public void VegaFacts()
{
var t = 1.0;
var k = 100;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
//vega closely matches numerical estimate
var PV1 = BlackFunctions.BlackPV(f, k, rf, t, vol - 0.00005, cp);
var PV2 = BlackFunctions.BlackPV(f, k, rf, t, vol + 0.00005, cp);
var vegaEst = (PV2 - PV1) / 0.0001 * 0.01;
var vega = BlackFunctions.BlackVega(f, k, rf, t, vol);
Assert.Equal(vegaEst, vega, 6);
//all else the same, more time==more vega
var vegaNear = BlackFunctions.BlackVega(f, k, rf, t, vol);
var vegaFar = BlackFunctions.BlackVega(f, k, rf, t * 2, vol);
Assert.True(vegaFar > vegaNear);
//cases for zero vega
vega = BlackFunctions.BlackVega(f, 0, rf, t, vol);
Assert.Equal(0, vega, 8);
vega = BlackFunctions.BlackVega(f, 1e6, rf, t, vol);
Assert.Equal(0, vega, 8);
}
public double CDF(DateTime expiry, double fwd, double strike)
{
var t = TimeBasis.CalculateYearFraction(OriginDate, expiry);
var vol = GetVolForAbsoluteStrike(strike, expiry, fwd);
var nu = vol * Sqrt(t);
(var d1, var d2) = BlackFunctions.D1d2(fwd, strike, t, vol);
var vega = BlackFunctions.BlackVega(fwd, strike, 0.0, t, vol) / 0.01;
var digi = BlackFunctions.BlackDigitalPV(fwd, strike, 0.0, t, vol, OptionType.P);
var dvdk = Dvdk(strike, expiry, fwd);
return(digi + vega * dvdk);
//var dk = fwd * 1e-10;
//var volU = GetVolForAbsoluteStrike(strike + dk, expiry, fwd);
//var volD = GetVolForAbsoluteStrike(strike - dk, expiry, fwd);
//var pU = BlackFunctions.BlackPV(fwd, strike + dk, 0.0, t, volU, OptionType.P);
//var pD = BlackFunctions.BlackPV(fwd, strike - dk, 0.0, t, volD, OptionType.P);
//var dPdK = (pU - pD) / (2.0 * dk);
//return dPdK;
}
public void BlackGammaVega_Facts()
{
Assert.Equal(0.0, BlackFunctions.BlackGamma(0.1, 1.0, 0.5, 0.0, 0.001));
Assert.Equal(0.0, BlackFunctions.BlackVega(0.1, 1.0, 0.5, 0.0, 0.001));
}