public override double GetOptionValue(EquityOption option,
DateTime currentDate,
GbmParameters gbmParams,
double discountFactor,
int numberSims)
///<summary>
/// simulate the payoff of the given equity option and
/// take the average discounted value as the option value
///</summary>
{
var simulatedValues = new List <double>();
var simulationLengthDays = currentDate.GetWorkingDaysTo(option.ExpiryDate) + 1;
var dailyTimePeriod = 1.0 / TimePeriods.BusinessDaysInYear;
for (int i = 0; i < numberSims; i++)
{
var rawStockPrices = GetGeometricBrownianSeries(gbmParams, dailyTimePeriod, simulationLengthDays);
var rawStockTimeSeries = rawStockPrices.AsBDTimeSeries(currentDate);
var optionPayoff = option.GetPayoff(rawStockTimeSeries);
simulatedValues.Add(optionPayoff);
}
var avgPayoff = simulatedValues.Sum() / numberSims;
var discountedAvgPayoff = avgPayoff * discountFactor;
return(discountedAvgPayoff);
}
public override List <double> GetBrownianMotionSeries(GbmParameters parameters,
double timeStep,
int length,
int?seed = null)
///<summary>
/// Returns a list of size length consisting of observations of
/// a brownian motion
/// <paramref name="mean"/> annual drift of the process
/// <paramref name="vol"/> annual standard deviation of modelled returns
/// <paramref name="timeStep"/> period in years between each observation
/// <paramref name="length"/> number of observations to be generated
///</summary>
{
var brownianMotion = new List <double> {
0
};
var standardNormalNumbers = Sampler.GetRandStandardNormal(length - 1, seed);
double prev = 0;
foreach (double x in standardNormalNumbers)
{
var brownian = prev + parameters.Mean * timeStep + parameters.Vol * x * Math.Sqrt(timeStep);
prev = brownian;
brownianMotion.Add(prev);
}
return(brownianMotion);
}
public override List <double> GetStandardBrownianMotionSeries(double timestep,
int length,
int?seed = null)
{
var standardParameters = new GbmParameters(0, 1);
return(GetBrownianMotionSeries(standardParameters, timestep, length, seed));
}
public override List <double> GetGeometricBrownianSeries(GbmParameters parameters,
double timestep,
int length,
int?seed = null)
///<summary>
/// generates a series of observations of a geometric brownian
/// variable for projecting investable assets
/// <paramref name="parameters"/> parameters for brownian motion
/// <paramref name="timeStep"/> period in years between each observation
/// <paramref name="length"/> number of observations to be generated
///</summary>
{
var gbSeries = new List <double>();
var geomParameters = new GbmParameters(parameters.Mean - 0.5 * Math.Pow(parameters.Vol, 2), parameters.Vol);
var brownianSeries = GetBrownianMotionSeries(geomParameters, timestep, length, seed);
foreach (double brownianVal in brownianSeries)
{
var geomBrownianVal = parameters.InitialVal * Math.Exp(brownianVal);
gbSeries.Add(geomBrownianVal);
}
return(gbSeries);
}
public abstract double GetOptionValue(EquityOption option, DateTime currentDate,
GbmParameters gbmParams, double interestRate,
int numberSims);
public abstract List <double> GetBrownianMotionSeries(GbmParameters parameters, double timestep, int length, int?seed = null);
