/// <summary>
/// Constructor for the Cox-Ingersoll-Ross Calibration Problem based on caps matrices,
/// using an <see cref="InterestRateMarketData"/> to derive the required data.
/// </summary>
/// <param name="irmd">
/// An <see cref="InterestRateMarketData"/> containing the
/// required information for the optimization problem.
/// </param>
public CapCIROptimizationProblem(InterestRateMarketData irmd)
{
this.capMaturity = irmd.CapMaturity;
this.capRate = irmd.CapRate;
this.tau = irmd.CapTenor;
PFunction zr = new PFunction(null);
zr.m_Function.iType = DVPLUtils.EInterpolationType.LINEAR;
double[,] zrval = (double[, ])ArrayHelper.Concat(irmd.ZRMarketDates.ToArray(),
irmd.ZRMarket.ToArray());
zr.Expr = zrval;
this.r0 = zr.Evaluate(0.0);
BlackModel bm = new BlackModel(zr);
this.blackCaps = new Matrix(this.capMaturity.Length, this.capRate.Length);
for (int i = 0; i < this.capMaturity.Length; i++)
{
for (int j = 0; j < this.capRate.Length; j++)
{
if (irmd.CapVolatility[i, j] == 0)
{
this.blackCaps[i, j] = 0;
}
else
{
this.blackCaps[i, j] = bm.Cap(this.capRate[j], irmd.CapVolatility[i, j],
this.tau, this.capMaturity[i]);
}
if (double.IsNaN(this.blackCaps[i, j]))
{
throw new Exception("Error on cap market price calculation");
}
}
}
}
public void TestCalibration()
{
InterestRateMarketData IData = InterestRateMarketData.FromFile("../../TestData/IRMD-sample.xml");
CallPriceMarketData HData = CallPriceMarketData.FromFile("../../TestData/CallData-sample.xml");
//InterestRateMarketData IData = InterestRateMarketData.FromFile("../../../EquityModels.Tests/TestData/IRMD-EU-30102012-close.xml");
//CallPriceMarketData HData = CallPriceMarketData.FromFile("../../../EquityModels.Tests/TestData/30102012-SX5E_Index-HestonData.xml");
//CallPriceMarketData HData = ObjectSerialization.ReadFromXMLFile("../../../EquityModels.Tests/TestData/FTSE.xml") as CallPriceMarketData;
List <object> l = new List <object>();
l.Add(IData.DiscountingCurve);
l.Add(HData);
DupireEstimator DE = new DupireEstimator();
DupireCalibrationSettings settings = new DupireCalibrationSettings();
settings.LocalVolatilityCalculation = LocalVolatilityCalculation.Method1;
//settings.LocalVolatilityCalculation = LocalVolatilityCalculation.QuantLib;
EstimationResult res = DE.Estimate(l, settings);
//int nmat = HData.Maturity.Length;
//int nstrike = HData.Strike.Length;
int i = 5; // Maturity.
int j = 4; // Strike.
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 10000;
int n_steps = 500;
double strike = HData.Strike[j];
//double volatility = HData.Volatility[i, j];
/*
* PFunction2D.PFunction2D impvolfunc = new PFunction2D.PFunction2D(rov);
* impvolfunc = res.Objects[3] as PFunction2D.PFunction2D;
* impvolfunc.VarName = "impvol";
* rov.Symbols.Add(impvolfunc);
* double volatility = impvolfunc.Evaluate(HData.Maturity[i], HData.Strike[j]);
*/
double volatility = 0.2;
double maturity = HData.Maturity[i];
ModelParameter Pstrike = new ModelParameter(strike, string.Empty, "strike");
rov.Symbols.Add(Pstrike);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
bool found;
double S0 = PopulateHelper.GetValue("S0", res.Names, res.Values, out found);
ModelParameter PS0 = new ModelParameter(S0, string.Empty, "S0");
rov.Symbols.Add(PS0);
PFunction rfunc = new PFunction(rov);
rfunc = res.Objects[0] as PFunction;
rfunc.VarName = "r";
rov.Symbols.Add(rfunc);
PFunction qfunc = new PFunction(rov);
qfunc = res.Objects[1] as PFunction;
qfunc.VarName = "q";
rov.Symbols.Add(qfunc);
PFunction2D.PFunction2D volfunc = new PFunction2D.PFunction2D(rov);
volfunc = res.Objects[2] as PFunction2D.PFunction2D;
volfunc.VarName = "localvol";
rov.Symbols.Add(volfunc);
DupireProcess process = new DupireProcess();
process.s0 = (ModelParameter)"S0";
process.r = (ModelParameter)"@r";
process.q = (ModelParameter)"@q";
process.localVol = (ModelParameter)"@localvol";
double rate = rfunc.Evaluate(maturity);
double dy = qfunc.Evaluate(maturity);
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = rate;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
op.PayoffInfo.European = true;
rov.Map.Root = op;
rov.NMethods.Technology = ETechType.T_SIMULATION;
rov.NMethods.PathsNumber = n_sim;
rov.NMethods.SimulationSteps = n_steps;
ROVSolver solver = new ROVSolver();
solver.BindToProject(rov);
solver.DoValuation(-1);
if (rov.HasErrors)
{
rov.DisplayErrors();
}
Assert.IsFalse(rov.HasErrors);
ResultItem price = rov.m_ResultList[0] as ResultItem;
double samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
Console.WriteLine("Surf = " + volfunc.Expr);
// Calculation of the theoretical value of the call.
double theoreticalPrice = BlackScholes.Call(rate, S0, strike, volatility, maturity, dy);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
doc.WriteToXMLFile("Dupire.fair");
Assert.LessOrEqual(Math.Abs(theoreticalPrice - samplePrice), tol);
}
/// <summary>
/// Sets several variables used to solve the optimization problem.
/// </summary>
/// <param name="callMarketPrice">A matrix containing call option market prices.</param>
/// <param name="maturity">
/// Vector of call option maturities relative to callMarketPrice matrix.
/// </param>
/// <param name="strike">
/// Vector of call option strikes relative to callMarketPrice matrix.
/// </param>
/// <param name="rate">
/// Vector of zero coupon bond rates calculated relative to maturity vector maturities.
/// </param>
/// <param name="dividendYield">
/// Vector of dividend yield rates calculated relative to maturity vector maturities.
/// </param>
/// <param name="s0">Index/Equity value at the time of calibration.</param>
/// <param name="matBound">
/// A vector containing the minimum and maximum values
/// for maturities to be used in calibration.
/// </param>
/// <param name="strikeBound">
/// A vector containing the minimum and maximum values
/// for strikes to be used in calibration.</param>
private void SetVariables(Matrix callMarketPrice, Vector maturity, Vector strike, Vector rate, Vector dividendYield, double s0)
{
this.s0 = s0;
//var rf = new PFunction(maturity, rate);
var dy = new PFunction(maturity, dividendYield);
//var rfF = new Fairmat.Math.Integrate(x => rf.Evaluate(x));
var dyF = new Fairmat.Math.Integrate(x => dy.Evaluate(x));
this.rate = new Vector(maturity.Length);
this.dividendYield = new Vector(maturity.Length);
for (int z = 0; z < maturity.Length; z++)
{
//this.rate[z] = rfF.AdaptLobatto(0, maturity[z]) / maturity[z];
this.dividendYield[z] = dyF.AdaptLobatto(0, maturity[z]) / maturity[z];
}
this.rate = rate;
this.maturity = maturity;
//this.drift = this.rate - this.dividendYield;
this.strike = strike;
this.callMarketPrice = callMarketPrice;
this.numCall = 0;
callWeight = new Matrix(this.callMarketPrice.R, this.callMarketPrice.C);
putWeight = new Matrix(this.callMarketPrice.R, this.callMarketPrice.C);
for (int r = 0; r < this.callMarketPrice.R; r++)
{
if (this.maturity[r] >= matBound[0] && this.maturity[r]<= matBound[1])
{
for (int c = 0; c < this.callMarketPrice.C; c++)
{
if (this.strike[c] >= s0 * strikeBound[0] && this.strike[c] <= s0 * strikeBound[1])
{
if (calibrateOnCallOptions)
if (this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0)
{
this.callWeight[r, c] = CalculateWeight(this.cpmd.CallVolume[r, c]);
this.numCall++;
this.totalVolume += CalculateWeight(this.cpmd.CallVolume[r, c]) ;
}
if (calibrateOnPutOptions)
if (this.cpmd.PutPrice != null && this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0)
{
this.putWeight[r, c] = CalculateWeight(this.cpmd.PutVolume[r, c]);
this.numPut++;
this.totalVolume += CalculateWeight(this.cpmd.PutVolume[r, c]);
}
}
}
}
}
//calibrate minVolatility: actually in this.cpmd.Volatility there is sigma not sigma^2
if (this.cpmd.Volatility != null)
{
//Rows maturities, columns strikes
vLastMin = 0.5 * Math.Pow(this.cpmd.Volatility.Min().Min(), 2);
v0Min = 0.99 * Math.Pow(this.cpmd.Volatility[0, Range.All].Min().Min(), 2);
v0Max = 1.01 * Math.Pow(this.cpmd.Volatility[0, Range.All].Max().Max(), 2);
}
Console.WriteLine("Options weighting:\t" + weighting);
Console.WriteLine("OptionThreshold:\t" + optionThreshold);
Console.WriteLine("Strike Bounds:\t" + strikeBound);
Console.WriteLine("Maturity Bounds:\t" + matBound);
Console.WriteLine("Lb:\t" + Bounds.Lb);
Console.WriteLine("Ub:\t" + Bounds.Ub);
if(Engine.Verbose>=2)
PutCallTest();
}
/// <summary>
/// Calculates call put prices for several strikes using controlled interpolation.
/// </summary>
/// <param name="context"></param>
private void CalculateSingleRowWithInterpolation(object context)
{
HestonCall hc = context as HestonCall;
int r = hc.row;
hc.sum = 0;
// Finds upper extreme for call and put
int max_c =0;
for (int c = this.callMarketPrice.C-1; c > 0; c--)
{
bool callCondition = this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0;
bool putCondition = this.cpmd.PutPrice!=null && this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0;
if (callCondition || putCondition)
{
max_c = c;
break;
}
}
var strikes = new List<double>();
var calls = new List<double>();
var puts = new List<double>();
//Evaluates in strategic points
for (int c = 0; c < this.callMarketPrice.C; c++)
{
bool callCondition = this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0;
bool putCondition = this.cpmd.PutPrice!=null&& this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0;
if (callCondition || putCondition)
{
hc.K = this.strike[c];
var callPut = hc.HestonCallPutPrice();
strikes.Add(hc.K);
calls.Add(callPut[0]);
puts.Add(callPut[1]);
if (c == max_c)
break;
c += 1;//skip the subsequent strikes
if (c > max_c)
c = max_c;
}
}
// Builds interpolated call and put values.
var callFun = new PFunction((Vector)strikes.ToArray(), (Vector)calls.ToArray());
callFun.m_Function.iType = DVPLUtils.EInterpolationType.SPLINE;
var putFun = new PFunction((Vector)strikes.ToArray(), (Vector)puts.ToArray());
putFun.m_Function.iType = DVPLUtils.EInterpolationType.SPLINE;
// Evaluates at the requested strikes
for (int c = 0; c < this.callMarketPrice.C; c++)
{
bool callCondition = this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0;
bool putCondition = this.cpmd.PutPrice!=null && this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0;
if (callCondition)
{
hc.hestonCallPrice[r, c] = callFun.Evaluate(this.strike[c]);
if (HestonCallOptimizationProblem.optimizeRelativeError)
{
double mkt = pricingMin + this.callMarketPrice[r, c];
double model = pricingMin + hc.hestonCallPrice[r, c];
hc.sum += callWeight[r,c] * Math.Pow((model - mkt) / mkt, 2);
}
else
{
hc.sum += callWeight[r, c] * Math.Pow(hc.hestonCallPrice[r, c] - this.callMarketPrice[r, c], 2);
}
}
if (putCondition)
{
hc.hestonPutPrice[r, c] = putFun.Evaluate(this.strike[c]);
if (HestonCallOptimizationProblem.optimizeRelativeError)
{
double mkt = pricingMin + this.cpmd.PutPrice[r, c];
double model = pricingMin + hc.hestonPutPrice[r, c];
hc.sum += putWeight[r, c] * Math.Pow((model - mkt) / mkt, 2);
}
else
{
hc.sum += putWeight[r, c] * Math.Pow(hc.hestonPutPrice[r, c] - this.cpmd.PutPrice[r, c], 2);
}
}
}
return;
}
/// <summary>
/// Calculates call put prices for several strikes using controlled interpolation.
/// </summary>
/// <param name="context"></param>
private void CalculateSingleRowWithInterpolation(object context)
{
HestonCall hc = context as HestonCall;
int r = hc.row;
hc.sum = 0;
// Finds upper extreme for call and put
int max_c = 0;
for (int c = this.callMarketPrice.C - 1; c > 0; c--)
{
bool callCondition = this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0;
bool putCondition = this.cpmd.PutPrice != null && this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0;
if (callCondition || putCondition)
{
max_c = c;
break;
}
}
var strikes = new List <double>();
var calls = new List <double>();
var puts = new List <double>();
//Evaluates in strategic points
for (int c = 0; c < this.callMarketPrice.C; c++)
{
bool callCondition = this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0;
bool putCondition = this.cpmd.PutPrice != null && this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0;
if (callCondition || putCondition)
{
hc.K = this.strike[c];
var callPut = hc.HestonCallPutPrice();
strikes.Add(hc.K);
calls.Add(callPut[0]);
puts.Add(callPut[1]);
if (c == max_c)
{
break;
}
c += 1;//skip the subsequent strikes
if (c > max_c)
{
c = max_c;
}
}
}
// Builds interpolated call and put values.
var callFun = new PFunction((Vector)strikes.ToArray(), (Vector)calls.ToArray());
callFun.m_Function.iType = DVPLUtils.EInterpolationType.SPLINE;
var putFun = new PFunction((Vector)strikes.ToArray(), (Vector)puts.ToArray());
putFun.m_Function.iType = DVPLUtils.EInterpolationType.SPLINE;
// Evaluates at the requested strikes
for (int c = 0; c < this.callMarketPrice.C; c++)
{
bool callCondition = this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0;
bool putCondition = this.cpmd.PutPrice != null && this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0;
if (callCondition)
{
hc.hestonCallPrice[r, c] = callFun.Evaluate(this.strike[c]);
if (HestonCallOptimizationProblem.optimizeRelativeError)
{
double mkt = pricingMin + this.callMarketPrice[r, c];
double model = pricingMin + hc.hestonCallPrice[r, c];
hc.sum += callWeight[r, c] * Math.Pow((model - mkt) / mkt, 2);
}
else
{
hc.sum += callWeight[r, c] * Math.Pow(hc.hestonCallPrice[r, c] - this.callMarketPrice[r, c], 2);
}
}
if (putCondition)
{
hc.hestonPutPrice[r, c] = putFun.Evaluate(this.strike[c]);
if (HestonCallOptimizationProblem.optimizeRelativeError)
{
double mkt = pricingMin + this.cpmd.PutPrice[r, c];
double model = pricingMin + hc.hestonPutPrice[r, c];
hc.sum += putWeight[r, c] * Math.Pow((model - mkt) / mkt, 2);
}
else
{
hc.sum += putWeight[r, c] * Math.Pow(hc.hestonPutPrice[r, c] - this.cpmd.PutPrice[r, c], 2);
}
}
}
return;
}
/// <summary>
/// Sets several variables used to solve the optimization problem.
/// </summary>
/// <param name="callMarketPrice">A matrix containing call option market prices.</param>
/// <param name="maturity">
/// Vector of call option maturities relative to callMarketPrice matrix.
/// </param>
/// <param name="strike">
/// Vector of call option strikes relative to callMarketPrice matrix.
/// </param>
/// <param name="rate">
/// Vector of zero coupon bond rates calculated relative to maturity vector maturities.
/// </param>
/// <param name="dividendYield">
/// Vector of dividend yield rates calculated relative to maturity vector maturities.
/// </param>
/// <param name="s0">Index/Equity value at the time of calibration.</param>
/// <param name="matBound">
/// A vector containing the minimum and maximum values
/// for maturities to be used in calibration.
/// </param>
/// <param name="strikeBound">
/// A vector containing the minimum and maximum values
/// for strikes to be used in calibration.</param>
private void SetVariables(Matrix callMarketPrice, Vector maturity, Vector strike, Vector rate, Vector dividendYield, double s0)
{
this.s0 = s0;
//var rf = new PFunction(maturity, rate);
var dy = new PFunction(maturity, dividendYield);
//var rfF = new Fairmat.Math.Integrate(x => rf.Evaluate(x));
var dyF = new Fairmat.Math.Integrate(x => dy.Evaluate(x));
this.rate = new Vector(maturity.Length);
this.dividendYield = new Vector(maturity.Length);
for (int z = 0; z < maturity.Length; z++)
{
//this.rate[z] = rfF.AdaptLobatto(0, maturity[z]) / maturity[z];
this.dividendYield[z] = dyF.AdaptLobatto(0, maturity[z]) / maturity[z];
}
this.rate = rate;
this.maturity = maturity;
//this.drift = this.rate - this.dividendYield;
this.strike = strike;
this.callMarketPrice = callMarketPrice;
this.numCall = 0;
callWeight = new Matrix(this.callMarketPrice.R, this.callMarketPrice.C);
putWeight = new Matrix(this.callMarketPrice.R, this.callMarketPrice.C);
for (int r = 0; r < this.callMarketPrice.R; r++)
{
if (this.maturity[r] >= matBound[0] && this.maturity[r] <= matBound[1])
{
for (int c = 0; c < this.callMarketPrice.C; c++)
{
if (this.strike[c] >= s0 * strikeBound[0] && this.strike[c] <= s0 * strikeBound[1])
{
if (calibrateOnCallOptions)
{
if (this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0)
{
this.callWeight[r, c] = CalculateWeight(this.cpmd.CallVolume[r, c]);
this.numCall++;
this.totalVolume += CalculateWeight(this.cpmd.CallVolume[r, c]);
}
}
if (calibrateOnPutOptions)
{
if (this.cpmd.PutPrice != null && this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0)
{
this.putWeight[r, c] = CalculateWeight(this.cpmd.PutVolume[r, c]);
this.numPut++;
this.totalVolume += CalculateWeight(this.cpmd.PutVolume[r, c]);
}
}
}
}
}
}
//calibrate minVolatility: actually in this.cpmd.Volatility there is sigma not sigma^2
if (this.cpmd.Volatility != null)
{
//Rows maturities, columns strikes
vLastMin = 0.5 * Math.Pow(this.cpmd.Volatility.Min().Min(), 2);
v0Min = 0.99 * Math.Pow(this.cpmd.Volatility[0, Range.All].Min().Min(), 2);
v0Max = 1.01 * Math.Pow(this.cpmd.Volatility[0, Range.All].Max().Max(), 2);
}
Console.WriteLine("Options weighting:\t" + weighting);
Console.WriteLine("OptionThreshold:\t" + optionThreshold);
Console.WriteLine("Strike Bounds:\t" + strikeBound);
Console.WriteLine("Maturity Bounds:\t" + matBound);
Console.WriteLine("Lb:\t" + Bounds.Lb);
Console.WriteLine("Ub:\t" + Bounds.Ub);
if (Engine.Verbose >= 2)
{
PutCallTest();
}
}
/// <summary>
/// Constructor for the Cox-Ingersoll-Ross Calibration Problem based on caps matrices,
/// using an <see cref="InterestRateMarketData"/> to derive the required data.
/// </summary>
/// <param name="irmd">
/// An <see cref="InterestRateMarketData"/> containing the
/// required information for the optimization problem.
/// </param>
public CapCIROptimizationProblem(InterestRateMarketData irmd)
{
this.capMaturity = irmd.CapMaturity;
this.capRate = irmd.CapRate;
this.tau = irmd.CapTenor;
PFunction zr = new PFunction(null);
zr.m_Function.iType = DVPLUtils.EInterpolationType.LINEAR;
double[,] zrval = (double[,])ArrayHelper.Concat(irmd.ZRMarketDates.ToArray(),
irmd.ZRMarket.ToArray());
zr.Expr = zrval;
this.r0 = zr.Evaluate(0.0);
BlackModel bm = new BlackModel(zr);
this.blackCaps = new Matrix(this.capMaturity.Length, this.capRate.Length);
for (int i = 0; i < this.capMaturity.Length; i++)
{
for (int j = 0; j < this.capRate.Length; j++)
{
if (irmd.CapVolatility[i, j] == 0)
this.blackCaps[i, j] = 0;
else
this.blackCaps[i, j] = bm.Cap(this.capRate[j], irmd.CapVolatility[i, j],
this.tau, this.capMaturity[i]);
if (double.IsNaN(this.blackCaps[i, j]))
throw new Exception("Error on cap market price calculation");
}
}
}