@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);
}
