/// <summary>
/// Test method, displays a sensitivity on heston call and put prices.
/// </summary>
private void PutCallTest()
{
Console.WriteLine("Black-Sholes Calls Market Prices");
Console.WriteLine(this.callMarketPrice);
Console.WriteLine("Strikes");
Console.WriteLine(this.strike);
Console.WriteLine("Maturities");
Console.WriteLine(this.maturity);
var x = new Vector()
{
3.18344026504981,
0.0427882999286046,
0.644527074840708,
-0.659960749691282,
0.0150455464938991,
0.0211747510984717
};
HestonCall hc = new HestonCall(this, x, this.s0);
hc.T = .1;
hc.rate = this.rate[0];
Console.WriteLine("Strike\tCall\tPut");
for (int z = 200; z < 6500; z += 1000)
{
hc.K = z;
var call = hc.HestonCallPrice();
var put = hc.HestonPutPrice();
var callPut = hc.HestonCallPutPrice();
Console.WriteLine(z + "\t" + callPut[0] + "\t" + callPut[1]);
}
}
public void Test()
{
double k = 0.9;
double tau = 2.0;
double rate = 0.1;
double dy = 0.07;
double kappa = 2.5;
double theta = 0.4;
double sigma = 0.2;
double s0 = 1.0;
double v0 = 0.3;
double rho = -0.8;
// Calculates the theoretical value of the call.
Vector param = new Vector(5);
param[0] = kappa;
param[1] = theta;
param[2] = sigma;
param[3] = rho;
param[4] = v0;
HestonCall hestonCall = new HestonCall();
double fairmatPrice = hestonCall.HestonCallPrice(param, s0, tau, k, rate, dy);
double tol = 1e-9;
double benchmarkPrice = 0.339537359104676;
Console.WriteLine("Theoretical Benchmark Price = " + benchmarkPrice.ToString());
Console.WriteLine("Theoretical Fairmat Price = " + fairmatPrice);
Assert.Less(Math.Abs(fairmatPrice - benchmarkPrice), tol);
}
/// <summary>
/// Calculates a single row of the objective function. Basically
/// options with the same maturity and different strikes.
/// </summary>
/// <param name='context'>
/// An object of type <see cref="HestonCall"/> containing the context.
/// </param>
private void CalculateSingleRow(object context)
{
CalculateSingleRowWithInterpolation(context);
return;
HestonCall hc = context as HestonCall;
int r = hc.row;
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[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0;
if (callCondition)//||putCondition)
{
hc.K = this.strike[c];
var callPut = hc.HestonCallPutPrice();
hc.hestonCallPrice[r, c] = callPut[0];
hc.hestonPutPrice[r, c] = callPut[1];
if (callCondition)
{
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)
* {
* 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;
}
public void Test()
{
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 = 50000;
int n_steps = 512;
double strike = 100.0;
double tau = 5.0;
double rate = 0.1;
double dy = 0.07;
ModelParameter pStrike = new ModelParameter(strike, "strike");
pStrike.VarName = "strike";
rov.Symbols.Add(pStrike);
ModelParameter pRate = new ModelParameter(rate, "rfrate");
pRate.VarName = "rfrate";
rov.Symbols.Add(pRate);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
HestonProcess process = new HestonProcess();
process.r = (ModelParameter)rate;
process.q = (ModelParameter)dy;
process.k = (ModelParameter)2.5;
process.theta = (ModelParameter)0.4;
process.sigma = (ModelParameter)0.2;
process.S0 = (ModelParameter)100.0;
process.V0 = (ModelParameter)0.3;
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(v1a)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)tau;
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)
{
Console.WriteLine(rov.m_RuntimeErrorList[0]);
}
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);
// Calculates the theoretical value of the call.
Vector param = new Vector(5);
param[0] = process.k.V();
param[1] = process.theta.V();
param[2] = process.sigma.V();
param[3] = 0.0;
param[4] = process.V0.V();
HestonCall hestonCall = new HestonCall();
double thPrice = hestonCall.HestonCallPrice(param, process.S0.V(),
tau, strike, rate, dy);
Console.WriteLine("Theoretical Price = " + thPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(thPrice - samplePrice), tol);
}
/// <summary>
/// Test method, displays a sensitivity on heston call and put prices.
/// </summary>
private void PutCallTest()
{
Console.WriteLine("Black-Sholes Calls Market Prices");
Console.WriteLine(this.callMarketPrice);
Console.WriteLine("Strikes");
Console.WriteLine(this.strike);
Console.WriteLine("Maturities");
Console.WriteLine(this.maturity);
var x = new Vector() {3.18344026504981,
0.0427882999286046,
0.644527074840708,
-0.659960749691282,
0.0150455464938991,
0.0211747510984717};
HestonCall hc = new HestonCall(this, x, this.s0);
hc.T = .1;
hc.rate = this.rate[0];
Console.WriteLine("Strike\tCall\tPut");
for (int z = 200; z < 6500; z += 1000)
{
hc.K = z;
var call = hc.HestonCallPrice();
var put = hc.HestonPutPrice();
var callPut = hc.HestonCallPutPrice();
Console.WriteLine(z + "\t" + callPut[0] + "\t" + callPut[1]);
}
}
/// <summary>
/// Calibration objective function.
/// </summary>
/// <param name='x'>
/// The vector of parameters.
/// </param>
/// <returns>
/// Objective function value.
/// </returns>
public virtual double Obj(DVPLI.Vector x)
{
double sum = 0;
if(Engine.MultiThread && !displayObjInfo)
{
// Instantiate parallel computation if enabled.
List<Task> tl = new List<Task>();
// Context contains both input parameters and outputs.
List<HestonCall> context = new List<HestonCall>();
for (int r = 0; r < this.callMarketPrice.R; r++)
{
if (this.maturity[r] >= this.matBound[0])
{
HestonCall hc = new HestonCall(this, x, this.s0);
context.Add(hc);
hc.T = this.maturity[r];
hc.rate = this.rate[r];
if (HestonConstantDriftEstimator.impliedDividends)
hc.dividend = x[Range.End];
else
hc.dividend = this.dividendYield[r];
hc.row = r;
tl.Add(Task.Factory.StartNew(this.CalculateSingleRow, hc));
}
}
tsScheduler.WaitTaskList(tl);
for (int r = 0; r < tl.Count; r++)
sum += context[r].sum;
}
else
{
// Sequential version of the code, used when parallel computation is disabled.
HestonCall hc = new HestonCall(this, x, this.s0);
for (int r = 0; r < this.callMarketPrice.R; r++)
{
if (this.maturity[r] >= this.matBound[0])
{
hc.T = this.maturity[r];
hc.rate = this.rate[r];
if (HestonConstantDriftEstimator.impliedDividends)
hc.dividend = x[Range.End];
else
hc.dividend = this.dividendYield[r];
hc.row = r;
hc.sum = 0;
this.CalculateSingleRow(hc);
sum += hc.sum;
}
}
var pricingErrors = hc.hestonCallPrice - this.callMarketPrice;
if (displayObjInfo)
{
avgPricingError = 0;
for (int r = 0; r < this.callMarketPrice.R; r++)
if (this.maturity[r] >= this.matBound[0])
{
for (int c = 0; c < this.callMarketPrice.C; c++)
{
if (this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0)
avgPricingError += Math.Abs(pricingErrors[r, c]);
//if (this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0)
// avgPricingError += Math.Abs(pricingErrors[r, c]);
}
}
avgPricingError /= numCall;
int RR = Math.Min(12, this.callMarketPrice.R - 1);
int CC = Math.Min(12, this.callMarketPrice.C - 1);
Console.WriteLine("Mkt Price");
Console.WriteLine(this.callMarketPrice[Range.New(0,RR),Range.New(0,CC)]);
Console.WriteLine("Pricing Errors");
Console.WriteLine(pricingErrors[Range.New(0, RR), Range.New(0, CC)]);
}
objCount++;
}
//Calculate average distance...
sum = Math.Sqrt( sum /this.totalVolume);
if (this.useBoundPenalty)
sum += this.BoundPenalty(x);
if (this.useFellerPenalty)
sum +=this.FellerPenalty(x);
return sum;
}
/// <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>
/// Calibration objective function.
/// </summary>
/// <param name='x'>
/// The vector of parameters.
/// </param>
/// <returns>
/// Objective function value.
/// </returns>
public virtual double Obj(DVPLI.Vector x)
{
double sum = 0;
if (Engine.MultiThread && !displayObjInfo)
{
// Instantiate parallel computation if enabled.
List <Task> tl = new List <Task>();
// Context contains both input parameters and outputs.
List <HestonCall> context = new List <HestonCall>();
for (int r = 0; r < this.callMarketPrice.R; r++)
{
if (this.maturity[r] >= this.matBound[0])
{
HestonCall hc = new HestonCall(this, x, this.s0);
context.Add(hc);
hc.T = this.maturity[r];
hc.rate = this.rate[r];
if (HestonConstantDriftEstimator.impliedDividends)
{
hc.dividend = x[Range.End];
}
else
{
hc.dividend = this.dividendYield[r];
}
hc.row = r;
tl.Add(Task.Factory.StartNew(this.CalculateSingleRow, hc));
}
}
tsScheduler.WaitTaskList(tl);
for (int r = 0; r < tl.Count; r++)
{
sum += context[r].sum;
}
}
else
{
// Sequential version of the code, used when parallel computation is disabled.
HestonCall hc = new HestonCall(this, x, this.s0);
for (int r = 0; r < this.callMarketPrice.R; r++)
{
if (this.maturity[r] >= this.matBound[0])
{
hc.T = this.maturity[r];
hc.rate = this.rate[r];
if (HestonConstantDriftEstimator.impliedDividends)
{
hc.dividend = x[Range.End];
}
else
{
hc.dividend = this.dividendYield[r];
}
hc.row = r;
hc.sum = 0;
this.CalculateSingleRow(hc);
sum += hc.sum;
}
}
var pricingErrors = hc.hestonCallPrice - this.callMarketPrice;
if (displayObjInfo)
{
avgPricingError = 0;
for (int r = 0; r < this.callMarketPrice.R; r++)
{
if (this.maturity[r] >= this.matBound[0])
{
for (int c = 0; c < this.callMarketPrice.C; c++)
{
if (this.callMarketPrice[r, c] > s0 * optionThreshold && this.cpmd.CallVolume[r, c] > 0)
{
avgPricingError += Math.Abs(pricingErrors[r, c]);
}
//if (this.cpmd.PutPrice[r, c] > s0 * optionThreshold && this.cpmd.PutVolume[r, c] > 0)
// avgPricingError += Math.Abs(pricingErrors[r, c]);
}
}
}
avgPricingError /= numCall;
int RR = Math.Min(12, this.callMarketPrice.R - 1);
int CC = Math.Min(12, this.callMarketPrice.C - 1);
Console.WriteLine("Mkt Price");
Console.WriteLine(this.callMarketPrice[Range.New(0, RR), Range.New(0, CC)]);
Console.WriteLine("Pricing Errors");
Console.WriteLine(pricingErrors[Range.New(0, RR), Range.New(0, CC)]);
}
objCount++;
}
//Calculate average distance...
sum = Math.Sqrt(sum / this.totalVolume);
if (this.useBoundPenalty)
{
sum += this.BoundPenalty(x);
}
if (this.useFellerPenalty)
{
sum += this.FellerPenalty(x);
}
return(sum);
}
public static void Main(string[] args)
{
int Caso = 1;
if (Caso == 0)
{
InterestRateMarketData MData = InterestRateMarketData.FromFile("../../../TestData/InterestRatesModels/05052009-EU.xml");
CallPriceMarketData test = CallPriceMarketData.FromFile("../../../TestData/Heston/05052009-SX5E-HestonData.xml");
EquityCalibrationData CalData = new EquityCalibrationData(test, MData);
Matrix CallMarketPrice = (Matrix)test.CallPrice;
Vector Maturity = (Vector)test.Maturity;
Vector Strike = (Vector)test.Strike;
Vector DividendYield = (Vector)test.DividendYield;
Vector Drift = CalData.Rate - CalData.DividendYield;
Vector Rate = CalData.Rate;
double u, kappa, theta, sigma, rho, v0, s0, r, q, T, K, val;
u = 1.0;
kappa = 19.4;
theta = 0.235;
sigma = 0.00500999;
rho = -0.96;
v0 = 0.664;
s0 = 3872.15;
r = -0.0867303549580581;
q = 0;
T = 0.50;
K = 6000;
Vector MatBound = new Vector(2);
Vector StrikeBound = new Vector(2);
MatBound[0] = 0.0;
MatBound[1] = 2.0;
StrikeBound[0] = 0.7;
StrikeBound[1] = 1.3;
Matrix Volatility = new Matrix(test.CallPrice.R, test.CallPrice.C);
HestonCallOptimizationProblem HP = new HestonCallOptimizationProblem(CallMarketPrice, Maturity, Strike, Rate, DividendYield, test.S0, MatBound, StrikeBound, Volatility);
Complex Cval, Cu;
Cu = u - Complex.I;
HestonCall hc = new HestonCall(HP);
Cval = hc.phi(u, kappa, theta, sigma, rho, s0, v0, r, T);
Console.WriteLine("phi1 = {0}", Cval);
Cval = hc.phi(Cu, kappa, theta, sigma, rho, s0, v0, r, T);
Console.WriteLine("phi2 = {0}", Cval);
val = hc.IntegrandFunc(u, kappa, theta, sigma, rho, s0, v0, r, q, T, K);
Console.WriteLine("IntFunc = {0}", val);
Vector x = new Vector(5);
x[0] = kappa;
x[1] = theta;
x[2] = sigma;
x[3] = rho;
x[4] = v0;
DateTime T1, T2;
TimeSpan ElapsedTime;
double Time, Time2, Time3;
T1 = DateTime.Now;
val = hc.HestonCallPrice(x, s0, T, K, r, q);
T2 = DateTime.Now;
ElapsedTime = T2 - T1;
Time = (double)ElapsedTime.Milliseconds;
Time2 = (double)ElapsedTime.Seconds;
Console.WriteLine("Price = {0}", val);
Console.WriteLine("Elapsed Time = {0}", Time2 + Time / 1000);
int NProve = 10;
int NPassi = 1000;
double val2;
Random CasNum = new Random();
for (int i = 0; i < NProve; i++)
{
for (int j = 0; j < 5; j++)
{
val2 = ((double)CasNum.Next(0, NPassi)) / ((double)NPassi);
x[j] = HP.Bounds.Lb[j] + (HP.Bounds.Ub[j] - HP.Bounds.Lb[j]) * val2;
}
Console.Write("Trial {0} x = " + x.ToString(), i + 1);
T1 = DateTime.Now;
val = HP.Obj(x);
T2 = DateTime.Now;
ElapsedTime = T2 - T1;
Time = (double)ElapsedTime.Milliseconds;
Time2 = (double)ElapsedTime.Seconds;
Time3 = (double)ElapsedTime.Minutes;
Console.WriteLine(" Time = {0}' {1}'' Val = {2}", Time3, Time2 + Time / 1000, val);
}
}
if (Caso == 1)
{
TestHestonCallEstimation NewTest = new TestHestonCallEstimation();
bool Result = NewTest.Run();
}
}