@Test
public void testNormal() {
final ProbabilityDistribution<Double> highDOF = new StudentTDistribution(1000000, ENGINE);
final ProbabilityDistribution<Double> normal = new NormalDistribution(0, 1, ENGINE);
final double eps = 1e-4;
double x;
for (int i = 0; i < 100; i++) {
x = RANDOM.nextDouble();
assertEquals(highDOF.getCDF(x), normal.getCDF(x), eps);
assertEquals(highDOF.getPDF(x), normal.getPDF(x), eps);
assertEquals(highDOF.getInverseCDF(x), normal.getInverseCDF(x), eps);
}
}
/**
* Compute vega price of cash-or-nothing option
*
* @param spot The spot
* @param strike The strike
* @param timeToExpiry The time to expiry
* @param lognormalVol The log-normal volatility
* @param interestRate The interest rate
* @param costOfCarry The cost-of-carry
* @param isCall True for calls, false for puts
* @return The option price
*/
public static double vega(
final double spot,
final double strike,
final double timeToExpiry,
final double lognormalVol,
final double interestRate,
final double costOfCarry,
final boolean isCall) {
ArgumentChecker.isTrue(spot > 0.0, "negative/NaN spot; have {}", spot);
ArgumentChecker.isTrue(strike > 0.0, "negative/NaN strike; have {}", strike);
ArgumentChecker.isTrue(timeToExpiry > 0.0, "negative/NaN timeToExpiry; have {}", timeToExpiry);
ArgumentChecker.isTrue(lognormalVol > 0.0, "negative/NaN lognormalVol; have {}", lognormalVol);
ArgumentChecker.isFalse(Double.isNaN(interestRate), "interestRate is NaN");
ArgumentChecker.isFalse(Double.isNaN(costOfCarry), "costOfCarry is NaN");
final double rootT = Math.sqrt(timeToExpiry);
final double d =
(Math.log(spot / strike) + (costOfCarry - 0.5 * lognormalVol * lognormalVol) * timeToExpiry)
/ lognormalVol
/ rootT;
final double sign = isCall ? 1. : -1.;
final double div =
-(Math.log(spot / strike) + costOfCarry * timeToExpiry)
/ lognormalVol
/ lognormalVol
/ rootT
- 0.5 * rootT;
return sign * Math.exp(-interestRate * timeToExpiry) * NORMAL.getPDF(d) * div;
}
/**
* Compute driftless (forward) theta price of cash-or-nothing option
*
* @param forward The forward
* @param strike The strike
* @param timeToExpiry The time to expiry
* @param lognormalVol The log-normal volatility
* @param isCall True for calls, false for puts
* @return The option price
*/
public static double driftlessTheta(
final double forward,
final double strike,
final double timeToExpiry,
final double lognormalVol,
final boolean isCall) {
ArgumentChecker.isTrue(forward > 0.0, "negative/NaN forward; have {}", forward);
ArgumentChecker.isTrue(strike > 0.0, "negative/NaN strike; have {}", strike);
ArgumentChecker.isTrue(timeToExpiry > 0.0, "negative/NaN timeToExpiry; have {}", timeToExpiry);
ArgumentChecker.isTrue(lognormalVol > 0.0, "negative/NaN lognormalVol; have {}", lognormalVol);
final double sigmaRootT = lognormalVol * Math.sqrt(timeToExpiry);
final double d = Math.log(forward / strike) / sigmaRootT - 0.5 * sigmaRootT;
final double sign = isCall ? 1. : -1.;
final double div =
0.5
* (-Math.log(forward / strike) / Math.pow(timeToExpiry, 1.5) / lognormalVol
- 0.5 * lognormalVol / Math.pow(timeToExpiry, 0.5));
return -sign * NORMAL.getPDF(d) * div;
}