/// <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>
///</summary>
///<param name="ratedaysAsArray"></param>
///<param name="rateamtsAsArray"></param>
///<param name="divdaysAsArray"></param>
///<param name="divamtsAsArray"></param>
///<param name="voltimesAsArray"></param>
///<param name="volatilitiesAsRange"></param>
///<param name="spot"></param>
///<param name="callstrike"></param>
///<param name="putstrike"></param>
///<param name="maturity"></param>
///<param name="kappa"></param>
///<param name="theta"></param>
///<param name="sigma"></param>
///<param name="profiletimes"></param>
///<param name="confidence"></param>
///<param name="tstepSize"></param>
///<param name="simulations"></param>
///<param name="seed"></param>
///<returns></returns>
public double[,] GetCollarPCE(Excel.Range ratedaysAsArray,
Excel.Range rateamtsAsArray,
Excel.Range divdaysAsArray,
Excel.Range divamtsAsArray,
Excel.Range voltimesAsArray,
Excel.Range volatilitiesAsRange,
double spot,
double callstrike,
double putstrike,
double maturity,
double kappa,
double theta,
double sigma,
Excel.Range profiletimes,
double confidence,
double tstepSize,
int simulations,
int seed)
{
//Map Ranges
var rateamts = DataRangeHelper.StripDoubleRange(rateamtsAsArray);
var divamts = DataRangeHelper.StripDoubleRange(divamtsAsArray);
var voltimes = DataRangeHelper.StripDoubleRange(voltimesAsArray);
var divdays = DataRangeHelper.StripIntRange(divdaysAsArray);
var ratedays = DataRangeHelper.StripIntRange(ratedaysAsArray);
var profile = DataRangeHelper.StripDoubleRange(profiletimes);
var volatilities = volatilitiesAsRange.Value[System.Reflection.Missing.Value] as object[, ];
var volatilitiesAsDoubles = RangeHelper.RangeToDoubleMatrix(volatilities);
List <OrcWingParameters> volSurf = UnpackWing(volatilitiesAsDoubles, voltimes.ToArray(), spot, ratedays.ToArray(), rateamts.ToArray(), divdays.ToArray(), divamts.ToArray());
CleanDivs(ref divdays, ref divamts);
double[,] results = EquityPCEAnalytics.GetCollarPCE("CollarPCE",
ratedays.ToArray(),
rateamts.ToArray(),
divdays.ToArray(),
divamts.ToArray(),
volSurf,
spot,
callstrike,
putstrike,
maturity,
kappa,
theta,
sigma,
profile.ToArray(),
confidence,
tstepSize,
simulations,
seed);
//int n = profiletimes.Length;
//var lhs = new double[profiletimes.Length];
//for (int i = 0; i < n; i++)
//{
// lhs[i] = results[i, 1];
//}
return(results);
}
public void TestPCEProfile()
{
DateTime today = new DateTime(2010, 10, 22);
DateTime expiry = new DateTime(2011, 10, 22);
double maturity = Convert.ToDouble(expiry.Subtract(today).Days) / 365.0;
double spot = 4200.00;
int simuls = 10000;
double callstrike = 1.3 * spot;
double putstrike = 1.0 * spot;
int[] zerodays = { 0, 365 };
double r0 = 0.065;
double confidence = 0.95;
double[] zerorates = { r0, r0 };
int[] divdays = { 1, 51, 247 };
double[] divamts = { 22.5, 50, 50 };
double fwd = EquityAnalytics.GetForwardCCLin365(spot, maturity, divdays, divamts, zerodays, zerorates);
double histvol = 0.60;
double theta = Math.Log(spot);
double kappa = 0.9;
double[] times = { 7.0 / 365.0, 128.0 / 365.0, 250.0 / 365.0, 365.0 / 365.0, 730.0 / 365.0 };
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 = maturity, UpCutoff = 0.20, Usr = 0.50, Vcr = 0.0
};
List <OrcWingParameters> owpList = new List <OrcWingParameters> {
owp
};
double[,] results = EquityPCEAnalytics.GetCollarPCE("CollarPCE",
zerodays,
zerorates,
divdays,
divamts,
owpList,
spot,
callstrike,
putstrike,
maturity,
kappa,
theta,
histvol,
times,
confidence,
0.25 / 365.0,
simuls,
3151);
double lhs1 = PCEProxyCalc(spot, kappa, theta, histvol, times[0], maturity, callstrike, putstrike, zerodays, zerorates, divdays, divamts, owpList);
double lhs2 = PCEProxyCalc(spot, kappa, theta, histvol, times[1], maturity, callstrike, putstrike, zerodays, zerorates, divdays, divamts, owpList);
double lhs3 = PCEProxyCalc(spot, kappa, theta, histvol, times[2], maturity, callstrike, putstrike, zerodays, zerorates, divdays, divamts, owpList);
Assert.AreEqual(results[0, 1], lhs1, Math.Abs(0.10 * results[0, 1]));
Assert.AreEqual(results[1, 1], lhs2, Math.Abs(0.10 * results[1, 1]));
Assert.AreEqual(results[2, 1], lhs3, Math.Abs(0.10 * results[2, 1]));
}
/// <summary>
/// Before calculating any PCE numbers on the simulation set, first check the simulated asset values
/// at the time slices and compare to the expected values of the theoretical distribution.
/// Check we're within 3 standard errors, reason for 3 being that there is a discretisation error introduced
/// by the time scheme approximation as well as sample error introduced by the simulation sample mean.
/// </summary>
/// <param name="kappa"></param>
/// <param name="vol"></param>
/// <param name="theta"></param>
/// <param name="simuls"></param>
public void TestDistroConvergence(double kappa, double vol, double theta, int simuls)
{
DateTime today = new DateTime(2010, 10, 22);
DateTime expiry = new DateTime(2011, 10, 22);
double maturity = Convert.ToDouble(expiry.Subtract(today).Days) / 365.0;
double spot = 4200.00;
double callstrike = 1.3 * spot;
double putstrike = 1.0 * spot;
double confidence = 0.95;
int[] zerodays = { 0, 365 };
double[] zerorates = { 0.065, 0.065 };
int[] divdays = { 1, 51, 247 };
double[] divamts = { 22.5, 50, 50 };
double fwd = EquityAnalytics.GetForwardCCLin365(spot, maturity, divdays, divamts, zerodays, zerorates);
double histvol = vol;
double[] times = { 128.0 / 365.0, 250.0 / 365.0, 365.0 / 365.0 };
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 = maturity, UpCutoff = 0.20, Usr = 0.50, Vcr = 0.0
};
List <OrcWingParameters> owpList = new List <OrcWingParameters> {
owp
};
double[,] results = EquityPCEAnalytics.GetCollarPCE("Asset",
zerodays,
zerorates,
divdays,
divamts,
owpList,
spot,
callstrike,
putstrike,
maturity,
kappa,
theta,
histvol,
times, confidence, 1.0 / 365.0, simuls, 3151);
// Check convergence to mean ln(S_t) ~ N( theta + exp(-kappa*t)*( ln(S_0) - theta , sigma^2/(2*kappa)*(1-exp(-2*kappa*t) )
// => E(S_t) = exp(theta + 0.5*sigma^2)
//
double LNmean1 = EquityPCEAnalytics.OUMean(kappa, theta, spot, times[0]);
double LNmean2 = EquityPCEAnalytics.OUMean(kappa, theta, spot, times[1]);
double LNmean3 = EquityPCEAnalytics.OUMean(kappa, theta, spot, times[2]);
double Var_1 = EquityPCEAnalytics.OUVar(histvol, kappa, times[0]);
double Var_2 = EquityPCEAnalytics.OUVar(histvol, kappa, times[1]);
double Var_3 = EquityPCEAnalytics.OUVar(histvol, kappa, times[2]);
//lognormal moments
double lhs1 = Math.Exp(LNmean1 + Var_1 / 2.0);
double lhs2 = Math.Exp(LNmean2 + Var_2 / 2.0);
double lhs3 = Math.Exp(LNmean3 + Var_3 / 2.0);
//double deltat = 1.0/365.0;
double logvar1 = EquityPCEAnalytics.LNOUVar(spot, histvol, kappa, theta, times[0]);
double logvar2 = EquityPCEAnalytics.LNOUVar(spot, histvol, kappa, theta, times[1]);
double logvar3 = EquityPCEAnalytics.LNOUVar(spot, histvol, kappa, theta, times[2]);
double stderr1 = Math.Sqrt(logvar1 / simuls);
double stderr2 = Math.Sqrt(logvar2 / simuls);
double stderr3 = Math.Sqrt(logvar3 / simuls);
//double accuracy = histvol*histvol*(1/(2*kappa) - deltat /(1-Math.Exp(-2*kappa*deltat)))*(1-Math.Exp(-2*kappa*times[0]));
Assert.AreEqual(lhs1, results[0, 0], 3.0 * stderr1);
Assert.AreEqual(lhs2, results[1, 0], 3.0 * stderr2);
Assert.AreEqual(lhs3, results[2, 0], 3.0 * stderr3);
}
