//------------------------------------------------------------------------- // 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)); }