//-------------------------------------------------------------------------
// bumping a node point at (nodeExpiry, nodeStrike)
private double nodeSensitivity(BlackFxOptionSurfaceVolatilities provider, CurrencyPair pair, ZonedDateTime expiry, double strike, double forward, double nodeExpiry, double nodeStrike)
{
NodalSurface surface = (NodalSurface)provider.Surface;
DoubleArray xValues = surface.XValues;
DoubleArray yValues = surface.YValues;
DoubleArray zValues = surface.ZValues;
int nData = xValues.size();
int index = -1;
for (int i = 0; i < nData; ++i)
{
if (Math.Abs(xValues.get(i) - nodeExpiry) < TOLERANCE && Math.Abs(yValues.get(i) - nodeStrike) < TOLERANCE)
{
index = i;
}
}
Surface surfaceUp = surface.withZValues(zValues.with(index, zValues.get(index) + EPS));
Surface surfaceDw = surface.withZValues(zValues.with(index, zValues.get(index) - EPS));
BlackFxOptionSurfaceVolatilities provUp = BlackFxOptionSurfaceVolatilities.of(CURRENCY_PAIR, VAL_DATE_TIME, surfaceUp);
BlackFxOptionSurfaceVolatilities provDw = BlackFxOptionSurfaceVolatilities.of(CURRENCY_PAIR, VAL_DATE_TIME, surfaceDw);
double volUp = provUp.volatility(pair, expiry, strike, forward);
double volDw = provDw.volatility(pair, expiry, strike, forward);
return(0.5 * (volUp - volDw) / EPS);
}
private double volFromFormulaPrice(double r, double q, double time, double strike, NodalSurface surface)
{
double p = surface.zValue(time, strike);
double pT = 0.5 / FD_EPS * (surface.zValue(time + FD_EPS, strike) - surface.zValue(time - FD_EPS, strike));
double pK = 0.5 / FD_EPS * (surface.zValue(time, strike + FD_EPS) - surface.zValue(time, strike - FD_EPS));
double pKK = (surface.zValue(time, strike + FD_EPS) + surface.zValue(time, strike - FD_EPS) - 2d * p) / FD_EPS / FD_EPS;
double var = 2d * (pT + (r - q) * strike * pK + q * p) / (strike * strike * pKK);
return(Math.Sqrt(var));
}
private double volFromFormula(double r, double q, double time, double strike, NodalSurface surface)
{
double vol = surface.zValue(time, strike);
double volT = 0.5 / FD_EPS * (surface.zValue(time + FD_EPS, strike) - surface.zValue(time - FD_EPS, strike));
double volK = 0.5 / FD_EPS * (surface.zValue(time, strike + FD_EPS) - surface.zValue(time, strike - FD_EPS));
double volKK = (surface.zValue(time, strike + FD_EPS) + surface.zValue(time, strike - FD_EPS) - 2d * vol) / FD_EPS / FD_EPS;
double rootT = Math.Sqrt(time);
double d1 = (Math.Log(SPOT / strike) + (r - q + 0.5 * vol * vol) * time) / vol / rootT;
double d2 = (Math.Log(SPOT / strike) + (r - q - 0.5 * vol * vol) * time) / vol / rootT;
double den = 1d + 2d * d1 * strike * rootT * volK + strike * strike * time * (d1 * d2 * volK * volK + vol * volKK);
double var = (vol * vol + 2d * vol * time * (volT + (r - q) * strike * volK)) / den;
return(Math.Sqrt(var));
}
