public SviRawParameters SolveSviRaw(ATMStraddleConstraint atmConstraint, RRBFConstraint[] smileConstraints, DateTime buildDate,
DateTime expiry, double fwd, bool vegaWeightedFit = true)
{
_atmConstraint = atmConstraint;
_smileConstraints = smileConstraints;
_numberOfConstraints = smileConstraints.Length * 2 + 1;
_vegaWeighted = vegaWeightedFit;
_fwd = fwd;
_buildDate = buildDate;
_tExp = (expiry - buildDate).TotalDays / 365.0;
var startingPoint = new[] { atmConstraint.MarketVol *atmConstraint.MarketVol *_tExp - Sqrt(atmConstraint.MarketVol), 1.0, smileConstraints.Average(x => x.RisykVol) >= 0 ? 0.1 : -0.1, 0, Sqrt(atmConstraint.MarketVol) };
//var startingPoint = new[] { atmConstraint.MarketVol* atmConstraint.MarketVol *_tExp-Sqrt(atmConstraint.MarketVol), 0.5, smileConstraints.Average(x => x.RisykVol) >= 0 ? 0.25 : -0.25, 0, Sqrt(atmConstraint.MarketVol) };
var initialStep = new[] { atmConstraint.MarketVol *atmConstraint.MarketVol, 0.5, 0.5, 0.002, Sqrt(atmConstraint.MarketVol) / 2 };
//var startingPoint = new[] { atmConstraint.MarketVol, 1.0, 0.1, 0, 0.1 };
//var initialStep = new[] { 0.1, 0.25, 0.25, 0.01, 0.1 };
var currentError = new Func <double[], double>(x =>
{
var currentSVI = new SviRawParameters
{
A = x[0],
B = x[1],
Rho = x[2],
M = x[3],
Sigma = x[4],
};
var e = ComputeErrorsSviRaw(currentSVI);
return(Sqrt(e.Sum()));
});
SetupConstraints();
var optimal = NelderMead.MethodSolve(currentError, startingPoint, initialStep, 1e-10, 50000);
return(new SviRawParameters
{
A = optimal[0],
B = optimal[1],
Rho = optimal[2],
M = optimal[3],
Sigma = optimal[4],
});
}
public double[] Solve(ATMStraddleConstraint atmConstraint, RRBFConstraint[] smileConstraints, DateTime buildDate,
DateTime expiry, double fwd, double[] strikesToFit, Interpolator1DType interpType)
{
_atmConstraint = atmConstraint;
_smileConstraints = smileConstraints;
_numberOfConstraints = smileConstraints.Length * 2 + 1;
if (strikesToFit.Length != _numberOfConstraints)
{
throw new Exception($"{_numberOfConstraints} constraints provided to fit {strikesToFit.Length} strikes");
}
_fwd = fwd;
_buildDate = buildDate;
_tExp = (expiry - buildDate).TotalDays / 365.0;
_interpType = interpType;
_strikes = strikesToFit;
if (TrivialSolution(out var vols))
{
return(vols);
}
_currentGuess = Enumerable.Repeat(atmConstraint.MarketVol, _numberOfConstraints).ToArray();
SetupConstraints();
_currentErrors = ComputeErrors(_currentGuess);
ComputeJacobian();
for (var i = 0; i < MaxItterations; i++)
{
ComputeNextGuess();
NaNCheck();
_currentErrors = ComputeErrors(_currentGuess);
if (_currentErrors.Max(x => Abs(x)) < Tollerance)
{
UsedItterations = i + 1;
break;
}
ComputeJacobian();
}
return(_currentGuess);
}
public SABRParameters SolveSABR(ATMStraddleConstraint atmConstraint, RRBFConstraint[] smileConstraints, DateTime buildDate,
DateTime expiry, double fwd, double beta = 1.0, bool vegaWeightedFit = true)
{
_atmConstraint = atmConstraint;
_smileConstraints = smileConstraints;
_numberOfConstraints = smileConstraints.Length * 2 + 1;
_vegaWeighted = vegaWeightedFit;
_fwd = fwd;
_buildDate = buildDate;
_tExp = (expiry - buildDate).TotalDays / 365.0;
var startingPoint = new[] { atmConstraint.MarketVol, Sqrt(atmConstraint.MarketVol), smileConstraints.Average(x => x.RisykVol) >= 0 ? 0.1 : -0.1 };
var initialStep = new[] { 0.1, 0.25, 0.25 };
var currentError = new Func <double[], double>(x =>
{
var currentSABR = new SABRParameters
{
Alpha = x[0],
Beta = beta,
Nu = x[1],
Rho = x[2],
};
var e = ComputeErrorsSABR(currentSABR);
return(e.Sum(ee => ee * ee));
});
SetupConstraints();
var optimal = NelderMead.MethodSolve(currentError, startingPoint, initialStep, 1e-8, 10000);
return(new SABRParameters
{
Alpha = optimal[0],
Beta = beta,
Nu = optimal[1],
Rho = optimal[2],
});
}