public void Task_2_2_3()
{
// Variance Process Values
double Kappa = 1.5768;
double Theta = 0.0398;
double Sigma = 0.5751;
double V0 = 0.0175;
double Rho = -0.5711;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.025;
// Option Params
double StrikePrice = 100;
PayoffType Type = PayoffType.Call;
double Maturity = 3;
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
EuropeanOption euOption =
new EuropeanOption(StrikePrice, Type, Maturity);
EuropeanOptionFormula euFormula =
new EuropeanOptionFormula(hestonModel, euOption);
Assert.AreEqual(15.4793, euFormula.Price(), 1e-4);
}
/// <summary>
/// Initializes a new instance of the EuropeanOptionMC class.
/// </summary>
/// <param name="parameters">Interface holding Heston Model params.</param>
/// <param name="monteCarloSimulationSettings">Interface holding Monte carlo simulation settings.</param>
/// <param name="asianOption">Interface holding asian option.</param>
public AsianOptionMC(HestonModelParameters parameters,
MonteCarloSettings monteCarloSimulationSettings,
AsianOption asianOption)
: base(parameters, monteCarloSimulationSettings, asianOption)
{
_MonitoringTimes = asianOption.MonitoringTimes;
}
public void Task_2_8_5()
{
// Variance Process Values
double Kappa = 2;
double Theta = 0.06;
double Sigma = 0.4;
double V0 = 0.04;
double Rho = 0.5;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.1;
// Option Params
double Maturity = 9;
// MC Simulation Params
int NumberOfTrials = (int)1e5;
int NumberOfTimeSteps = (int)Math.Ceiling(365 * Maturity);
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
MonteCarloSettings monteCarloSettings =
new MonteCarloSettings(NumberOfTrials, NumberOfTimeSteps);
LookbackOptionMC lookbackOptionMC =
new LookbackOptionMC(hestonModel, monteCarloSettings, Maturity);
Assert.AreEqual(13.6299, lookbackOptionMC.Price(1), 1e-1);
}
public static void HestonModelParamPrint(VarianceProcessParameters parameters,
HestonModelParameters model)
{
System.Console.WriteLine("k={0}, Theta={1}, Sigma={2}, V0={3}, Rho={4}, r={5}",
parameters.Kappa, parameters.Theta, parameters.Sigma, parameters.V0,
parameters.Rho, model.RiskFreeRate);
}
/// <summary>
/// Method for calibrating the heston model.
/// </summary>
/// <param name="guessModelParameters">Object implementing IHestonModelParameters interface containing the risk-free rate, initial stock price
/// and initial guess parameters to be used in the calibration.</param>
/// <param name="referenceData">A collection of objects implementing IOptionMarketData<IEuropeanOption> interface. These should contain the reference data used for calibration.</param>
/// <param name="calibrationSettings">An object implementing ICalibrationSettings interface.</param>
/// <returns>Object implementing IHestonCalibrationResult interface which contains calibrated model parameters and additional diagnostic information</returns>
public static IHestonCalibrationResult CalibrateHestonParameters(IHestonModelParameters guessModelParameters, IEnumerable <IOptionMarketData <IEuropeanOption> > referenceData, ICalibrationSettings calibrationSettings)
{
try
{
// Copy Linked List
LinkedList <OptionMarketData <EuropeanOption> > data =
new LinkedList <OptionMarketData <EuropeanOption> >();
foreach (OptionMarketData <IEuropeanOption> marketData in referenceData)
{
OptionMarketData <EuropeanOption> newMarketData =
new OptionMarketData <EuropeanOption>((EuropeanOption)marketData.Option, marketData.Price);
data.AddLast(newMarketData);
}
// Heston Calibrator
HestonCalibrator calibrator =
new HestonCalibrator((HestonModelParameters)guessModelParameters,
data,
(CalibrationSettings)calibrationSettings);
// Calibration procedure
calibrator.Calibrate();
// Retrieve outcome
double error = 0;
CalibrationOutcome outcome = CalibrationOutcome.NotStarted;
calibrator.GetCalibrationStatus(ref outcome, ref error);
HestonModelParameters parameters = calibrator.GetCalibratedModel();
// Form calibration result object
HestonCalibrationResult result = new HestonCalibrationResult(error, outcome, parameters);
return(result);
}
catch (Exception ex)
{
throw ex;
}
}
/// <summary>
/// Calibrations the objective function.
/// </summary>
/// <param name="paramsArray">Parameters array.</param>
/// <param name="func">Objective Funtion.</param>
/// <param name="obj">Object.</param>
public void CalibrationObjectiveFunction(double[] paramsArray, ref double func, object obj)
{
VarianceProcessParameters varianceParams = new VarianceProcessParameters
(paramsArray[0], paramsArray[1], paramsArray[2], paramsArray[3], paramsArray[4]);
HestonModelParameters m = new HestonModelParameters(_InitialStockPrice, _RiskFreeRate, varianceParams);
func = CalcMeanSquareErrorBetweenModelAndMarket(m);
}
/// <summary>
/// Initializes a new instance of the EuropeanOptionMC class.
/// </summary>
/// <param name="parameters">Interface holding Heston Model params.</param>
/// <param name="monteCarloSimulationSettings">Interface holding Monte carlo simulation settings.</param>
/// <param name="europeanOption">Interface holding European option params.</param>
public EuropeanOptionMC(HestonModelParameters parameters,
MonteCarloSettings monteCarloSimulationSettings,
EuropeanOption europeanOption)
: base(parameters, monteCarloSimulationSettings, europeanOption.Maturity)
{
_StrikePrice = europeanOption.StrikePrice;
_Type = europeanOption.Type;
}
/// <summary>
/// Gets the calibrated model.
/// </summary>
/// <returns>The calibrated model.</returns>
public HestonModelParameters GetCalibratedModel()
{
VarianceProcessParameters varianceParams = new VarianceProcessParameters
(calibratedParams[0], calibratedParams[1], calibratedParams[2], calibratedParams[3], calibratedParams[4]);
HestonModelParameters m = new HestonModelParameters(_InitialStockPrice, _RiskFreeRate, varianceParams);
return(m);
}
public static void HestonModelParamPrint(VarianceProcessParameters parameters,
HestonModelParameters model,
MonteCarloSettings monteCarloSettings)
{
System.Console.WriteLine("k={0}, Theta={1}, Sigma={2}, V0={3}, Rho={4}, r={5}, #Trials={6}, #Steps={7}",
parameters.Kappa, parameters.Theta, parameters.Sigma, parameters.V0,
parameters.Rho, model.RiskFreeRate, monteCarloSettings.NumberOfTrials,
monteCarloSettings.NumberOfTimeSteps);
}
/// <summary>
/// Initializes a new instance of the European option
/// </summary>
/// <param name="parameters">Heston Model Parameter Object</param>
/// <param name="europeanOption">European option Parameter Object</param>
public EuropeanOptionFormula(HestonModelParameters parameters,
EuropeanOption europeanOption)
: base(parameters.InitialStockPrice, parameters.RiskFreeRate,
parameters.GetVariance())
{
_StrikePrice = europeanOption.StrikePrice;
_Type = europeanOption.Type;
_Maturity = europeanOption.Maturity;
}
public static void Task2()
{
// Task 2
// Variance Process Values
Console.WriteLine("Task 2");
double Kappa = 1.5768;
double Theta = 0.0398;
double Sigma = 0.5751;
double V0 = 0.0175;
double Rho = -0.5711;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.025;
// Option Params
double StrikePrice = 100;
PayoffType Type = PayoffType.Call;
int[] Maturity = new int[5] {
1, 2, 3, 4, 15
};
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
// ************Task 2.1 Print****************
System.Console.WriteLine("*********************");
HestonModelParamPrint(varParams, hestonModel);
//Prepare csv
var csv = new StringBuilder();
String newLine = string.Format("K, T, Price");
csv.AppendLine(newLine);
for (int i = 0; i < 5; i++)
{
EuropeanOption euOption =
new EuropeanOption(StrikePrice, Type, Maturity[i]);
double price = Heston.HestonEuropeanOptionPrice(hestonModel, euOption);
System.Console.WriteLine("K={0}, T={1}, C={2}", StrikePrice,
Maturity[i], price);
newLine = string.Format("{0}, {1}, {2}", StrikePrice, Maturity[i], price);
csv.AppendLine(newLine);
}
//Write to csv
File.WriteAllText(@"./task2.csv", csv.ToString());
System.Console.WriteLine("*********************");
System.Console.WriteLine("\n\n");
}
/// <summary>
/// Gets the calibration status.
/// </summary>
/// <param name="calibOutcome">Calibration outcome.</param>
/// <param name="pricingError">Pricing error.</param>
public void GetCalibrationStatus(ref CalibrationOutcome calibOutcome, ref double pricingError)
{
calibOutcome = outcome;
VarianceProcessParameters varianceParams = new VarianceProcessParameters
(calibratedParams[0], calibratedParams[1], calibratedParams[2], calibratedParams[3], calibratedParams[4]);
HestonModelParameters m = new HestonModelParameters(_InitialStockPrice, _RiskFreeRate, varianceParams);
pricingError = CalcMeanSquareErrorBetweenModelAndMarket(m);
}
/// <summary>
/// Initializes a new instance of Heston MC class.
/// </summary>
/// <param name="parameters">Interface holding Heston Model params.</param>
/// <param name="monteCarloSimulationSettings">Interface holding Monte carlo simulation settings.</param>
public HestonMC(HestonModelParameters parameters,
MonteCarloSettings monteCarloSimulationSettings,
double Maturity) :
base(parameters.InitialStockPrice,
parameters.RiskFreeRate,
parameters.GetVariance())
{
_NumberOfTrials = monteCarloSimulationSettings.NumberOfTrials;
_NumberOfTimeSteps = monteCarloSimulationSettings.NumberOfTimeSteps;
_Maturity = Maturity;
}
/// <summary>
/// Calculates the mean square error between model and market.
/// </summary>
/// <returns>The mean square error between model and market.</returns>
/// <param name="m">Current heston parameters</param>
public double CalcMeanSquareErrorBetweenModelAndMarket(HestonModelParameters m)
{
double meanSqErr = 0;
foreach (OptionMarketData <EuropeanOption> marketData in marketOptionsList)
{
EuropeanOptionFormula euFormula = new EuropeanOptionFormula(m, marketData.Option);
double modelPrice = euFormula.Price();
double difference = modelPrice - marketData.Price;
meanSqErr += difference * difference;
}
return(meanSqErr);
}
/// <summary>
/// Initializes a new instance of the HestonCalibrator class.
/// </summary>
/// <param name="parameters">Heston Model Parameters</param>
/// <param name="marketOptions">Observed Option prices</param>
/// <param name="calibrationSettings">Calibration settings</param>
public HestonCalibrator(HestonModelParameters parameters,
LinkedList <OptionMarketData <EuropeanOption> > marketOptions,
CalibrationSettings calibrationSettings)
{
// Heston Model Params
_RiskFreeRate = parameters.RiskFreeRate;
_InitialStockPrice = parameters.InitialStockPrice;
// Copy market data
marketOptionsList = new LinkedList <OptionMarketData <EuropeanOption> >(marketOptions);
// Calibration Settings
accuracy = calibrationSettings.Accuracy;
maxIterations = calibrationSettings.MaximumNumberOfIterations;
// Set default guess parameters
calibratedParams = parameters.CalibrationParamsToArray();
}
public void Task_2_7_1()
{
// Variance Process Values
double Kappa = 2;
double Theta = 0.06;
double Sigma = 0.4;
double V0 = 0.04;
double Rho = 0.5;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.1;
// Option Params
double StrikePrice = 100;
PayoffType Type = PayoffType.Call;
double Maturity = 1;
List <double> MonitoringTimes = new List <double>
{
0.75,
1.00
};
// MC Simulation Params
int NumberOfTrials = (int)1e5;
int NumberOfTimeSteps = (int)Math.Ceiling(365 * Maturity);
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
AsianOption asianOption =
new AsianOption(StrikePrice, Type, Maturity, MonitoringTimes);
MonteCarloSettings monteCarloSettings =
new MonteCarloSettings(NumberOfTrials, NumberOfTimeSteps);
AsianOptionMC asianOptionMC =
new AsianOptionMC(hestonModel, monteCarloSettings, asianOption);
Assert.AreEqual(13.6299, asianOptionMC.Price(1), 1e-1);
}
public void Task_2_3_3()
{
// Variance Process Values
double Kappa = 2;
double Theta = 0.06;
double Sigma = 0.4;
double V0 = 0.04;
double Rho = 0.5;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.1;
// Option Params
double StrikePrice = 100;
PayoffType Type = PayoffType.Call;
double Maturity = 3;
// MC Simulation Params
int NumberOfTrials = (int)1e5;
int NumberOfTimeSteps = (int)Math.Ceiling(365 * Maturity);
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
EuropeanOption euOption =
new EuropeanOption(StrikePrice, Type, Maturity);
MonteCarloSettings monteCarloSettings =
new MonteCarloSettings(NumberOfTrials, NumberOfTimeSteps);
EuropeanOptionMC euOptionMC = new EuropeanOptionMC(hestonModel,
monteCarloSettings, euOption);
Assert.AreEqual(29.9957, euOptionMC.Price(1), 1e-1);
}
/// <summary>
/// Initializes a new instance of the LookbackOptionMC class.
/// </summary>
/// <param name="parameters">Interface holding Heston Model params.</param>
/// <param name="monteCarloSimulationSettings">Interface holding Monte carlo simulation settings.</param>
/// <param name="maturity">Interface holding maturity.</param>
public LookbackOptionMC(HestonModelParameters parameters,
MonteCarloSettings monteCarloSimulationSettings,
double maturity)
: base(parameters, monteCarloSimulationSettings, maturity)
{
}
public void Task_2_5()
{
// Variance Process Values
double Kappa = 1.5768;
double Theta = 0.398;
double Sigma = 0.5751;
double V0 = 0.0175;
double Rho = -0.5711;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.025;
// Callibration Settings
double accuracy = 0.001;
int maxIter = 1000;
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
CalibrationSettings calibrationSettings = new CalibrationSettings(accuracy, maxIter);
// Market Data
LinkedList <OptionMarketData <EuropeanOption> > observedOptions =
new LinkedList <OptionMarketData <EuropeanOption> >();
EuropeanOption eu1 = new EuropeanOption(80, PayoffType.Call, 1);
OptionMarketData <EuropeanOption> marketData1 =
new OptionMarketData <EuropeanOption>(eu1, 25.72);
observedOptions.AddLast(marketData1);
EuropeanOption eu2 = new EuropeanOption(90, PayoffType.Call, 1);
OptionMarketData <EuropeanOption> marketData2 =
new OptionMarketData <EuropeanOption>(eu2, 18.93);
observedOptions.AddLast(marketData2);
EuropeanOption eu3 = new EuropeanOption(80, PayoffType.Call, 2);
OptionMarketData <EuropeanOption> marketData3 =
new OptionMarketData <EuropeanOption>(eu3, 30.49);
observedOptions.AddLast(marketData3);
EuropeanOption eu4 = new EuropeanOption(100, PayoffType.Call, 2);
OptionMarketData <EuropeanOption> marketData4 =
new OptionMarketData <EuropeanOption>(eu4, 19.36);
observedOptions.AddLast(marketData4);
EuropeanOption eu5 = new EuropeanOption(100, PayoffType.Call, 1.5);
OptionMarketData <EuropeanOption> marketData5 =
new OptionMarketData <EuropeanOption>(eu5, 16.58);
observedOptions.AddLast(marketData5);
// Heston Calibrator
HestonCalibrator calibrator = new HestonCalibrator(hestonModel, observedOptions, calibrationSettings);
calibrator.Calibrate();
double error = 0;
CalibrationOutcome outcome = CalibrationOutcome.NotStarted;
calibrator.GetCalibrationStatus(ref outcome, ref error);
Console.WriteLine("Calibration outcome: {0} and error: {1}", outcome, error);
}
public static void Task3()
{
// Variance Process Values
Console.WriteLine("Task 3");
// Variance Process Values
double Kappa = 2.0;
double Theta = 0.06;
double Sigma = 0.4;
double V0 = 0.04;
double Rho = 0.5;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.1;
// Option Params
double StrikePrice = 100;
PayoffType Type = PayoffType.Call;
double[] Maturity = new double[5] {
1, 2, 3, 4, 15
};
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
// ************Task 3 Print****************
System.Console.WriteLine("*********************");
HestonModelParamPrint(varParams, hestonModel);
//Prepare csv
var csv = new StringBuilder();
String newLine = string.Format("K, T, Price, refPrice");
csv.AppendLine(newLine);
for (int i = 0; i < 5; i++)
{
// MC Simulation Params
int NumberOfTrials = (int)1e5;
int NumberOfTimeSteps = (int)Math.Ceiling(365 * Maturity[i]);
EuropeanOption euOption =
new EuropeanOption(StrikePrice, Type, Maturity[i]);
MonteCarloSettings monteCarloSettings =
new MonteCarloSettings(NumberOfTrials, NumberOfTimeSteps);
double priceForm = Heston.HestonEuropeanOptionPrice(hestonModel, euOption);
double price = Heston.HestonEuropeanOptionPriceMC(hestonModel, euOption, monteCarloSettings);
System.Console.WriteLine("K={0}, T={1}, C_MC={2}, C_form={3}", StrikePrice,
Maturity[i], price, priceForm);
newLine = string.Format("{0}, {1}, {2}, {3}", StrikePrice, Maturity[i], price, priceForm);
csv.AppendLine(newLine);
}
//Write to csv
File.WriteAllText(@"./task3.csv", csv.ToString());
System.Console.WriteLine("*********************");
System.Console.WriteLine("\n\n");
}
public static void Task4()
{
// Variance Process Values
Console.WriteLine("Task 4");
// Variance Process Values
double Kappa = 2.0;
double Theta = 0.06;
double Sigma = 0.4;
double V0 = 0.04;
double Rho = 0.5;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.1;
// Option Params
double StrikePrice = 100;
PayoffType Type = PayoffType.Call;
double Maturity = 1;
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
// ************Task 4 Print****************
System.Console.WriteLine("*********************");
HestonModelParamPrint(varParams, hestonModel);
EuropeanOption euOption =
new EuropeanOption(StrikePrice, Type, Maturity);
double priceForm = Heston.HestonEuropeanOptionPrice(hestonModel, euOption);
System.Console.WriteLine("K={0}, T={1}, refPrice={2}", StrikePrice,
Maturity, priceForm);
//Prepare csv
var csv = new StringBuilder();
String newLine = string.Format("Trials, Time Steps, relError");
csv.AppendLine(newLine);
for (int i = 3; i < 5; i++)
{
// MC Simulation Params
int NumberOfTrials = (int)Math.Pow(10, i);
double[] factor = new double[3] {
0.5, 1, 2
};
for (int j = 0; j < 3; j++)
{
int NumberOfTimeSteps = (int)Math.Ceiling(factor[j] * 365 * Maturity);
MonteCarloSettings monteCarloSettings =
new MonteCarloSettings(NumberOfTrials, NumberOfTimeSteps);
double price = Heston.HestonEuropeanOptionPriceMC(hestonModel, euOption, monteCarloSettings);
System.Console.WriteLine("K={0}, T={1}, #Trials={2}, #TimeSteps={3}, rel_error={4}", StrikePrice,
Maturity, NumberOfTrials, NumberOfTimeSteps, Math.Abs(priceForm - price) / priceForm);
newLine = string.Format("{0}, {1}, {2}", NumberOfTrials, NumberOfTimeSteps, Math.Abs(priceForm - price) / priceForm);
csv.AppendLine(newLine);
}
}
//Write to csv
File.WriteAllText(@"./task4.csv", csv.ToString());
System.Console.WriteLine("*********************");
System.Console.WriteLine("\n\n");
}
public static void Task5()
{
// Variance Process Values
double Kappa = 1.5768;
double Theta = 0.398;
double Sigma = 0.5751;
double V0 = 1.0175;
double Rho = -0.5711;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.025;
// Callibration Settings
double accuracy = 0.001;
int maxIter = 1000;
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
CalibrationSettings calibrationSettings = new CalibrationSettings(accuracy, maxIter);
// Market Data
LinkedList <IOptionMarketData <IEuropeanOption> > observedOptions =
new LinkedList <IOptionMarketData <IEuropeanOption> >();
EuropeanOption eu1 = new EuropeanOption(80, PayoffType.Call, 1);
OptionMarketData <IEuropeanOption> marketData1 =
new OptionMarketData <IEuropeanOption>(eu1, 25.72);
observedOptions.AddLast(marketData1);
EuropeanOption eu2 = new EuropeanOption(90, PayoffType.Call, 1);
OptionMarketData <IEuropeanOption> marketData2 =
new OptionMarketData <IEuropeanOption>(eu2, 18.93);
observedOptions.AddLast(marketData2);
EuropeanOption eu3 = new EuropeanOption(80, PayoffType.Call, 2);
OptionMarketData <IEuropeanOption> marketData3 =
new OptionMarketData <IEuropeanOption>(eu3, 30.49);
observedOptions.AddLast(marketData3);
EuropeanOption eu4 = new EuropeanOption(100, PayoffType.Call, 2);
OptionMarketData <IEuropeanOption> marketData4 =
new OptionMarketData <IEuropeanOption>(eu4, 19.36);
observedOptions.AddLast(marketData4);
EuropeanOption eu5 = new EuropeanOption(100, PayoffType.Call, 1.5);
OptionMarketData <IEuropeanOption> marketData5 =
new OptionMarketData <IEuropeanOption>(eu5, 16.58);
observedOptions.AddLast(marketData5);
HestonCalibrationResult result;
result = (HestonCalibrationResult)
Heston.CalibrateHestonParameters(hestonModel, observedOptions, calibrationSettings);
Console.WriteLine("Calibration outcome: {0} and error: {1}", result.MinimizerStatus, result.PricingError);
}
public static void Task6()
{
Console.WriteLine("********Task 6*********");
// Variance Process Values
double Kappa = 1.5768;
double Theta = 0.398;
double Sigma = 0.5751;
double V0 = 0.0175;
double Rho = -0.5711;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.025;
// Callibration Settings
double accuracy = 1.0e-3;
int maxIter = 1000;
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
HestonModelParameters guess =
new HestonModelParameters(InitialStockPrice, RiskFreeRate,
new VarianceProcessParameters(1.55, 0.88, 1.5999, 0.4, -0.55));
CalibrationSettings calibrationSettings = new CalibrationSettings(accuracy, maxIter);
// Market Data
LinkedList <IOptionMarketData <IEuropeanOption> > observedOptions =
new LinkedList <IOptionMarketData <IEuropeanOption> >();
EuropeanOption eu1 = new EuropeanOption(80, PayoffType.Call, 1);
EuropeanOptionFormula eu1Form = new EuropeanOptionFormula(hestonModel, eu1);
OptionMarketData <IEuropeanOption> marketData1 =
new OptionMarketData <IEuropeanOption>(eu1, eu1Form.Price());
observedOptions.AddLast(marketData1);
EuropeanOption eu2 = new EuropeanOption(90, PayoffType.Call, 1);
EuropeanOptionFormula eu2Form = new EuropeanOptionFormula(hestonModel, eu2);
OptionMarketData <IEuropeanOption> marketData2 =
new OptionMarketData <IEuropeanOption>(eu2, eu2Form.Price());
observedOptions.AddLast(marketData2);
EuropeanOption eu3 = new EuropeanOption(80, PayoffType.Call, 2);
EuropeanOptionFormula eu3Form = new EuropeanOptionFormula(hestonModel, eu3);
OptionMarketData <IEuropeanOption> marketData3 =
new OptionMarketData <IEuropeanOption>(eu3, eu3Form.Price());
observedOptions.AddLast(marketData3);
EuropeanOption eu4 = new EuropeanOption(100, PayoffType.Call, 2);
EuropeanOptionFormula eu4Form = new EuropeanOptionFormula(hestonModel, eu4);
OptionMarketData <IEuropeanOption> marketData4 =
new OptionMarketData <IEuropeanOption>(eu4, eu4Form.Price());
observedOptions.AddLast(marketData4);
EuropeanOption eu5 = new EuropeanOption(100, PayoffType.Call, 1.5);
EuropeanOptionFormula eu5Form = new EuropeanOptionFormula(hestonModel, eu5);
OptionMarketData <IEuropeanOption> marketData5 =
new OptionMarketData <IEuropeanOption>(eu5, eu5Form.Price());
observedOptions.AddLast(marketData5);
HestonCalibrationResult result;
result = (HestonCalibrationResult)
Heston.CalibrateHestonParameters(guess, observedOptions, calibrationSettings);
Console.WriteLine("Calibration outcome: {0} and error: {1}", result.MinimizerStatus, result.PricingError);
}
public static void Task7()
{
// Variance Process Values
Console.WriteLine("Task 7");
// Variance Process Values
double Kappa = 2.0;
double Theta = 0.06;
double Sigma = 0.4;
double V0 = 0.04;
double Rho = 0.5;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.1;
// Option Params
double StrikePrice = 100;
PayoffType Type = PayoffType.Call;
double[] Maturity = new double[3] {
1, 2, 3
};
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
// ************Task 7 Print****************
System.Console.WriteLine("*********************");
HestonModelParamPrint(varParams, hestonModel);
// Monitoring Times
List <double> monTimes1 = new List <double>
{
0.75,
1.00
};
List <double> monTimes2 = new List <double>
{
0.25, 0.5, 0.75, 1.00, 1.25, 1.5, 1.75
};
List <double> monTimes3 = new List <double>
{
1.00, 2.00, 3.00
};
List <List <double> > MonitoringTimes = new List <List <double> >
{
monTimes1, monTimes2, monTimes3
};
//Prepare csv
var csv = new StringBuilder();
String newLine = string.Format("K, T, Price");
csv.AppendLine(newLine);
for (int i = 0; i < 3; i++)
{
// MC Simulation Params
int NumberOfTrials = (int)1e5;
int NumberOfTimeSteps = (int)Math.Ceiling(365 * Maturity[i]);
AsianOption asianOption =
new AsianOption(StrikePrice, Type, Maturity[i], MonitoringTimes[i]);
MonteCarloSettings monteCarloSettings =
new MonteCarloSettings(NumberOfTrials, NumberOfTimeSteps);
double price = Heston.HestonAsianOptionPriceMC(hestonModel,
asianOption, monteCarloSettings);
System.Console.WriteLine("K={0}, T={1}, C_MC={2}", StrikePrice,
Maturity[i], price);
newLine = string.Format("{0}, {1}, {2}", StrikePrice, Maturity[i], price);
csv.AppendLine(newLine);
}
//Write to csv
File.WriteAllText(@"./task7.csv", csv.ToString());
System.Console.WriteLine("*********************");
System.Console.WriteLine("\n\n");
}
public static void Task8()
{
// Variance Process Values
Console.WriteLine("Task 8");
// Variance Process Values
double Kappa = 2.0;
double Theta = 0.06;
double Sigma = 0.4;
double V0 = 0.04;
double Rho = 0.5;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.1;
// Option Params
double[] Maturity = new double[5] {
1, 3, 5, 7, 9
};
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
// ************Task 7 Print****************
System.Console.WriteLine("*********************");
HestonModelParamPrint(varParams, hestonModel);
//Prepare csv
var csv = new StringBuilder();
String newLine = string.Format("T, Price");
csv.AppendLine(newLine);
for (int i = 0; i < 5; i++)
{
// MC Simulation Params
int NumberOfTrials = (int)1e5;
int NumberOfTimeSteps = (int)Math.Ceiling(365 * Maturity[i]);
MonteCarloSettings monteCarloSettings =
new MonteCarloSettings(NumberOfTrials, NumberOfTimeSteps);
Option maturity = new Option(Maturity[i]);
double price = Heston.HestonLookbackOptionPriceMC(hestonModel, maturity, monteCarloSettings);
System.Console.WriteLine("T={0}, C_MC={1}",
Maturity[i], price);
newLine = string.Format("{0}, {1}", Maturity[i], price);
csv.AppendLine(newLine);
}
//Write to csv
File.WriteAllText(@"./task8.csv", csv.ToString());
System.Console.WriteLine("*********************");
System.Console.WriteLine("\n\n");
}
public static void TaskThreadScaling()
{
// Variance Process Values
Console.WriteLine("Task Thread Scaling");
// Variance Process Values
double Kappa = 2.0;
double Theta = 0.06;
double Sigma = 0.4;
double V0 = 0.04;
double Rho = 0.5;
// Heston Model Params
double InitialStockPrice = 100;
double RiskFreeRate = 0.1;
// Option Params
double StrikePrice = 100;
PayoffType Type = PayoffType.Call;
double Maturity = 3;
VarianceProcessParameters varParams =
new VarianceProcessParameters(Kappa, Theta, Sigma, V0, Rho);
HestonModelParameters hestonModel =
new HestonModelParameters(InitialStockPrice, RiskFreeRate, varParams);
// ************Task 3 Print****************
System.Console.WriteLine("*********************");
HestonModelParamPrint(varParams, hestonModel);
//Prepare csv
var csv = new StringBuilder();
String newLine = string.Format("Number of Trials, cores, time");
csv.AppendLine(newLine);
int[] cores = new int[5] {
1, 2, 4, 8, 16
};
for (int i = 0; i < 5; i++)
{
// MC Simulation Params
int NumberOfTrials = (int)1e6;
int NumberOfTimeSteps = (int)Math.Ceiling(365 * Maturity);
EuropeanOption euOption =
new EuropeanOption(StrikePrice, Type, Maturity);
MonteCarloSettings monteCarloSettings =
new MonteCarloSettings(NumberOfTrials, NumberOfTimeSteps);
double priceForm = Heston.HestonEuropeanOptionPrice(hestonModel, euOption);
// Create Monte Carlo EU option object
EuropeanOptionMC euOptionMC = new EuropeanOptionMC(hestonModel, monteCarloSettings, euOption);
var stopwatch = new Stopwatch();
stopwatch.Start();
double price = euOptionMC.Price(cores[i]);
stopwatch.Stop();
long elapsed_time = stopwatch.ElapsedMilliseconds;
System.Console.WriteLine("K={0}, T={1}, cores={2}, C_MC={3}, C_form={4}, time={5}",
StrikePrice, Maturity, cores[i], price, priceForm, elapsed_time);
newLine = string.Format("{0}, {1}, {2}", NumberOfTrials, cores[i], elapsed_time);
csv.AppendLine(newLine);
}
//Write to csv
File.WriteAllText(@"./taskThreadScaling.csv", csv.ToString());
System.Console.WriteLine("*********************");
System.Console.WriteLine("\n\n");
}
