/// Main Code.
static void Main(string[] args)
{
///Defining variables
double[] UnderlyingPrice;
double[] CallPrice;
Random r = new Random(); ///this is the Class used to generate random variables
Discretization disc = new Discretization(); ///class that was coded above used to call the Euler function later in the code
System.Windows.Forms.DataVisualization.Charting.Chart chart = new System.Windows.Forms.DataVisualization.Charting.Chart(); ///class to set up Plot of underlying price
chart.ChartAreas.Add("ChartArea1"); ///set up the initial plot
///The following lines ask the user for the inputs needed to price the option and run the simulation
///Additionally, the inputs provided by the user are assigned the appropriate variables.
Console.WriteLine("Please Enter The Initial Asset Price:");
double X0 = Convert.ToDouble(Console.ReadLine());
Console.WriteLine("Please Enter The Strike Price of the Option:");
double K = Convert.ToDouble(Console.ReadLine());
Console.WriteLine("Please Enter The Time To Expiration:");
double T = Convert.ToDouble(Console.ReadLine());
Console.WriteLine("Please Enter mu:");
double mu = Convert.ToDouble(Console.ReadLine());
Console.WriteLine("Please Enter sigma:");
double sigma = Convert.ToDouble(Console.ReadLine());
/// Console.WriteLine("Please enter The Number of Simulations to Run:");
///int N = Convert.ToInt32(Console.ReadLine());
int N = 5000; ///Number of simulations
int m = 200; ///Number of increments between t = 0 and t = T
double delta = T / m; ///size of the increment
CallPrice = new double[N]; ///now allocating the size of array based on the number of simulations
UnderlyingPrice = new double[m + 1]; //now allocating the size of the array based on the number of increments
double U1; ///Represents uniform random variable between 0 and 1
double U2; ///Also represents uniform random variable between 0 and 1
double Z; ///Will represent the Normal Random Variable with mean 0 and variance 1
double sum1 = 0; //variable used to keep track of the sum in order to find the average of all the Call Prices for each of the simulations
double sum2 = 0; //variable used to keep track of the sum in order to ultimately find the Standard Error of the simulation
double OptionPrice; //Final European Call Option Price calculated
double StandardError; //Standard error of the simulation
for (int i = 0; i < N; i++) ///Each run through this loop represents 1 simulation
{
///Set up a new series that will be plotted on the graph
chart.Series.Add(Convert.ToString(i));
///Set chart type to Line graph
chart.Series[Convert.ToString(i)].ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.Line;
///Initialize the Underlying Price array based on the input given by the user
UnderlyingPrice[0] = X0;
///Plot this initial t = 0 and Underlying price on the graph
chart.Series[Convert.ToString(i)].Points.AddXY(0, UnderlyingPrice[0]);
for (int j = 0; j < m; j++) ///Each run through this loop represents the next increment closer to t = T
{
///Because the Random() Class only allows the creation of uniform random variables between 0 and 1,
///a transform must be done to create a normal random variable with mean 0 and variance 1.
///The transform that was done is called the Box-Muller Transform
U1 = r.NextDouble(); ///Get first uniform random variable
U2 = r.NextDouble(); ///Get second uniform random variable
Z = Math.Sqrt(-2 * Math.Log(U1)) * Math.Cos(2 * Math.PI * U2); ///Box-Muller Transform to generate Z ~ N(0,1)
UnderlyingPrice[j + 1] = disc.Euler(UnderlyingPrice[j], mu, sigma, delta, Z); ///Generate the next X value based on the Euler Discretization
chart.Series[Convert.ToString(i)].Points.AddXY(delta*(j + 1), UnderlyingPrice[j + 1]); ///Plot the t value as well as X(t) value onto the graph for series i
}
CallPrice[i] = Math.Max(0, UnderlyingPrice[m] - K); ///Value of the call option.
}
///Find the sum of all the Call Prices that were simulated (used for the average)
for (int a = 0; a < N; a++ )
{
sum1 = sum1 + CallPrice[a];
}
//Calculate the average which represents the option price
OptionPrice = sum1 / N;
///Same procedure, but to calculate the Standard Error
for (int b = 0; b < N; b++)
{
sum2 = sum2 + Math.Pow((CallPrice[b] - OptionPrice), 2);
}
///SE = s / sqrt(N), where s is the sample standard deviation
StandardError = Math.Sqrt(sum2 / (N - 1)) / Math.Sqrt(N);
///Print out the required output: Price of the European Call Option and the Standard Error of the simulation
Console.WriteLine("The Price of the Option is: " + OptionPrice);
Console.WriteLine("The Standard Error of the Simulation is: " + StandardError);
///Save the graph of the Asset Prices for each simulation in a png file that is saved in the same folder as the location of the .exe
chart.SaveImage("StockPath.png", System.Drawing.Imaging.ImageFormat.Png);
///The console won't close until the user hits any key another time
Console.ReadKey();
}
/// Main Code.
static void Main(string[] args)
{
///Defining variables
double[] UnderlyingPrice;
double[] CallPrice;
Random r = new Random(); ///this is the Class used to generate random variables
Discretization disc = new Discretization(); ///class that was coded above used to call the Euler function later in the code
System.Windows.Forms.DataVisualization.Charting.Chart chart = new System.Windows.Forms.DataVisualization.Charting.Chart(); ///class to set up Plot of underlying price
chart.ChartAreas.Add("ChartArea1"); ///set up the initial plot
///The following lines ask the user for the inputs needed to price the option and run the simulation
///Additionally, the inputs provided by the user are assigned the appropriate variables.
Console.WriteLine("Please Enter The Initial Asset Price:");
double X0 = Convert.ToDouble(Console.ReadLine());
Console.WriteLine("Please Enter The Strike Price of the Option:");
double K = Convert.ToDouble(Console.ReadLine());
Console.WriteLine("Please Enter The Time To Expiration:");
double T = Convert.ToDouble(Console.ReadLine());
Console.WriteLine("Please Enter mu:");
double mu = Convert.ToDouble(Console.ReadLine());
Console.WriteLine("Please Enter sigma:");
double sigma = Convert.ToDouble(Console.ReadLine());
/// Console.WriteLine("Please enter The Number of Simulations to Run:");
///int N = Convert.ToInt32(Console.ReadLine());
int N = 5000; ///Number of simulations
int m = 200; ///Number of increments between t = 0 and t = T
double delta = T / m; ///size of the increment
CallPrice = new double[N]; ///now allocating the size of array based on the number of simulations
UnderlyingPrice = new double[m + 1]; //now allocating the size of the array based on the number of increments
double U1; ///Represents uniform random variable between 0 and 1
double U2; ///Also represents uniform random variable between 0 and 1
double Z; ///Will represent the Normal Random Variable with mean 0 and variance 1
double sum1 = 0; //variable used to keep track of the sum in order to find the average of all the Call Prices for each of the simulations
double sum2 = 0; //variable used to keep track of the sum in order to ultimately find the Standard Error of the simulation
double OptionPrice; //Final European Call Option Price calculated
double StandardError; //Standard error of the simulation
for (int i = 0; i < N; i++) ///Each run through this loop represents 1 simulation
{
///Set up a new series that will be plotted on the graph
chart.Series.Add(Convert.ToString(i));
///Set chart type to Line graph
chart.Series[Convert.ToString(i)].ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.Line;
///Initialize the Underlying Price array based on the input given by the user
UnderlyingPrice[0] = X0;
///Plot this initial t = 0 and Underlying price on the graph
chart.Series[Convert.ToString(i)].Points.AddXY(0, UnderlyingPrice[0]);
for (int j = 0; j < m; j++) ///Each run through this loop represents the next increment closer to t = T
{
///Because the Random() Class only allows the creation of uniform random variables between 0 and 1,
///a transform must be done to create a normal random variable with mean 0 and variance 1.
///The transform that was done is called the Box-Muller Transform
U1 = r.NextDouble(); ///Get first uniform random variable
U2 = r.NextDouble(); ///Get second uniform random variable
Z = Math.Sqrt(-2 * Math.Log(U1)) * Math.Cos(2 * Math.PI * U2); ///Box-Muller Transform to generate Z ~ N(0,1)
UnderlyingPrice[j + 1] = disc.Euler(UnderlyingPrice[j], mu, sigma, delta, Z); ///Generate the next X value based on the Euler Discretization
chart.Series[Convert.ToString(i)].Points.AddXY(delta * (j + 1), UnderlyingPrice[j + 1]); ///Plot the t value as well as X(t) value onto the graph for series i
}
CallPrice[i] = Math.Max(0, UnderlyingPrice[m] - K); ///Value of the call option.
}
///Find the sum of all the Call Prices that were simulated (used for the average)
for (int a = 0; a < N; a++)
{
sum1 = sum1 + CallPrice[a];
}
//Calculate the average which represents the option price
OptionPrice = sum1 / N;
///Same procedure, but to calculate the Standard Error
for (int b = 0; b < N; b++)
{
sum2 = sum2 + Math.Pow((CallPrice[b] - OptionPrice), 2);
}
///SE = s / sqrt(N), where s is the sample standard deviation
StandardError = Math.Sqrt(sum2 / (N - 1)) / Math.Sqrt(N);
///Print out the required output: Price of the European Call Option and the Standard Error of the simulation
Console.WriteLine("The Price of the Option is: " + OptionPrice);
Console.WriteLine("The Standard Error of the Simulation is: " + StandardError);
///Save the graph of the Asset Prices for each simulation in a png file that is saved in the same folder as the location of the .exe
chart.SaveImage("StockPath.png", System.Drawing.Imaging.ImageFormat.Png);
///The console won't close until the user hits any key another time
Console.ReadKey();
}
