public void TestSkewDigitalEuroCallPut()
{
DateTime today = new DateTime(2010, 06, 22);
DateTime expiry = new DateTime(2011, 03, 24);
double tau = System.Convert.ToDouble(expiry.Subtract(today).Days) / 365.0;
double spot = 42.00;
double upperbarrier = 44.00;
double lowerbarrier = 40.00;
int[] zerodays = { 0, 10 };
double[] zerorates = { 0.05, 0.05 };
int[] divdays = new int[] { 0, 51, 247 };
double[] divAmts = new double[] { 4, 1.350, 1.420 };
double fwd = EquityAnalytics.GetForwardCCLin365(spot, tau, divdays, divAmts, zerodays, zerorates);
OrcWingParameters owp = new OrcWingParameters()
{
AtmForward = fwd, CallCurve = 0.1250, CurrentVol = 0.26, DnCutoff = -0.25, Dsr = 0.9, PutCurve = 0.10, RefFwd = fwd, RefVol = 0.26, Scr = 0.0, SlopeRef = -0.1750, Ssr = 100, TimeToMaturity = tau, UpCutoff = 0.20, Usr = 0.50, Vcr = 0.0
};
List <OrcWingParameters> owpList = new List <OrcWingParameters>();
owpList.Add(owp);
double skew1 = EquityAnalytics.GetWingSkew(owpList, new LinearInterpolation(), tau, upperbarrier);
double vol = EquityAnalytics.GetWingValue(owpList, new LinearInterpolation(), tau, upperbarrier);
BinaryEuro op1 = new BinaryEuro(spot, upperbarrier, true, tau, vol, zerodays, zerorates, divdays, divAmts, skew1);
double pr1 = op1.GetPrice();
Assert.AreEqual(0.35784, pr1, 0.005);
double skew2 = EquityAnalytics.GetWingSkew(owpList, new LinearInterpolation(), tau, lowerbarrier);
BinaryEuro op2 = new BinaryEuro(spot, lowerbarrier, false, tau, vol, zerodays, zerorates, divdays, divAmts, skew2);
double pr2 = op2.GetPrice();
Assert.AreEqual(0.43275, pr2, 0.005);
}
/// <summary>
/// We can roughly proxy the alpha-th percentile of the simulation
/// by calculating the upper alpha percentile confidence point for a given time slice
/// of the ln-OU process and pricing the collar with this asset value for a given profile point
/// This should roughly compare to the calculated (1-alpha)-worst PCE point.
/// </summary>
/// <param name="spot"></param>
/// <param name="kappa"></param>
/// <param name="theta"></param>
/// <param name="histvol"></param>
/// <param name="time0"></param>
/// <param name="maturity"></param>
/// <param name="callstrike"></param>
/// <param name="putstrike"></param>
/// <param name="zerodays"></param>
/// <param name="zerorates"></param>
/// <param name="divdays"></param>
/// <param name="divamts"></param>
/// <param name="volSurface"></param>
/// <returns></returns>
public static double PCEProxyCalc(double spot,
double kappa,
double theta,
double histvol,
double time0,
double maturity,
double callstrike,
double putstrike,
int[] zerodays,
double[] zerorates,
int[] divdays,
double[] divamts,
List <OrcWingParameters> volSurface)
{
double tau = maturity - time0;
double upperBound = EquityPCEAnalytics.LNOUUpperBound(spot, 0.95, kappa, theta, histvol, time0);
double fStar = EquityAnalytics.GetForwardCCLin365(upperBound, time0, maturity, divdays, divamts, zerodays, zerorates);
double callvol = EquityAnalytics.GetWingValue(volSurface, new LinearInterpolation(), tau, callstrike);
double putvol = EquityAnalytics.GetWingValue(volSurface, new LinearInterpolation(), tau, putstrike);
double r0 = EquityAnalytics.GetRateCCLin365(time0, maturity, zerodays, zerorates);
BlackScholes bs = new BlackScholes();
double lhs = Math.Max(bs.BSprice(fStar, tau, callstrike, r0, callvol, true) - bs.BSprice(fStar, tau, putstrike, r0, putvol, false), 0);
return(lhs);
}
/// <summary>
/// Evaluate the PCE for a collar given the parameters passed below
/// </summary>
/// <param name="ratedays"></param>
/// <param name="rateamts"></param>
/// <param name="divdays"></param>
/// <param name="divamts"></param>
/// <param name="volSurface"></param>
/// <param name="spot"></param>
/// <param name="s"></param>
/// <param name="callstrike"></param>
/// <param name="putstrike"></param>
/// <param name="t0"></param>
/// <param name="maturity"></param>
/// <returns></returns>
private static double CollarPCEFunction(int[] ratedays,
double[] rateamts,
int[] divdays,
double[] divamts,
List <OrcWingParameters> volSurface,
double spot,
double s,
double callstrike,
double putstrike,
double t0,
double maturity)
{
t0 = Math.Min(t0, maturity); // cap profile point to maturity;
double tau = maturity - t0;
double r = EquityAnalytics.GetRateCCLin365(t0, maturity, ratedays, rateamts);
double q = EquityAnalytics.GetYieldCCLin365(spot, t0, maturity, divdays, divamts, ratedays, rateamts);
double callvol = EquityAnalytics.GetWingValue(volSurface, new LinearInterpolation(), tau, callstrike);
double putvol = EquityAnalytics.GetWingValue(volSurface, new LinearInterpolation(), tau, putstrike);
double fwd = s * Math.Exp((r - q) * tau);
BlackScholes bs = new BlackScholes();
double lhs = Math.Max(bs.BSprice(fwd, tau, callstrike, r, callvol, true) - bs.BSprice(fwd, tau, putstrike, r, putvol, false), 0);
return(lhs);
}
