@Test
public void testGetters() {
assertEquals(SURFACE.getName(), NAME1);
assertEquals(SURFACE.getFunction(), F1);
assertEquals(SURFACE.getZValue(1., 2.), F1.evaluate(1., 2.), 0);
assertEquals(SURFACE.getZValue(DoublesPair.of(1., 4.)), F1.evaluate(1., 4.), 0);
}
/**
* Get the coefficients (a, b and c) for the PDE governing the evolution of the transition density
* for a single underlying (i.e. 1 spatial dimension). The PDE is of the form $frac{\partial
* V}{\partial t} + a(x,t)\frac{\partial^2V}{\partial x^2}+b(x,t)\frac{\partial V}{\partial x}
* +c(x,t)V=0$ where $V(x,t)$ is the density
*
* @param forward the forward curve
* @param localVol the local volatility surface (parameterised by strike)
* @return The coefficients a, b & c - which are all functions of time and asset value (space)
*/
public static ConvectionDiffusionPDE1DCoefficients getStandardCoefficients(
final ForwardCurve forward, final LocalVolatilitySurfaceStrike localVol) {
final Function<Double, Double> a =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
final double s = ts[1];
final double sigma = localVol.getVolatility(t, s) * s;
return -0.5 * sigma * sigma;
}
};
final Function<Double, Double> b =
new Function<Double, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
final double s = ts[1];
final double lvDiv = getLocalVolFirstDiv(localVol, t, s);
final double lv = localVol.getVolatility(t, s);
return s * (forward.getDrift(t) - 2 * lv * (s * lvDiv + lv));
}
};
final Function<Double, Double> c =
new Function<Double, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
final double s = ts[1];
final double lv1Div = getLocalVolFirstDiv(localVol, t, s);
final double lv2Div = getLocalVolSecondDiv(localVol, t, s);
final double lv = localVol.getVolatility(t, s);
final double temp1 = (lv + s * lv1Div);
final double temp2 = lv * s * (s * lv2Div + 2 * lv1Div);
return forward.getDrift(t) - temp1 * temp1 - temp2;
}
};
// //using a log-normal distribution with a very small Standard deviation as a proxy for a
// Dirac delta
return new ConvectionDiffusionPDE1DStandardCoefficients(
FunctionalDoublesSurface.from(a),
FunctionalDoublesSurface.from(b),
FunctionalDoublesSurface.from(c));
}
@Test
public void testStaticConstruction() {
FunctionalDoublesSurface surface = new FunctionalDoublesSurface(F1);
FunctionalDoublesSurface other = FunctionalDoublesSurface.from(F1);
assertEquals(surface.getFunction(), other.getFunction());
assertFalse(surface.equals(other));
surface = new FunctionalDoublesSurface(F1, NAME1);
other = FunctionalDoublesSurface.from(F1, NAME1);
assertEquals(surface, other);
}
@Test
public void ImpliedTreeEuropeanRecoveryTest() {
final double interest = 0.06;
final YieldAndDiscountCurve yCrv = YieldCurve.from(ConstantDoublesCurve.from(interest));
final double cost = 0.02;
final double atmVol = 0.47;
final ZonedDateTime date = DateUtils.getUTCDate(2010, 7, 1);
final double spot = 100;
final Function<Double, Double> smile =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... tk) {
ArgChecker.isTrue(tk.length == 2);
final double k = tk[1];
return atmVol + (spot - k) * 0.0005;
}
};
final StandardOptionDataBundle data =
new StandardOptionDataBundle(
yCrv, cost, new VolatilitySurface(FunctionalDoublesSurface.from(smile)), spot, date);
final double[] strikes = new double[] {spot * 0.9, spot, spot * 1.11};
final int nSteps = 7;
final double time = 1.;
for (int i = 0; i < strikes.length; ++i) {
final double strike = strikes[i];
final boolean isCall = strike >= spot ? true : false;
final OptionFunctionProvider1D function =
new EuropeanVanillaOptionFunctionProvider(strike, time, nSteps, isCall);
final double tree = _modelTrinomial.getPrice(function, data);
final double black =
BlackScholesFormulaRepository.price(
spot, strike * 0.9, time, data.getVolatility(time, strike), interest, cost, isCall);
assertEquals(tree, black, black * 0.2);
}
try {
_model.getPrice(
new EuropeanVanillaOptionFunctionProvider(strikes[2], time, nSteps, true), data);
throw new RuntimeException();
} catch (Exception e) {
assertTrue(e instanceof IllegalArgumentException);
}
}
@Test
public void testEqualsAndHashCode() {
FunctionalDoublesSurface other = new FunctionalDoublesSurface(F1, NAME1);
assertEquals(SURFACE, other);
assertEquals(SURFACE.hashCode(), other.hashCode());
other = new FunctionalDoublesSurface(F2, NAME1);
assertFalse(SURFACE.equals(other));
other = new FunctionalDoublesSurface(F1, NAME2);
assertFalse(SURFACE.equals(other));
other = new FunctionalDoublesSurface(F1);
assertFalse(SURFACE.equals(other));
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void testNullPair() {
SURFACE.getZValue(null);
}
@Test(expectedExceptions = UnsupportedOperationException.class)
public void testGetSize() {
SURFACE.size();
}
static {
PURE_LOG_PAY_OFF =
new Function1D<Double, Double>() {
final double fT = DIV_CURVES.getF(EXPIRY);
final double dT = DIV_CURVES.getD(EXPIRY);
@Override
public Double evaluate(final Double x) {
final double s = (fT - dT) * Math.exp(x) + dT;
return Math.log(s);
}
};
final Function<Double, Double> localVol =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
final double t = ts[0];
final double s = ts[1];
final double d = DIV_CURVES.getD(t);
if (s < d) {
return 0.0;
}
return PURE_VOL * (s - d) / s;
}
};
LOCAL_VOL = new LocalVolatilitySurfaceStrike(FunctionalDoublesSurface.from(localVol));
final Function<Double, Double> localVolSpecial =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... tf) {
final double t = tf[0];
final double f = tf[1];
final double rtT = DIV_CURVES.getR(t);
final double dtT = DIV_CURVES.getD(t);
final double ftT = DIV_CURVES.getF(t);
// if (f < d) {
// return 0.0;
// }
final double x = f / rtT / (ftT - dtT);
return PURE_LOCAL_VOL.getVolatility(t, x);
}
};
LOCAL_VOL_SPECIAL =
new LocalVolatilitySurfaceStrike(FunctionalDoublesSurface.from(localVolSpecial));
final Function<Double, Double> pureLocalVol =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... tx) {
final double t = tx[0];
final double x = tx[1];
final double f = DIV_CURVES.getF(t);
final double d = DIV_CURVES.getD(t);
return VOL * ((f - d) * x + d) / (f - d) / x;
}
};
PURE_LOCAL_VOL =
new LocalVolatilitySurfaceMoneyness(
FunctionalDoublesSurface.from(pureLocalVol), new ForwardCurve(1.0));
PURE_LOCAL_VOL_FLAT =
new LocalVolatilitySurfaceMoneyness(
ConstantDoublesSurface.from(PURE_VOL), new ForwardCurve(1.0));
LOCAL_VOL_FLAT = new LocalVolatilitySurfaceStrike(ConstantDoublesSurface.from(VOL));
}
public static ExtendedCoupledPDEDataBundle getExtendedCoupledPDEDataBundle(
final ForwardCurve forward,
final LocalVolatilitySurfaceStrike localVol,
final double lambda1,
final double lambda2,
final double initialProb) {
final Function<Double, Double> a =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
return -1.0;
}
};
final Function<Double, Double> alpha =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
final double s = ts[1];
final double temp = s * localVol.getVolatility(t, s);
return 0.5 * temp * temp;
}
};
final Function<Double, Double> b =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
final double s = ts[1];
return s * forward.getDrift(t);
}
};
final Function<Double, Double> beta =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
return 1.0;
}
};
final Function<Double, Double> c =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
return forward.getDrift(t) + lambda1;
}
};
// using a log-normal distribution with a very small Standard deviation as a proxy for a Dirac
// delta
final Function1D<Double, Double> initialCondition =
new Function1D<Double, Double>() {
private final double _volRootTOffset = 0.01;
@Override
public Double evaluate(final Double s) {
if (s == 0) {
return 0.0;
}
final double x = Math.log(s / forward.getSpot());
final NormalDistribution dist = new NormalDistribution(0, _volRootTOffset);
return initialProb * dist.getPDF(x) / s;
}
};
return new ExtendedCoupledPDEDataBundle(
FunctionalDoublesSurface.from(a),
FunctionalDoublesSurface.from(b),
FunctionalDoublesSurface.from(c),
FunctionalDoublesSurface.from(alpha),
FunctionalDoublesSurface.from(beta),
lambda2,
initialCondition);
}
/**
* Get the coefficients (a, b, c, $\alpha$ & $\beta$) for the PDE governing the evolution of the
* transition density for a single underlying (i.e. 1 spatial dimension). The PDE is of the form
* $frac{\partial V}{\partial t} + a(x,t)\frac{\alpha(x,t)\partial^2V}{\partial
* x^2}+b(x,t)\frac{\beta(x,t)\partial V}{\partial x} +c(x,t)V=0$ where $V(x,t)$ is the density
*
* @param forward the forward curve
* @param localVol the local volatility surface (parameterised by strike)
* @return The coefficients a, b, c, $\alpha$ & $\beta$ - which are all functions of time and
* asset value (space)
*/
public static ConvectionDiffusionPDE1DFullCoefficients getFullCoefficients(
final ForwardCurve forward, final LocalVolatilitySurfaceStrike localVol) {
final Function<Double, Double> a =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
return -1.0;
}
};
final Function<Double, Double> alpha =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
final double s = ts[1];
final double temp = s * localVol.getVolatility(t, s);
return 0.5 * temp * temp;
}
};
final Function<Double, Double> b =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
final double s = ts[1];
return s * forward.getDrift(t);
}
};
final Function<Double, Double> beta =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
return 1.0;
}
};
final Function<Double, Double> c =
new Function<Double, Double>() {
@Override
public Double evaluate(final Double... ts) {
ArgChecker.isTrue(ts.length == 2);
final double t = ts[0];
return forward.getDrift(t);
}
};
return new ConvectionDiffusionPDE1DFullCoefficients(
FunctionalDoublesSurface.from(a),
FunctionalDoublesSurface.from(b),
FunctionalDoublesSurface.from(c),
FunctionalDoublesSurface.from(alpha),
FunctionalDoublesSurface.from(beta));
}
