/* Simple routine to print the fit results */
private static void PrintResult(double[] x, double[] xact, mp_result result)
{
int i;
if (x == null)
{
return;
}
Console.Write(" CHI-SQUARE = {0} ({1} DOF)\n",
result.bestnorm, result.nfunc - result.nfree);
Console.Write(" NPAR = {0}\n", result.npar);
Console.Write(" NFREE = {0}\n", result.nfree);
Console.Write(" NPEGGED = {0}\n", result.npegged);
Console.Write(" NITER = {0}\n", result.niter);
Console.Write(" NFEV = {0}\n", result.nfev);
Console.Write("\n");
if (xact != null)
{
for (i = 0; i < result.npar; i++)
{
Console.Write(" P[{0}] = {1} +/- {2} (ACTUAL {3})\n",
i, x[i], result.xerror[i], xact[i]);
}
}
else
{
for (i = 0; i < result.npar; i++)
{
Console.Write(" P[{0}] = {1} +/- {2}\n",
i, x[i], result.xerror[i]);
}
}
}
protected override OptimizationRunProperties RunOptimization()
{
try
{
var result = new mp_result(_constraints.Count);
var pars = createMPConstraints();
var startValues = CreateVectorFor(x => x.StartValue);
var config = new mp_config
{
ftol = ftol,
xtol = xtol,
gtol = gtol,
stepfactor = stepfactor,
maxiter = maxiter,
maxfev = maxfev,
epsfcn = epsfcn,
nofinitecheck = 0
};
_objectiveFunctionErrorMessage = string.Empty;
int status = MPFit.Solve(objectiveFunction, _numberOfResiduals, _constraints.Count, startValues, pars, config, null, ref result);
evaluateStatus(status);
return(new OptimizationRunProperties(result.nfev));
}
finally
{
_constraints = null;
_objectiveFunc = null;
}
}
private static void TestAnalyticDerivatives()
{
const double intercept = 7.0;
const double slope = -3.0;
var pactual = new double[] { intercept, slope };
var p = new double[] { 5.9, -1.1 };
var x = new double[] { -5, -3, -1, 0, 1, 3, 5 };
var y = new double[x.Length];
for (uint i = 0; i < x.Length; i++)
{
y[i] = intercept + slope * x[i];
}
var mpPar = new mp_par[] { new mp_par(), new mp_par() };
mpPar[0].side = 3;
mpPar[1].side = 3;
var result = new mp_result(2);
var status = MPFit.Solve(ForwardModels.LineFunc, x.Length, 2, p, mpPar, null, new LineFitData(x, y), ref result);
Console.Write("*** TestLineFit status = {0}\n", status);
PrintResult(p, pactual, result);
}
/// <summary>
/// Optimization method. This calls MPFit Levenberg Marquardt solver with constraints.
/// </summary>
/// <param name="a">optimization parameter initial guess</param>
/// <param name="ia">accompanying array to <paramref name="a"/> that specifies which parameters to fit (held constant otherwise)</param>
/// <param name="lowerBounds">accompanying array that specifies lower bounds for parameters</param>
/// <param name="upperBounds">accompanying array that specifies upper bounds</param>
/// <param name="y">"measured" values</param>
/// <param name="ey">standard deviation values of <paramref name="y"/></param>
/// <param name="forwardFunc">delegate function that evaluates the objective function given a parameter optimization array and (optional) constant variables</param>
/// <param name="forwardVariables"></param>
public double[] SolveWithConstraints(double[] a, bool[] ia, double[] lowerBounds, double[] upperBounds, double[] y, double[] ey, Func <double[], object[], double[]> forwardFunc, params object[] forwardVariables)
{
var data = new OptimizationData
{
Y = y,
Ey = ey,
ForwardFunc = forwardFunc,
ForwardVariables = forwardVariables
};
mp_par[] pars = a.Select((ai, i) => new mp_par {
isFixed = ia[i] ? 0 : 1
}).ToArray();
for (int i = 0; i < pars.Length; i++)
{
pars[i].limited[0] = 1; // specify lower bound exists
pars[i].limited[1] = 1; // specify upper bound exists
pars[i].limits[0] = lowerBounds[i];
pars[i].limits[1] = upperBounds[i];
}
mp_result result = new mp_result(a.Length);
int status = MPFit.Solve(MPFitFunc, data.Y.Length, pars.Length, a, pars, null, data, ref result);
return(a);
}
/* Test harness routine, which contains test gaussian-peak data
*
* Example of fixing two parameter
*
* Commented example of how to put boundary constraints
*/
private static int TestGaussFix()
{
double[] x = { -1.7237128E+00, 1.8712276E+00, -9.6608055E-01,
-2.8394297E-01, 1.3416969E+00, 1.3757038E+00,
-1.3703436E+00, 4.2581975E-02, -1.4970151E-01,
8.2065094E-01 };
double[] y = { -4.4494256E-02, 8.7324673E-01, 7.4443483E-01,
4.7631559E+00, 1.7187297E-01, 1.1639182E-01,
1.5646480E+00, 5.2322268E+00, 4.2543168E+00,
6.2792623E-01 };
double[] ey = new double[10];
double[] p = { 0.0, 1.0, 0.0, 0.1 }; /* Initial conditions */
double[] pactual = { 0.0, 4.70, 0.0, 0.5 }; /* Actual values used to make data*/
//double[] perror = new double[4]; /* Returned parameter errors */
int i;
int status;
mp_result result = new mp_result(4);
//result.xerror = perror;
mp_par[] pars = new mp_par[4]/* Parameter constraints */
{
new mp_par {
isFixed = 1
}, /* Fix parameters 0 and 2 */
new mp_par(),
new mp_par {
isFixed = 1
},
new mp_par()
};
/* How to put limits on a parameter. In this case, parameter 3 is
* limited to be between -0.3 and +0.2.
* pars[3].limited[0] = 0;
* pars[3].limited[1] = 1;
* pars[3].limits[0] = -0.3;
* pars[3].limits[1] = +0.2;
*/
for (i = 0; i < 10; i++)
{
ey[i] = 0.5;
}
CustomUserVariable v = new CustomUserVariable {
X = x, Y = y, Ey = ey
};
/* Call fitting function for 10 data points and 4 parameters (2
* parameters fixed) */
status = MPFit.Solve(ForwardModels.GaussFunc, 10, 4, p, pars, null, v, ref result);
Console.Write("*** TestGaussFix status = {0}\n", status);
PrintResult(p, pactual, result);
return(0);
}
private static void TestGaussianWithDerivs()
{
double[] x =
{
-1.7237128E+00, 1.8712276E+00, -9.6608055E-01,
-2.8394297E-01, 1.3416969E+00, 1.3757038E+00,
-1.3703436E+00, 4.2581975E-02, -1.4970151E-01,
8.2065094E-01
};
double[] y =
{
-4.4494256E-02, 8.7324673E-01, 7.4443483E-01,
4.7631559E+00, 1.7187297E-01, 1.1639182E-01,
1.5646480E+00, 5.2322268E+00, 4.2543168E+00,
6.2792623E-01
};
double[] ey = new double[10];
double[] p = { 0.0, 1.0, 1.0, 1.0 }; // Initial conditions
double[] pactual = { 0.0, 4.70, 0.0, 0.5 }; // Actual values used to make data
mp_par[] pars =
{
new mp_par {
side = 3, deriv_debug = 0
},
new mp_par {
side = 1, deriv_debug = 0
},
new mp_par {
side = 3, deriv_debug = 0
},
new mp_par {
side = 1, deriv_debug = 0
}
};
mp_result result = new mp_result(4);
/* No constraints */
for (uint i = 0; i < 10; i++)
{
ey[i] = 0.5;
}
CustomUserVariable v = new CustomUserVariable {
X = x, Y = y, Ey = ey
};
/* Call fitting function for 10 data points and 4 parameters (no
* parameters fixed) */
var logger = new System.IO.StringWriter();
int status = MPFit.Solve(ForwardModels.GaussianFuncAndDerivs, 10, 4, p, pars, null, v, ref result, logger);
Console.Write("*** TestGaussFitWithDerivs status = {0}\n", status);
PrintResult(p, pactual, result);
Console.WriteLine(logger.ToString());
}
/* Test harness routine, which contains test quadratic data;
* Example of how to fix a parameter
*/
private static int TestQuadFix()
{
double[] x = { -1.7237128E+00, 1.8712276E+00, -9.6608055E-01,
-2.8394297E-01, 1.3416969E+00, 1.3757038E+00,
-1.3703436E+00, 4.2581975E-02, -1.4970151E-01,
8.2065094E-01 };
double[] y = { 2.3095947E+01, 2.6449392E+01, 1.0204468E+01,
5.40507, 1.5787588E+01, 1.6520903E+01,
1.5971818E+01, 4.7668524E+00, 4.9337711E+00,
8.7348375E+00 };
double[] ey = new double[10];
double[] p = { 1.0, 0.0, 1.0 }; /* Initial conditions */
double[] pactual = { 4.7, 0.0, 6.2 }; /* Actual values used to make data */
//double[] perror = new double[3]; /* Returned parameter errors */
int i;
int status;
mp_result result = new mp_result(3);
//result.xerror = perror;
mp_par[] pars = new mp_par[3] /* Parameter constraints */
{
new mp_par(),
new mp_par()
{
isFixed = 1
}, /* Fix parameter 1 */
new mp_par()
};
for (i = 0; i < 10; i++)
{
ey[i] = 0.2;
}
CustomUserVariable v = new CustomUserVariable()
{
X = x, Y = y, Ey = ey
};
/* Call fitting function for 10 data points and 3 parameters (1
* parameter fixed) */
status = MPFit.Solve(ForwardModels.QuadFunc, 10, 3, p, pars, null, v, ref result);
Console.Write("*** TestQuadFix status = {0}\n", status);
PrintResult(p, pactual, result);
return(0);
}
/* Test harness routine, which contains test gaussian-peak data */
public static double[] TestGaussFit(double[] xinc, double[] yinc, double[] p)
{
double[] x = xinc;
double[] y = yinc;
double[] ey = new double[yinc.Length];
//double[] p = { 0.0, 1.0, 1.0, 1.0 }; /* Initial conditions */
double[] pactual = { 0.0, 4.70, 0.0, 0.5 }; /* Actual values used to make data*/
//double[] perror = new double[4]; /* Returned parameter errors */
mp_par[] pars = new mp_par[4] /* Parameter constraints */
{
new mp_par(),
new mp_par(),
new mp_par(),
new mp_par()
};
int i;
int status;
mp_result result = new mp_result(4);
//result.xerror = perror;
/* No constraints */
for (i = 0; i < yinc.Length; i++)
{
ey[i] = 0.02;
}
for (i = 0; i < p.Length; i++)
{
Console.Write("P" + i + " : " + p[i]);
}
CustomUserVariable v = new CustomUserVariable {
X = x, Y = y, Ey = ey
};
/* Call fitting function for 10 data points and 4 parameters (no
* parameters fixed) */
status = MPFit.Solve(ForwardModels.GaussFunc, yinc.Length, 4, p, pars, null, v, ref result);
Console.Write("*** TestGaussFit status = {0}\n", status);
PrintResult(p, pactual, result);
double[] retval = { p[0], p[1], p[2], p[3], result.xerror[0], result.xerror[1], result.xerror[2], result.xerror[3] };
return(retval);
}
/* Test harness routine, which contains test data, invokes mpfit() */
private static int TestLinFit()
{
double[] x = { -1.7237128E+00, 1.8712276E+00, -9.6608055E-01,
-2.8394297E-01, 1.3416969E+00, 1.3757038E+00,
-1.3703436E+00, 4.2581975E-02, -1.4970151E-01,
8.2065094E-01 };
double[] y = { 1.9000429E-01, 6.5807428E+00, 1.4582725E+00,
2.7270851E+00, 5.5969253E+00, 5.6249280E+00,
0.787615, 3.2599759E+00, 2.9771762E+00,
4.5936475E+00 };
double[] ey = new double[10];
/* y = a + b * x */
/* a b */
double[] p = { 1.0, 1.0 }; /* Parameter initial conditions */
double[] pactual = { 3.20, 1.78 }; /* Actual values used to make data */
//double[] perror = { 0.0, 0.0 }; /* Returned parameter errors */
int i;
int status;
mp_result result = new mp_result(2);
//result.xerror = perror;
for (i = 0; i < 10; i++)
{
ey[i] = 0.07; /* Data errors */
}
CustomUserVariable v = new CustomUserVariable();
v.X = x;
v.Y = y;
v.Ey = ey;
/* Call fitting function for 10 data points and 2 parameters */
status = MPFit.Solve(ForwardModels.LinFunc, 10, 2, p, null, null, v, ref result);
Console.Write("*** TestLinFit status = {0}\n", status);
PrintResult(p, pactual, result);
return(0);
}
/// <summary>
/// Optimization method. This calls MPFit Levenberg Marquardt solver.
/// For examples of usage, see TestMPFit.cs:
/// https://csmpfit.codeplex.com/SourceControl/latest#src/MPFitLib.Test/TestMPFit.cs
/// For an example of a call with the objective function:
/// https://csmpfit.codeplex.com/SourceControl/latest#src/MPFitLib.Test/ForwardModels.cs
/// </summary>
/// <param name="a">optimization parameter initial guess</param>
/// <param name="ia">accompanying array to <paramref name="a"/> that specifies which parameters to fit (held constant otherwise)</param>
/// <param name="y">"measured" values</param>
/// <param name="ey">standard deviation values of <paramref name="y"/></param>
/// <param name="forwardFunc">delegate function that evaluates the objective function given a parameter optimization array and (optional) constant variables</param>
/// <param name="forwardVariables"></param>
public double[] Solve(double[] a, bool[] ia, double[] y, double[] ey, Func <double[], object[], double[]> forwardFunc, params object[] forwardVariables)
{
var data = new OptimizationData
{
Y = y,
Ey = ey,
ForwardFunc = forwardFunc,
ForwardVariables = forwardVariables
};
mp_par[] pars = a.Select((ai, i) => new mp_par {
isFixed = ia[i] ? 0 : 1
}).ToArray();
mp_result result = new mp_result(a.Length);
int status = MPFit.Solve(MPFitFunc, data.Y.Length, pars.Length, a, pars, null, data, ref result);
return(a);
}
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);
}
