaData.of(alpha, beta, rho + shift, nu);
SabrFormulaData sabrDataNP = SabrFormulaData.of(alpha, beta, rho, nu + shift);
SabrExtrapolationRightFunction sabrExtrapolationAP = SabrExtrapolationRightFunction.of(forward, t, sabrDataAP, cutOff, mu);
SabrExtrapolationRightFunction sabrExtrapolationBP = SabrExtrapolationRightFunction.of(forward, t, sabrDataBP, cutOff, mu);
SabrExtrapolationRightFunction sabrExtrapolationRP = SabrExtrapolationRightFunction.of(forward, t, sabrDataRP, cutOff, mu);
SabrExtrapolationRightFunction sabrExtrapolationNP = SabrExtrapolationRightFunction.of(forward, t, sabrDataNP, cutOff, mu);
// Above cut-off strike
double[] abc = sabrExtrapolation.Parameter;
double[][] abcDP = sabrExtrapolation.ParameterDerivativeSabr;
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] abcPP = new double[4][3];
double[][] abcPP = RectangularArrays.ReturnRectangularDoubleArray(4, 3);
abcPP[0] = sabrExtrapolationAP.Parameter;
abcPP[1] = sabrExtrapolationBP.Parameter;
abcPP[2] = sabrExtrapolationRP.Parameter;
abcPP[3] = sabrExtrapolationNP.Parameter;
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] abcDPExpected = new double[4][3];
double[][] abcDPExpected = RectangularArrays.ReturnRectangularDoubleArray(4, 3);
for (int loopparam = 0; loopparam < 4; loopparam++)
{
for (int loopabc = 0; loopabc < 3; loopabc++)
{
abcDPExpected[loopparam][loopabc] = (abcPP[loopparam][loopabc] - abc[loopabc]) / shift;
assertEquals(1.0, abcDPExpected[loopparam][loopabc] / abcDP[loopparam][loopabc], 5.0E-2);
}
}
double priceOutExpected = sabrExtrapolation.price(option.Strike, option.PutCall);
double[] priceOutPP = new double[4];
priceOutPP[0] = sabrExtrapolationAP.price(option.Strike, option.PutCall);
priceOutPP[1] = sabrExtrapolationBP.price(option.Strike, option.PutCall);
priceOutPP[2] = sabrExtrapolationRP.price(option.Strike, option.PutCall);
priceOutPP[3] = sabrExtrapolationNP.price(option.Strike, option.PutCall);
ValueDerivatives resOut = sabrExtrapolation.priceAdjointSabr(option.Strike, option.PutCall);
double priceOut = resOut.Value;
double[] priceOutDsabr = resOut.Derivatives.toArray();
assertEquals(priceOutExpected, priceOut, 1E-5);
double[] priceOutDsabrExpected = new double[4];
for (int loopparam = 0; loopparam < 4; loopparam++)
{
priceOutDsabrExpected[loopparam] = (priceOutPP[loopparam] - priceOut) / shift;
assertEquals(1.0, priceOutDsabrExpected[loopparam] / priceOutDsabr[loopparam], 4.0E-4);
}
}
/// <summary>
/// Tests the price derivative with respect to forward for options in SABR model with extrapolation.
/// </summary>
public virtual void priceDerivativeSabrPut()
{
SabrExtrapolationRightFunction func = SabrExtrapolationRightFunction.of(FORWARD, SABR_DATA, CUT_OFF_STRIKE, TIME_TO_EXPIRY, MU, SabrHaganVolatilityFunctionProvider.DEFAULT);
double strikeIn = 0.08;
double strikeAt = CUT_OFF_STRIKE;
double strikeOut = 0.12;
EuropeanVanillaOption optionIn = EuropeanVanillaOption.of(strikeIn, TIME_TO_EXPIRY, PutCall.PUT);
EuropeanVanillaOption optionAt = EuropeanVanillaOption.of(strikeAt, TIME_TO_EXPIRY, PutCall.PUT);
EuropeanVanillaOption optionOut = EuropeanVanillaOption.of(strikeOut, TIME_TO_EXPIRY, PutCall.PUT);
double shift = 0.000001;
SabrFormulaData sabrDataAP = SabrFormulaData.of(ALPHA + shift, BETA, RHO, NU);
SabrFormulaData sabrDataBP = SabrFormulaData.of(ALPHA, BETA + shift, RHO, NU);
SabrFormulaData sabrDataRP = SabrFormulaData.of(ALPHA, BETA, RHO + shift, NU);
SabrFormulaData sabrDataNP = SabrFormulaData.of(ALPHA, BETA, RHO, NU + shift);
SabrExtrapolationRightFunction sabrExtrapolationAP = SabrExtrapolationRightFunction.of(FORWARD, TIME_TO_EXPIRY, sabrDataAP, CUT_OFF_STRIKE, MU);
SabrExtrapolationRightFunction sabrExtrapolationBP = SabrExtrapolationRightFunction.of(FORWARD, TIME_TO_EXPIRY, sabrDataBP, CUT_OFF_STRIKE, MU);
SabrExtrapolationRightFunction sabrExtrapolationRP = SabrExtrapolationRightFunction.of(FORWARD, TIME_TO_EXPIRY, sabrDataRP, CUT_OFF_STRIKE, MU);
SabrExtrapolationRightFunction sabrExtrapolationNP = SabrExtrapolationRightFunction.of(FORWARD, TIME_TO_EXPIRY, sabrDataNP, CUT_OFF_STRIKE, MU);
// Below cut-off strike
double priceInExpected = func.price(optionIn.Strike, optionIn.PutCall);
double[] priceInPP = new double[4];
priceInPP[0] = sabrExtrapolationAP.price(optionIn.Strike, optionIn.PutCall);
priceInPP[1] = sabrExtrapolationBP.price(optionIn.Strike, optionIn.PutCall);
priceInPP[2] = sabrExtrapolationRP.price(optionIn.Strike, optionIn.PutCall);
priceInPP[3] = sabrExtrapolationNP.price(optionIn.Strike, optionIn.PutCall);
ValueDerivatives resIn = func.priceAdjointSabr(optionIn.Strike, optionIn.PutCall);
double priceIn = resIn.Value;
double[] priceInDsabr = resIn.Derivatives.toArray();
assertEquals(priceInExpected, priceIn, TOLERANCE_PRICE);
double[] priceInDsabrExpected = new double[4];
for (int loopparam = 0; loopparam < 3; loopparam++)
{
priceInDsabrExpected[loopparam] = (priceInPP[loopparam] - priceIn) / shift;
assertEquals(priceInDsabrExpected[loopparam], priceInDsabr[loopparam], 1E-5);
}
// At cut-off strike
double priceAtExpected = func.price(optionAt.Strike, optionAt.PutCall);
double[] priceAtPP = new double[4];
priceAtPP[0] = sabrExtrapolationAP.price(optionAt.Strike, optionAt.PutCall);
priceAtPP[1] = sabrExtrapolationBP.price(optionAt.Strike, optionAt.PutCall);
priceAtPP[2] = sabrExtrapolationRP.price(optionAt.Strike, optionAt.PutCall);
priceAtPP[3] = sabrExtrapolationNP.price(optionAt.Strike, optionAt.PutCall);
ValueDerivatives resAt = func.priceAdjointSabr(optionAt.Strike, optionAt.PutCall);
double priceAt = resAt.Value;
double[] priceAtDsabr = resAt.Derivatives.toArray();
assertEquals(priceAtExpected, priceAt, TOLERANCE_PRICE);
double[] priceAtDsabrExpected = new double[4];
for (int loopparam = 0; loopparam < 3; loopparam++)
{
priceAtDsabrExpected[loopparam] = (priceAtPP[loopparam] - priceAt) / shift;
assertEquals(priceAtDsabrExpected[loopparam], priceAtDsabr[loopparam], 1E-5);
}
// Above cut-off strike
double priceOutExpected = func.price(optionOut.Strike, optionOut.PutCall);
double[] priceOutPP = new double[4];
priceOutPP[0] = sabrExtrapolationAP.price(optionOut.Strike, optionOut.PutCall);
priceOutPP[1] = sabrExtrapolationBP.price(optionOut.Strike, optionOut.PutCall);
priceOutPP[2] = sabrExtrapolationRP.price(optionOut.Strike, optionOut.PutCall);
priceOutPP[3] = sabrExtrapolationNP.price(optionOut.Strike, optionOut.PutCall);
ValueDerivatives resOut = func.priceAdjointSabr(optionOut.Strike, optionOut.PutCall);
double priceOut = resOut.Value;
double[] priceOutDsabr = resOut.Derivatives.toArray();
assertEquals(priceOutExpected, priceOut, TOLERANCE_PRICE);
double[] abc = func.Parameter;
double[][] abcDP = func.ParameterDerivativeSabr;
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] abcPP = new double[4][3];
double[][] abcPP = RectangularArrays.ReturnRectangularDoubleArray(4, 3);
abcPP[0] = sabrExtrapolationAP.Parameter;
abcPP[1] = sabrExtrapolationBP.Parameter;
abcPP[2] = sabrExtrapolationRP.Parameter;
abcPP[3] = sabrExtrapolationNP.Parameter;
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] abcDPExpected = new double[4][3];
double[][] abcDPExpected = RectangularArrays.ReturnRectangularDoubleArray(4, 3);
for (int loopparam = 0; loopparam < 4; loopparam++)
{
for (int loopabc = 0; loopabc < 3; loopabc++)
{
abcDPExpected[loopparam][loopabc] = (abcPP[loopparam][loopabc] - abc[loopabc]) / shift;
assertEquals(1.0, abcDPExpected[loopparam][loopabc] / abcDP[loopparam][loopabc], 5.0E-2);
}
}
double[] priceOutDsabrExpected = new double[4];
for (int loopparam = 0; loopparam < 4; loopparam++)
{
priceOutDsabrExpected[loopparam] = (priceOutPP[loopparam] - priceOut) / shift;
assertEquals(1.0, priceOutDsabrExpected[loopparam] / priceOutDsabr[loopparam], 4.0E-4);
}
}