@Test
/**
* Tests the 'In-Out Parity' condition: Without rebates, the price of a Knock-In plus a Knock-Out
* of arbitrary barrier level must equal that of the underlying vanilla option
*/
public void inOutParityWithoutRebate() {
// Vanilla
final Function1D<BlackFunctionData, Double> fcnVanillaCall =
BLACK_FUNCTION.getPriceFunction(VANILLA_CALL_K100);
final double pxVanillaCall = fcnVanillaCall.evaluate(DATA_BLACK);
// Barriers without rebate
final double noRebate = 0.0;
final double priceDownIn =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
noRebate,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
final double priceDownOut =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
noRebate,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Knock In-Out Parity fails", 1.0, pxVanillaCall / (priceDownIn + priceDownOut), 1.e-6);
}
@Test
/**
* Tests the 'In-Out Parity' condition: Knock-In's pay rebate at maturity if barrier isn't hit.
* Knock-Out pays at moment barrier is hit. The discounting issue can be sidestepped by setting
* rates to 0.
*/
public void inOutParityWithRebate() {
// Vanilla
final Function1D<BlackFunctionData, Double> fcnVanillaCall =
BLACK_FUNCTION.getPriceFunction(VANILLA_CALL_K100);
final BlackFunctionData zeroRatesMarket = new BlackFunctionData(SPOT, 1.0, VOLATILITY);
final double pxVanillaCall = fcnVanillaCall.evaluate(zeroRatesMarket);
// Barriers with rebate
final double priceDownInRebate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, SPOT, 0.0, 0.0, VOLATILITY);
final double priceDownOutRebate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_OUT, REBATE, SPOT, 0.0, 0.0, VOLATILITY);
assertEquals(
"Knock In-Out Parity fails",
1.0,
(pxVanillaCall + REBATE) / (priceDownInRebate + priceDownOutRebate),
1.e-6);
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void exceptionUp() {
final Barrier barrierUp =
new Barrier(KnockType.IN, BarrierType.UP, ObservationType.CONTINUOUS, 90);
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, barrierUp, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
}
@Test
/** Tests the adjoint implementation (with computation of the derivatives). */
public void adjointDerivatives() {
final double shiftSpot = 0.001;
final double shiftRate = 1.0E-8;
final double shiftCoC = 1.0E-8;
final double shiftVol = 1.0E-8;
final double[] derivatives = new double[5];
// DOWN-IN
final double priceDI =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
final double priceDISpot =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT + shiftSpot,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint spot derivative - Down In",
(priceDISpot - priceDI) / shiftSpot,
derivatives[0],
1.0E-5);
final double priceDIRate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM + shiftRate,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint rate derivative - Down In",
(priceDIRate - priceDI) / shiftRate,
derivatives[2],
1.0E-5);
final double priceDICoC =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY + shiftCoC,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Down In",
(priceDICoC - priceDI) / shiftCoC,
derivatives[3],
1.0E-5);
final double priceDIVol =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY + shiftVol);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Down In",
(priceDIVol - priceDI) / shiftVol,
derivatives[4],
1.0E-4);
// DOWN-OUT
final double priceDO =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
final double priceDOSpot =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT + shiftSpot,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint spot derivative - Down Out",
(priceDOSpot - priceDO) / shiftSpot,
derivatives[0],
2.0E-4);
final double priceDORate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM + shiftRate,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint rate derivative - Down Out",
(priceDORate - priceDO) / shiftRate,
derivatives[2],
1.0E-5);
final double priceDOCoC =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY + shiftCoC,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Down Out",
(priceDOCoC - priceDO) / shiftCoC,
derivatives[3],
1.0E-4);
final double priceDOVol =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY + shiftVol);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Down Out",
(priceDOVol - priceDO) / shiftVol,
derivatives[4],
1.0E-4);
// UP-IN
final double priceUI =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
final double priceUISpot =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT + shiftSpot,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint spot derivative - Up In",
(priceUISpot - priceUI) / shiftSpot,
derivatives[0],
2.0E-4);
final double priceUIRate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM + shiftRate,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint rate derivative - Up In",
(priceUIRate - priceUI) / shiftRate,
derivatives[2],
1.0E-5);
final double priceUICoC =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY + shiftCoC,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Up In",
(priceUICoC - priceUI) / shiftCoC,
derivatives[3],
1.0E-4);
final double priceUIVol =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY + shiftVol);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Up In",
(priceUIVol - priceUI) / shiftVol,
derivatives[4],
1.0E-5);
// UP-OUT
final double priceUO =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
final double priceUOSpot =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT + shiftSpot,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint spot derivative - Up Out",
(priceUOSpot - priceUO) / shiftSpot,
derivatives[0],
1.0E-4);
final double priceUORate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM + shiftRate,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint rate derivative - Up Out",
(priceUORate - priceUO) / shiftRate,
derivatives[2],
1.0E-5);
final double priceUOCoC =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY + shiftCoC,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Up Out",
(priceUOCoC - priceUO) / shiftCoC,
derivatives[3],
1.0E-5);
final double priceUOVol =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY + shiftVol);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Up Out",
(priceUOVol - priceUO) / shiftVol,
derivatives[4],
2.0E-5);
}
@Test
/** Tests the adjoint implementation (with computation of the derivatives). */
public void adjointPrice() {
final double[] derivatives = new double[5];
final double priceDI =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final double priceDIAdjoint =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
assertEquals("Black single barrier: Adjoint price Down In", priceDI, priceDIAdjoint, 1.0E-10);
final double priceDO =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_OUT, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final double priceDOAdjoint =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
assertEquals("Black single barrier: Adjoint price Down Out", priceDO, priceDOAdjoint, 1.0E-10);
final double priceUI =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final double priceUIAdjoint =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
assertEquals("Black single barrier: Adjoint price Up In", priceUI, priceUIAdjoint, 1.0E-10);
final double priceUO =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_OUT, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final double priceUOAdjoint =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
assertEquals("Black single barrier: Adjoint price Up Out", priceUO, priceUOAdjoint, 1.0E-10);
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void exceptionDown() {
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, 85.0, COST_OF_CARRY, RATE_DOM, VOLATILITY);
}
@Test
/**
* Tests the comparison with the other implementation. This test may be removed when only one
* version remains.
*/
public void comparison() {
final AnalyticOptionModel<EuropeanStandardBarrierOptionDefinition, StandardOptionDataBundle>
model = new EuropeanStandardBarrierOptionModel();
final StandardOptionDataBundle data =
new StandardOptionDataBundle(
YieldCurve.from(ConstantDoublesCurve.from(RATE_DOM)),
COST_OF_CARRY,
new VolatilitySurface(ConstantDoublesSurface.from(VOLATILITY)),
SPOT,
REFERENCE_DATE);
final Expiry expiry = new Expiry(EXPIRY_DATE);
final double priceDI1 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final EuropeanStandardBarrierOptionDefinition optionBarrierDI =
new EuropeanStandardBarrierOptionDefinition(
STRIKE_MID, expiry, IS_CALL, BARRIER_DOWN_IN, REBATE);
final double priceDI2 = model.getPricingFunction(optionBarrierDI).evaluate(data);
assertEquals("Comparison Down In", priceDI2, priceDI1, 1.0E-10);
final double priceDO1 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_OUT, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final EuropeanStandardBarrierOptionDefinition optionBarrierDO =
new EuropeanStandardBarrierOptionDefinition(
STRIKE_MID, expiry, IS_CALL, BARRIER_DOWN_OUT, REBATE);
final double priceDO2 = model.getPricingFunction(optionBarrierDO).evaluate(data);
assertEquals("Comparison Down Out", priceDO2, priceDO1, 1.0E-10);
final double priceUI1 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final EuropeanStandardBarrierOptionDefinition optionBarrierUI =
new EuropeanStandardBarrierOptionDefinition(
STRIKE_MID, expiry, IS_CALL, BARRIER_UP_IN, REBATE);
final double priceUI2 = model.getPricingFunction(optionBarrierUI).evaluate(data);
assertEquals("Comparison Up In", priceUI2, priceUI1, 1.0E-10);
final double priceUO1 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_OUT, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final EuropeanStandardBarrierOptionDefinition optionBarrierUO =
new EuropeanStandardBarrierOptionDefinition(
STRIKE_MID, expiry, IS_CALL, BARRIER_UP_OUT, REBATE);
final double priceUO2 = model.getPricingFunction(optionBarrierUO).evaluate(data);
assertEquals("Comparison Up Out", priceUO2, priceUO1, 1.0E-10);
final double vol0 = 0.0;
final double priceVol01 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, vol0);
final StandardOptionDataBundle data0 =
new StandardOptionDataBundle(
YieldCurve.from(ConstantDoublesCurve.from(RATE_DOM)),
COST_OF_CARRY,
new VolatilitySurface(ConstantDoublesSurface.from(vol0)),
SPOT,
REFERENCE_DATE);
final double priceVol02 = model.getPricingFunction(optionBarrierDI).evaluate(data0);
assertEquals(priceVol02, priceVol01, 1.0E-10);
}
public class BlackBarrierPriceFunctionTest {
private static final ZonedDateTime REFERENCE_DATE = DateUtils.getUTCDate(2011, 7, 1);
private static final ZonedDateTime EXPIRY_DATE = DateUtils.getUTCDate(2015, 1, 2);
private static final double EXPIRY_TIME =
DateUtils.getDifferenceInYears(REFERENCE_DATE, EXPIRY_DATE);
private static final double STRIKE_MID = 100;
private static final double STRIKE_HIGH = 120;
private static final boolean IS_CALL = true;
private static final EuropeanVanillaOption VANILLA_CALL_K100 =
new EuropeanVanillaOption(STRIKE_MID, EXPIRY_TIME, IS_CALL);
private static final EuropeanVanillaOption VANILLA_PUT_K100 =
new EuropeanVanillaOption(STRIKE_MID, EXPIRY_TIME, !IS_CALL);
private static final EuropeanVanillaOption VANILLA_CALL_KHI =
new EuropeanVanillaOption(STRIKE_HIGH, EXPIRY_TIME, IS_CALL);
private static final EuropeanVanillaOption VANILLA_PUT_KHI =
new EuropeanVanillaOption(STRIKE_HIGH, EXPIRY_TIME, !IS_CALL);
private static final Barrier BARRIER_DOWN_IN =
new Barrier(KnockType.IN, BarrierType.DOWN, ObservationType.CONTINUOUS, 90);
private static final Barrier BARRIER_DOWN_OUT =
new Barrier(KnockType.OUT, BarrierType.DOWN, ObservationType.CONTINUOUS, 90);
private static final Barrier BARRIER_UP_IN =
new Barrier(KnockType.IN, BarrierType.UP, ObservationType.CONTINUOUS, 110);
private static final Barrier BARRIER_UP_OUT =
new Barrier(KnockType.OUT, BarrierType.UP, ObservationType.CONTINUOUS, 110);
private static final double REBATE = 2;
private static final double SPOT = 105;
private static final double RATE_DOM = 0.05; // Domestic rate
private static final double RATE_FOR = 0.02; // Foreign rate
private static final double COST_OF_CARRY = RATE_DOM - RATE_FOR; // Domestic - Foreign rate
private static final double VOLATILITY = 0.20;
private static final BlackBarrierPriceFunction BARRIER_FUNCTION =
BlackBarrierPriceFunction.getInstance();
private static final double DF_FOR = Math.exp(-RATE_FOR * EXPIRY_TIME); // 'Base Ccy
private static final double DF_DOM = Math.exp(-RATE_DOM * EXPIRY_TIME); // 'Quote Ccy
private static final double FWD_FX = SPOT * DF_FOR / DF_DOM;
private static final BlackFunctionData DATA_BLACK =
new BlackFunctionData(FWD_FX, DF_DOM, VOLATILITY);
private static final BlackPriceFunction BLACK_FUNCTION = new BlackPriceFunction();
@Test
/**
* Tests the 'In-Out Parity' condition: Without rebates, the price of a Knock-In plus a Knock-Out
* of arbitrary barrier level must equal that of the underlying vanilla option
*/
public void inOutParityWithoutRebate() {
// Vanilla
final Function1D<BlackFunctionData, Double> fcnVanillaCall =
BLACK_FUNCTION.getPriceFunction(VANILLA_CALL_K100);
final double pxVanillaCall = fcnVanillaCall.evaluate(DATA_BLACK);
// Barriers without rebate
final double noRebate = 0.0;
final double priceDownIn =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
noRebate,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
final double priceDownOut =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
noRebate,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Knock In-Out Parity fails", 1.0, pxVanillaCall / (priceDownIn + priceDownOut), 1.e-6);
}
@Test
/**
* Tests the 'In-Out Parity' condition: Knock-In's pay rebate at maturity if barrier isn't hit.
* Knock-Out pays at moment barrier is hit. The discounting issue can be sidestepped by setting
* rates to 0.
*/
public void inOutParityWithRebate() {
// Vanilla
final Function1D<BlackFunctionData, Double> fcnVanillaCall =
BLACK_FUNCTION.getPriceFunction(VANILLA_CALL_K100);
final BlackFunctionData zeroRatesMarket = new BlackFunctionData(SPOT, 1.0, VOLATILITY);
final double pxVanillaCall = fcnVanillaCall.evaluate(zeroRatesMarket);
// Barriers with rebate
final double priceDownInRebate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, SPOT, 0.0, 0.0, VOLATILITY);
final double priceDownOutRebate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_OUT, REBATE, SPOT, 0.0, 0.0, VOLATILITY);
assertEquals(
"Knock In-Out Parity fails",
1.0,
(pxVanillaCall + REBATE) / (priceDownInRebate + priceDownOutRebate),
1.e-6);
}
@Test
/**
* Tests the 'In-Out Parity' condition: The price of a Knock-In plus a Knock-Out of arbitrary
* barrier level must equal that of the underlying vanilla option + value of the rebate
*/
public void inOutParityMorePathsWithRebate() {
// Market with zero rates, domestic and foreign
final BlackFunctionData zeroRatesMarket = new BlackFunctionData(SPOT, 1.0, VOLATILITY);
final double rateDomestic = 0.0;
final double rateForeign = 0.0;
final double costOfCarry = rateDomestic - rateForeign;
// Rebate
final double pxRebate = REBATE;
// 2 - Vanillas - Call and Put
final Function1D<BlackFunctionData, Double> fcnVanillaCall =
BLACK_FUNCTION.getPriceFunction(VANILLA_CALL_K100);
final double pxVanillaCall = fcnVanillaCall.evaluate(zeroRatesMarket);
final Function1D<BlackFunctionData, Double> fcnVanillaPut =
BLACK_FUNCTION.getPriceFunction(VANILLA_PUT_K100);
final double pxVanillaPut = fcnVanillaPut.evaluate(zeroRatesMarket);
// Barriers: Up and Down, Call and Put, In and Out
final double pxDownInCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
costOfCarry,
rateDomestic,
VOLATILITY);
final double pxDownOutCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
costOfCarry,
rateDomestic,
VOLATILITY);
assertEquals(
"Knock In-Out Parity fails",
1.0,
(pxVanillaCall + pxRebate) / (pxDownInCall + pxDownOutCall),
1.e-6);
// assertTrue("Knock In-Out Parity fails", Math.abs((pxVanillaCall + pxRebate) / (pxDownInCall +
// pxDownOutCall) - 1) < 1.e-6);
final double pxDownInPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100, BARRIER_DOWN_IN, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
final double pxDownOutPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
costOfCarry,
rateDomestic,
VOLATILITY);
assertTrue(
"Knock In-Out Parity fails",
Math.abs((pxVanillaPut + pxRebate) / (pxDownInPut + pxDownOutPut) - 1) < 1.e-6);
final double pxUpInCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_IN, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
final double pxUpOutCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_OUT, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
assertTrue(
"Knock In-Out Parity fails",
Math.abs((pxVanillaCall + pxRebate) / (pxUpInCall + pxUpOutCall) - 1) < 1.e-6);
final double pxUpInPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100, BARRIER_UP_IN, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
final double pxUpOutPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100, BARRIER_UP_OUT, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
assertTrue(
"Knock In-Out Parity fails",
Math.abs((pxVanillaPut + pxRebate) / (pxUpInPut + pxUpOutPut) - 1) < 1.e-6);
// Let's try the Up case with Barrier < Strike. To do this, I create a new vanilla with K120 (>
// Barrier110)
final Function1D<BlackFunctionData, Double> fcnVanillaPutHiK =
BLACK_FUNCTION.getPriceFunction(VANILLA_PUT_KHI);
final double pxVanillaPutHiK = fcnVanillaPutHiK.evaluate(zeroRatesMarket);
final double pxUpInPutHiK =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_KHI, BARRIER_UP_IN, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
final double pxUpOutPutHiK =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_KHI, BARRIER_UP_OUT, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
assertTrue(
"Knock In-Out Parity fails",
Math.abs((pxVanillaPutHiK + pxRebate) / (pxUpInPutHiK + pxUpOutPutHiK) - 1) < 1.e-6);
}
@Test
/**
* Tests the 'In-Out Parity' condition: The price of a Knock-In plus a Knock-Out of arbitrary
* barrier level must equal that of the underlying vanilla option + value of the rebate
*/
public void impossibleToHitBarrierIsVanilla() {
final Barrier veryLowKnockIn =
new Barrier(KnockType.IN, BarrierType.DOWN, ObservationType.CONTINUOUS, 1e-6);
final Barrier veryLowKnockOut =
new Barrier(KnockType.OUT, BarrierType.DOWN, ObservationType.CONTINUOUS, 1e-6);
final Barrier veryHighKnockIn =
new Barrier(KnockType.IN, BarrierType.UP, ObservationType.CONTINUOUS, 1e6);
final Barrier veryHighKnockOut =
new Barrier(KnockType.OUT, BarrierType.UP, ObservationType.CONTINUOUS, 1e6);
final double pxRebate = DF_DOM * REBATE;
final Function1D<BlackFunctionData, Double> fcnVanillaCall =
BLACK_FUNCTION.getPriceFunction(VANILLA_CALL_K100);
final double pxVanillaCall = fcnVanillaCall.evaluate(DATA_BLACK);
// KnockIn's with impossible to reach barrier's are guaranteed to pay the rebate at maturity
final double pxDownInPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100, veryLowKnockIn, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
assertTrue("VeryLowKnockInBarrier doesn't match rebate", pxDownInPut / pxRebate - 1 < 1e-6);
final double pxDownInCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, veryLowKnockIn, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
assertTrue("VeryLowKnockInBarrier doesn't match rebate", pxDownInCall / pxRebate - 1 < 1e-6);
final double pxUpInCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, veryHighKnockIn, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
assertTrue("VeryHighKnockInBarrier doesn't match rebate", pxUpInCall / pxRebate - 1 < 1e-6);
// KnockOut's with impossible to reach barrier's are guaranteed to pay the value of the
// underlying vanilla
final double pxDownOutCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, veryLowKnockOut, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
assertTrue(
"VeryLowKnockInBarrier doesn't match rebate",
Math.abs(pxDownOutCall / pxVanillaCall - 1) < 1e-6);
// Derivatives
final double[] derivs = new double[5];
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
veryLowKnockIn,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivs);
assertTrue(
"Impossible KnockIn: rate sens is incorrect",
derivs[2] / Math.abs((-1 * EXPIRY_TIME * DF_DOM * REBATE) - 1) < 1e-6);
assertEquals(
"Impossible KnockIn: Encountered derivative, other than d/dr, != 0",
0.0,
derivs[0] + derivs[1] + derivs[3] + derivs[4],
1.0e-6);
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
veryHighKnockIn,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivs);
assertTrue(
"Impossible KnockIn: rate sens is incorrect",
derivs[2] / Math.abs((-1 * EXPIRY_TIME * DF_DOM * REBATE) - 1) < 1e-6);
assertEquals(
"Impossible KnockIn: Encountered derivative, other than d/dr, != 0",
0.0,
derivs[0] + derivs[1] + derivs[3] + derivs[4],
1.0e-6);
// Barrier: [0] spot, [1] strike, [2] rate, [3] cost-of-carry, [4] volatility.
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
veryLowKnockOut,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivs);
// Vanilla: [0] the price, [1] the derivative with respect to the forward, [2] the derivative
// with respect to the volatility and [3] the derivative with respect to the strike.
final double[] vanillaDerivs = BLACK_FUNCTION.getPriceAdjoint(VANILLA_CALL_K100, DATA_BLACK);
assertEquals(
"Impossible KnockOut: Vega doesn't match vanilla", vanillaDerivs[2], derivs[4], 1e-6);
assertEquals(
"Impossible KnockOut: Dual Delta (d/dK) doesn't match vanilla",
vanillaDerivs[3],
derivs[1],
1e-6);
assertEquals(
"Impossible KnockOut: Delta doesn't match vanilla",
vanillaDerivs[1] * DF_FOR / DF_DOM,
derivs[0],
1e-6);
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
veryHighKnockOut,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivs);
assertEquals(
"Impossible KnockOut: Vega doesn't match vanilla", vanillaDerivs[2], derivs[4], 1e-6);
assertEquals(
"Impossible KnockOut: Dual Delta (d/dK) doesn't match vanilla",
vanillaDerivs[3],
derivs[1],
1e-6);
assertEquals(
"Impossible KnockOut: Delta doesn't match vanilla",
vanillaDerivs[1] * DF_FOR / DF_DOM,
derivs[0],
1e-6);
}
@Test
/**
* Tests the comparison with the other implementation. This test may be removed when only one
* version remains.
*/
public void comparison() {
final AnalyticOptionModel<EuropeanStandardBarrierOptionDefinition, StandardOptionDataBundle>
model = new EuropeanStandardBarrierOptionModel();
final StandardOptionDataBundle data =
new StandardOptionDataBundle(
YieldCurve.from(ConstantDoublesCurve.from(RATE_DOM)),
COST_OF_CARRY,
new VolatilitySurface(ConstantDoublesSurface.from(VOLATILITY)),
SPOT,
REFERENCE_DATE);
final Expiry expiry = new Expiry(EXPIRY_DATE);
final double priceDI1 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final EuropeanStandardBarrierOptionDefinition optionBarrierDI =
new EuropeanStandardBarrierOptionDefinition(
STRIKE_MID, expiry, IS_CALL, BARRIER_DOWN_IN, REBATE);
final double priceDI2 = model.getPricingFunction(optionBarrierDI).evaluate(data);
assertEquals("Comparison Down In", priceDI2, priceDI1, 1.0E-10);
final double priceDO1 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_OUT, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final EuropeanStandardBarrierOptionDefinition optionBarrierDO =
new EuropeanStandardBarrierOptionDefinition(
STRIKE_MID, expiry, IS_CALL, BARRIER_DOWN_OUT, REBATE);
final double priceDO2 = model.getPricingFunction(optionBarrierDO).evaluate(data);
assertEquals("Comparison Down Out", priceDO2, priceDO1, 1.0E-10);
final double priceUI1 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final EuropeanStandardBarrierOptionDefinition optionBarrierUI =
new EuropeanStandardBarrierOptionDefinition(
STRIKE_MID, expiry, IS_CALL, BARRIER_UP_IN, REBATE);
final double priceUI2 = model.getPricingFunction(optionBarrierUI).evaluate(data);
assertEquals("Comparison Up In", priceUI2, priceUI1, 1.0E-10);
final double priceUO1 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_OUT, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final EuropeanStandardBarrierOptionDefinition optionBarrierUO =
new EuropeanStandardBarrierOptionDefinition(
STRIKE_MID, expiry, IS_CALL, BARRIER_UP_OUT, REBATE);
final double priceUO2 = model.getPricingFunction(optionBarrierUO).evaluate(data);
assertEquals("Comparison Up Out", priceUO2, priceUO1, 1.0E-10);
final double vol0 = 0.0;
final double priceVol01 =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, vol0);
final StandardOptionDataBundle data0 =
new StandardOptionDataBundle(
YieldCurve.from(ConstantDoublesCurve.from(RATE_DOM)),
COST_OF_CARRY,
new VolatilitySurface(ConstantDoublesSurface.from(vol0)),
SPOT,
REFERENCE_DATE);
final double priceVol02 = model.getPricingFunction(optionBarrierDI).evaluate(data0);
assertEquals(priceVol02, priceVol01, 1.0E-10);
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void exceptionDown() {
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, 85.0, COST_OF_CARRY, RATE_DOM, VOLATILITY);
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void exceptionUp() {
final Barrier barrierUp =
new Barrier(KnockType.IN, BarrierType.UP, ObservationType.CONTINUOUS, 90);
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, barrierUp, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
}
@Test
/** Tests the adjoint implementation (with computation of the derivatives). */
public void adjointPrice() {
final double[] derivatives = new double[5];
final double priceDI =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final double priceDIAdjoint =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
assertEquals("Black single barrier: Adjoint price Down In", priceDI, priceDIAdjoint, 1.0E-10);
final double priceDO =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_DOWN_OUT, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final double priceDOAdjoint =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
assertEquals("Black single barrier: Adjoint price Down Out", priceDO, priceDOAdjoint, 1.0E-10);
final double priceUI =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_IN, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final double priceUIAdjoint =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
assertEquals("Black single barrier: Adjoint price Up In", priceUI, priceUIAdjoint, 1.0E-10);
final double priceUO =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_OUT, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
final double priceUOAdjoint =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
assertEquals("Black single barrier: Adjoint price Up Out", priceUO, priceUOAdjoint, 1.0E-10);
}
@Test
/** Tests the adjoint implementation (with computation of the derivatives). */
public void adjointDerivatives() {
final double shiftSpot = 0.001;
final double shiftRate = 1.0E-8;
final double shiftCoC = 1.0E-8;
final double shiftVol = 1.0E-8;
final double[] derivatives = new double[5];
// DOWN-IN
final double priceDI =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
final double priceDISpot =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT + shiftSpot,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint spot derivative - Down In",
(priceDISpot - priceDI) / shiftSpot,
derivatives[0],
1.0E-5);
final double priceDIRate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM + shiftRate,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint rate derivative - Down In",
(priceDIRate - priceDI) / shiftRate,
derivatives[2],
1.0E-5);
final double priceDICoC =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY + shiftCoC,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Down In",
(priceDICoC - priceDI) / shiftCoC,
derivatives[3],
1.0E-5);
final double priceDIVol =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY + shiftVol);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Down In",
(priceDIVol - priceDI) / shiftVol,
derivatives[4],
1.0E-4);
// DOWN-OUT
final double priceDO =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
final double priceDOSpot =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT + shiftSpot,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint spot derivative - Down Out",
(priceDOSpot - priceDO) / shiftSpot,
derivatives[0],
2.0E-4);
final double priceDORate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM + shiftRate,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint rate derivative - Down Out",
(priceDORate - priceDO) / shiftRate,
derivatives[2],
1.0E-5);
final double priceDOCoC =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY + shiftCoC,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Down Out",
(priceDOCoC - priceDO) / shiftCoC,
derivatives[3],
1.0E-4);
final double priceDOVol =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY + shiftVol);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Down Out",
(priceDOVol - priceDO) / shiftVol,
derivatives[4],
1.0E-4);
// UP-IN
final double priceUI =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
final double priceUISpot =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT + shiftSpot,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint spot derivative - Up In",
(priceUISpot - priceUI) / shiftSpot,
derivatives[0],
2.0E-4);
final double priceUIRate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM + shiftRate,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint rate derivative - Up In",
(priceUIRate - priceUI) / shiftRate,
derivatives[2],
1.0E-5);
final double priceUICoC =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY + shiftCoC,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Up In",
(priceUICoC - priceUI) / shiftCoC,
derivatives[3],
1.0E-4);
final double priceUIVol =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_IN,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY + shiftVol);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Up In",
(priceUIVol - priceUI) / shiftVol,
derivatives[4],
1.0E-5);
// UP-OUT
final double priceUO =
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivatives);
final double priceUOSpot =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT + shiftSpot,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint spot derivative - Up Out",
(priceUOSpot - priceUO) / shiftSpot,
derivatives[0],
1.0E-4);
final double priceUORate =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM + shiftRate,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint rate derivative - Up Out",
(priceUORate - priceUO) / shiftRate,
derivatives[2],
1.0E-5);
final double priceUOCoC =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY + shiftCoC,
RATE_DOM,
VOLATILITY);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Up Out",
(priceUOCoC - priceUO) / shiftCoC,
derivatives[3],
1.0E-5);
final double priceUOVol =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_UP_OUT,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY + shiftVol);
assertEquals(
"Black single barrier: Adjoint cost-of-carry derivative - Up Out",
(priceUOVol - priceUO) / shiftVol,
derivatives[4],
2.0E-5);
}
}
@Test
/**
* Tests the 'In-Out Parity' condition: The price of a Knock-In plus a Knock-Out of arbitrary
* barrier level must equal that of the underlying vanilla option + value of the rebate
*/
public void impossibleToHitBarrierIsVanilla() {
final Barrier veryLowKnockIn =
new Barrier(KnockType.IN, BarrierType.DOWN, ObservationType.CONTINUOUS, 1e-6);
final Barrier veryLowKnockOut =
new Barrier(KnockType.OUT, BarrierType.DOWN, ObservationType.CONTINUOUS, 1e-6);
final Barrier veryHighKnockIn =
new Barrier(KnockType.IN, BarrierType.UP, ObservationType.CONTINUOUS, 1e6);
final Barrier veryHighKnockOut =
new Barrier(KnockType.OUT, BarrierType.UP, ObservationType.CONTINUOUS, 1e6);
final double pxRebate = DF_DOM * REBATE;
final Function1D<BlackFunctionData, Double> fcnVanillaCall =
BLACK_FUNCTION.getPriceFunction(VANILLA_CALL_K100);
final double pxVanillaCall = fcnVanillaCall.evaluate(DATA_BLACK);
// KnockIn's with impossible to reach barrier's are guaranteed to pay the rebate at maturity
final double pxDownInPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100, veryLowKnockIn, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
assertTrue("VeryLowKnockInBarrier doesn't match rebate", pxDownInPut / pxRebate - 1 < 1e-6);
final double pxDownInCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, veryLowKnockIn, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
assertTrue("VeryLowKnockInBarrier doesn't match rebate", pxDownInCall / pxRebate - 1 < 1e-6);
final double pxUpInCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, veryHighKnockIn, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
assertTrue("VeryHighKnockInBarrier doesn't match rebate", pxUpInCall / pxRebate - 1 < 1e-6);
// KnockOut's with impossible to reach barrier's are guaranteed to pay the value of the
// underlying vanilla
final double pxDownOutCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, veryLowKnockOut, REBATE, SPOT, COST_OF_CARRY, RATE_DOM, VOLATILITY);
assertTrue(
"VeryLowKnockInBarrier doesn't match rebate",
Math.abs(pxDownOutCall / pxVanillaCall - 1) < 1e-6);
// Derivatives
final double[] derivs = new double[5];
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
veryLowKnockIn,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivs);
assertTrue(
"Impossible KnockIn: rate sens is incorrect",
derivs[2] / Math.abs((-1 * EXPIRY_TIME * DF_DOM * REBATE) - 1) < 1e-6);
assertEquals(
"Impossible KnockIn: Encountered derivative, other than d/dr, != 0",
0.0,
derivs[0] + derivs[1] + derivs[3] + derivs[4],
1.0e-6);
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
veryHighKnockIn,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivs);
assertTrue(
"Impossible KnockIn: rate sens is incorrect",
derivs[2] / Math.abs((-1 * EXPIRY_TIME * DF_DOM * REBATE) - 1) < 1e-6);
assertEquals(
"Impossible KnockIn: Encountered derivative, other than d/dr, != 0",
0.0,
derivs[0] + derivs[1] + derivs[3] + derivs[4],
1.0e-6);
// Barrier: [0] spot, [1] strike, [2] rate, [3] cost-of-carry, [4] volatility.
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
veryLowKnockOut,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivs);
// Vanilla: [0] the price, [1] the derivative with respect to the forward, [2] the derivative
// with respect to the volatility and [3] the derivative with respect to the strike.
final double[] vanillaDerivs = BLACK_FUNCTION.getPriceAdjoint(VANILLA_CALL_K100, DATA_BLACK);
assertEquals(
"Impossible KnockOut: Vega doesn't match vanilla", vanillaDerivs[2], derivs[4], 1e-6);
assertEquals(
"Impossible KnockOut: Dual Delta (d/dK) doesn't match vanilla",
vanillaDerivs[3],
derivs[1],
1e-6);
assertEquals(
"Impossible KnockOut: Delta doesn't match vanilla",
vanillaDerivs[1] * DF_FOR / DF_DOM,
derivs[0],
1e-6);
BARRIER_FUNCTION.getPriceAdjoint(
VANILLA_CALL_K100,
veryHighKnockOut,
REBATE,
SPOT,
COST_OF_CARRY,
RATE_DOM,
VOLATILITY,
derivs);
assertEquals(
"Impossible KnockOut: Vega doesn't match vanilla", vanillaDerivs[2], derivs[4], 1e-6);
assertEquals(
"Impossible KnockOut: Dual Delta (d/dK) doesn't match vanilla",
vanillaDerivs[3],
derivs[1],
1e-6);
assertEquals(
"Impossible KnockOut: Delta doesn't match vanilla",
vanillaDerivs[1] * DF_FOR / DF_DOM,
derivs[0],
1e-6);
}
@Test
/**
* Tests the 'In-Out Parity' condition: The price of a Knock-In plus a Knock-Out of arbitrary
* barrier level must equal that of the underlying vanilla option + value of the rebate
*/
public void inOutParityMorePathsWithRebate() {
// Market with zero rates, domestic and foreign
final BlackFunctionData zeroRatesMarket = new BlackFunctionData(SPOT, 1.0, VOLATILITY);
final double rateDomestic = 0.0;
final double rateForeign = 0.0;
final double costOfCarry = rateDomestic - rateForeign;
// Rebate
final double pxRebate = REBATE;
// 2 - Vanillas - Call and Put
final Function1D<BlackFunctionData, Double> fcnVanillaCall =
BLACK_FUNCTION.getPriceFunction(VANILLA_CALL_K100);
final double pxVanillaCall = fcnVanillaCall.evaluate(zeroRatesMarket);
final Function1D<BlackFunctionData, Double> fcnVanillaPut =
BLACK_FUNCTION.getPriceFunction(VANILLA_PUT_K100);
final double pxVanillaPut = fcnVanillaPut.evaluate(zeroRatesMarket);
// Barriers: Up and Down, Call and Put, In and Out
final double pxDownInCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_IN,
REBATE,
SPOT,
costOfCarry,
rateDomestic,
VOLATILITY);
final double pxDownOutCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
costOfCarry,
rateDomestic,
VOLATILITY);
assertEquals(
"Knock In-Out Parity fails",
1.0,
(pxVanillaCall + pxRebate) / (pxDownInCall + pxDownOutCall),
1.e-6);
// assertTrue("Knock In-Out Parity fails", Math.abs((pxVanillaCall + pxRebate) / (pxDownInCall +
// pxDownOutCall) - 1) < 1.e-6);
final double pxDownInPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100, BARRIER_DOWN_IN, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
final double pxDownOutPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100,
BARRIER_DOWN_OUT,
REBATE,
SPOT,
costOfCarry,
rateDomestic,
VOLATILITY);
assertTrue(
"Knock In-Out Parity fails",
Math.abs((pxVanillaPut + pxRebate) / (pxDownInPut + pxDownOutPut) - 1) < 1.e-6);
final double pxUpInCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_IN, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
final double pxUpOutCall =
BARRIER_FUNCTION.getPrice(
VANILLA_CALL_K100, BARRIER_UP_OUT, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
assertTrue(
"Knock In-Out Parity fails",
Math.abs((pxVanillaCall + pxRebate) / (pxUpInCall + pxUpOutCall) - 1) < 1.e-6);
final double pxUpInPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100, BARRIER_UP_IN, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
final double pxUpOutPut =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_K100, BARRIER_UP_OUT, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
assertTrue(
"Knock In-Out Parity fails",
Math.abs((pxVanillaPut + pxRebate) / (pxUpInPut + pxUpOutPut) - 1) < 1.e-6);
// Let's try the Up case with Barrier < Strike. To do this, I create a new vanilla with K120 (>
// Barrier110)
final Function1D<BlackFunctionData, Double> fcnVanillaPutHiK =
BLACK_FUNCTION.getPriceFunction(VANILLA_PUT_KHI);
final double pxVanillaPutHiK = fcnVanillaPutHiK.evaluate(zeroRatesMarket);
final double pxUpInPutHiK =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_KHI, BARRIER_UP_IN, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
final double pxUpOutPutHiK =
BARRIER_FUNCTION.getPrice(
VANILLA_PUT_KHI, BARRIER_UP_OUT, REBATE, SPOT, costOfCarry, rateDomestic, VOLATILITY);
assertTrue(
"Knock In-Out Parity fails",
Math.abs((pxVanillaPutHiK + pxRebate) / (pxUpInPutHiK + pxUpOutPutHiK) - 1) < 1.e-6);
}
