public int SabrFunc(double[] p, double[] dy, IList <double>[] dvec, object vars)
{
var b = _initBeta; // beta = 0.5
var r = p[0]; // rho
var nv = p[1]; // nu
var a = _estimateAlpha // alpha
? p[2]
: FindAlpha(b, r, nv, MaturityInYears, _spotPrice, AtmVol);
CustomUserVariable v = (CustomUserVariable)vars;
double[] x, y, ey;
x = v.X;
y = v.Y;
ey = v.Ey;
for (var i = 0; i < dy.Length; i++)
{
var estVol = SabrVolSurface.SABRVolFineTune(a, b, r, nv, _spotPrice, _strikes[i], MaturityInYears, _useFineTune);
dy[i] = (Math.Abs(r) > 1 || nv < 0) ? 1e100 : estVol - _marketVols[i]; //Impose the constraint that -1<=rho <=1 and v>0
}
return(0);
}
public SabrCoeffOptimizer(
double maturity,
double spotPrice,
double atmVol,
IList <double> strikes,
IList <double> marketVols,
bool estimateAlpha,
bool useFineTune,
double initAlpha = 0.3,
double initBeta = 0.5,
double initNu = 0.3,
double initRho = 0.3)
{
MaturityInYears = maturity;
_spotPrice = spotPrice;
AtmVol = atmVol;
_strikes = strikes;
_marketVols = marketVols;
_estimateAlpha = estimateAlpha;
_useFineTune = useFineTune;
_initBeta = initBeta;
if (strikes.Count != marketVols.Count)
{
throw new PricingLibraryException("strikes and marketVols should have same number of elements!");
}
double bestAlpha, bestBeta, bestRho, bestNu;
var nDataPoints = _marketVols.Count();
double[] ey = new double[nDataPoints];
for (int i = 0; i < nDataPoints; ++i)
{
ey[i] = 0.1; // error for data points, we do not need to use this
}
const int nParams = 3;
mp_par[] pars = new mp_par[nParams] // parameter constraints
{
new mp_par(), // no constraint
new mp_par(),
new mp_par()
};
if (!estimateAlpha) // fix alpha
{
pars[2] = new mp_par()
{
isFixed = 1
};
}
CustomUserVariable v = new CustomUserVariable()
{
X = _strikes.ToArray(), Y = _marketVols.ToArray(), Ey = ey
};
double[] p = new double[nParams] {
initRho, initNu, initAlpha
};
mp_result result = new mp_result(nParams);
int status = MPFit.Solve(SabrFunc, nDataPoints, nParams, p, pars, null, v, ref result);
bestRho = p[0];
bestNu = p[1];
bestAlpha = estimateAlpha ? p[2] : FindAlpha(_initBeta, p[0], p[1], MaturityInYears, _spotPrice, AtmVol);
bestBeta = _initBeta;
Result = new SabrCoeffOptimizerResult(MaturityInYears, bestAlpha, bestBeta, bestRho, bestNu);
}