/**
* Computes the fair value strike of a spot starting VarianceSwap parameterized in 'variance'
* terms, It is quoted as an annual variance value, hence 1/T * integral(0,T) {sigmaSquared dt}
*
* <p>
*
* @param expiry Time from spot until last observation
* @param market VarianceSwapDataBundle containing volatility surface, forward underlying, and
* funding curve
* @param cutoff The cutoff
* @return presentValue of the *remaining* variance in the swap.
*/
protected double impliedVarianceFromSpot(
final double expiry, final VarianceSwapDataBundle market, final DoublesPair cutoff) {
// 1. Unpack Market data
final double fwd = market.getForwardCurve().getForward(expiry);
final BlackVolatilitySurface<?> volSurf = market.getVolatilitySurface();
VarianceCalculator varCal;
if (cutoff == null) {
varCal = new VarianceCalculator(fwd, expiry);
} else {
final ExtrapolationParameters exParCal = new ExtrapolationParameters(fwd, expiry);
final Pair<double[], double[]> pars = exParCal.getparameters(volSurf, cutoff);
final double[] ks = pars.getFirst();
final double[] vols = pars.getSecond();
final double res = getResidual(fwd, expiry, ks, vols);
varCal = new VarianceCalculator(fwd, expiry, res, ks[0]);
}
return varCal.getVariance(volSurf);
}
public double presentValue(
final VarianceSwap deriv, final VarianceSwapDataBundle market, final DoublesPair cutoff) {
Validate.notNull(deriv, "VarianceSwap deriv");
Validate.notNull(market, "VarianceSwapDataBundle market");
if (deriv.getTimeToSettlement() < 0) {
return 0.0; // All payments have been settled
}
// Compute contribution from past realizations
final double realizedVar =
new RealizedVariance().evaluate(deriv); // Realized variance of log returns already observed
// Compute contribution from future realizations
final double remainingVar =
impliedVariance(deriv, market, cutoff); // Remaining variance implied by option prices
// Compute weighting
final double nObsExpected = deriv.getObsExpected(); // Expected number as of trade inception
final double nObsDisrupted =
deriv.getObsDisrupted(); // Number of observations missed due to market disruption
double nObsActual = 0;
if (deriv.getTimeToObsStart() <= 0) {
Validate.isTrue(
deriv.getObservations().length > 0,
"presentValue requested after first observation date, yet no observations have been provided.");
nObsActual = deriv.getObservations().length - 1; // From observation start until valuation
}
final double totalVar =
realizedVar * (nObsActual / nObsExpected)
+ remainingVar * (nObsExpected - nObsActual - nObsDisrupted) / nObsExpected;
final double finalPayment = deriv.getVarNotional() * (totalVar - deriv.getVarStrike());
final double df = market.getDiscountCurve().getDiscountFactor(deriv.getTimeToSettlement());
return df * finalPayment;
}
