//Runs monte carlo for the "other values" in Task 2.1 using the answer designed for Task 2.2
static void doTask22(SSVIparametrisasion ssvi, int timesteps, int nrofpaths)
{
Console.WriteLine("\nTask 2.2 compared to task 2.1");
double price = 0;
double[] K = new double[] { 102.5313, 105.1271, 103.8212, 80, 80, 90, 120, 90 }; //Values to test
double[] T = new double[] { 1, 2, 1.5, 1, 2, 1, 1, 2 }; //Compare with Task 2.1
Stopwatch sw = new Stopwatch(); //for measuring how long this simulation takes
sw.Start();
for (int i = 0; i < T.Length; ++i)
{
if (i < 6) //Call options
{
price = ssvi.MonteCarloEuropeanCall(T[i], K[i], nrofpaths, timesteps);
Console.WriteLine("For K = {0}, T = {1}, Call option price = {2}", K[i], T[i], Math.Round(price, 2));
}
else //Put options
{
price = ssvi.MonteCarloEuropeanPut(T[i], K[i], nrofpaths, timesteps);
Console.WriteLine("For K = {0}, T = {1}, Put option price = {2}", K[i], T[i], Math.Round(price, 2));
}
}
sw.Stop();
Console.WriteLine("\nTime with parallel for loops elapsed = {0}", sw.Elapsed);
}
public double T, K, S; // Parameters needed for path
public GeneratePath(SSVIparametrisasion ssvi)
{
numericalDerivative = new MathNet.Numerics.Differentiation.NumericalDerivative(); //to approximate derivaties with the finite diff method.
this.ssvi = ssvi; //The surface we are working with
this.S = ssvi.S;
this.T = ssvi.T;
}
//Do monte carlo simulations for lookback options as described in task 2.5
static void doTask25(SSVIparametrisasion ssvi, int timesteps, int nrofpaths)
{
Console.WriteLine("\nValues for Task 2.5");
double[] T = new double[] { 0.5, 1, 1.5 };
double K = 100;
foreach (double t in T)
{
double MCprice = ssvi.PricingLookbackOpt(t, K, nrofpaths, timesteps);
Console.WriteLine("Pricing lookback option MC price: {0} for T: {1} ", Math.Round(MCprice, 2), t);
}
}
//Compare performance of monte carlo wtih parallel for loops and regular loops
static void doTaskExtra(SSVIparametrisasion ssvi, int timesteps, int nrofpaths)
{
Console.WriteLine("\nCompare speed of parallel Monte Carlo and regular Monte Carlo");
double price; //option price
double[] K = new double[] { 80, 80, 90, 120, 90 }; //Values to test
double[] T = new double[] { 1, 2, 1, 1, 2 }; //Compare with Task 2.1
for (int pths = 100; pths <= nrofpaths; pths *= 10)
{
Stopwatch sw = new Stopwatch(); //Object to time this method
Console.WriteLine("\nRunning European option price monte carlo simulation with {0} paths using regular loops", pths);
sw.Start();
for (int i = 0; i < T.Length; ++i)
{
if (i < 3) //Call options
{
price = ssvi.MonteCarloEuropeanCallSlow(T[i], K[i], pths, timesteps);
}
else //Put options
{
price = ssvi.MonteCarloEuropeanPutSlow(T[i], K[i], pths, timesteps);
}
}
sw.Stop();
Console.WriteLine("\nTask 2.2 completed with number of paths {0}", pths);
Console.WriteLine("Time with regular loops elapsed = {0}", sw.Elapsed);
sw = new Stopwatch(); //Object to time this method
Console.WriteLine("\nRunning European option price monte carlo simulation with {0} paths using parallel loops", pths);
sw.Start();
for (int i = 0; i < T.Length; ++i)
{
if (i < 3) //Call options
{
price = ssvi.MonteCarloEuropeanCall(T[i], K[i], pths, timesteps);
}
else //Put options
{
price = ssvi.MonteCarloEuropeanPut(T[i], K[i], pths, timesteps);
}
}
sw.Stop();
Console.WriteLine("\nTask 2.2 completed with number of pths {0}", pths);
Console.WriteLine("Time with parallel loops elapsed = {0}", sw.Elapsed);
}
}
//Does monte carlo simulation to get asian arithmetic call options as described in task 2.4
static void doTask24(SSVIparametrisasion ssvi, int timesteps, int nrofpaths)
{
Console.WriteLine("\nValues for Task 2.4");
double[][] Tsteps = new double[][]
{
new double[] { 0.1, 0.2, 0.3, 0.4, 0.5 },
new double[] { 0.25, 0.50, 0.75, 1.00 },
new double[] { 0.5, 1 }
};
double[] T = { 0.5, 1, 1.5 };
double K = 100;
for (int i = 0; i < T.Length; i++)
{
double MCprice = ssvi.AsianArithmeticCallMonteCarlo(T[i], Tsteps[i], K, nrofpaths, timesteps);
Console.WriteLine("Asian arithmetic call option MC price: {0} for T: {1} ", Math.Round(MCprice, 2), string.Join(", ", Tsteps[i]));
}
}
//Method that does everything needed in task 2.1 gives the values for the table
static void doTask21(SSVIparametrisasion ssvi)
{
double sigma;
double[] K = new double[] { 102.5313, 105.1271, 103.8212 }; //Ks for on the money
double[] T = new double[] { 1, 2, 1.5 }; //Ts for on the money
Console.WriteLine("Task 2.1");
Console.WriteLine("On the money prices");
//Loop to get call option prices "on the money"
for (int i = 0; i < K.Length; ++i)
{
ssvi.T = T[i];
sigma = ssvi.SSVI_Impliedvolatility(T[i], 0);
double call_price = (BlackScholesFormula.CalculateCallOptionPrice(ssvi.S, ssvi.r, sigma, K[i], T[i]));
Console.WriteLine("For K = {0}, T = {1}, C(0, S) = {2}", K[i], T[i], Math.Round(call_price, 2));
}
double k;
Console.WriteLine("\nOther prices");
//Values for "other prices"
K = new double[] { 80, 80, 90, 120, 90 };
T = new double[] { 1, 2, 1, 1, 2 };
//Loop that gets call option prices where k is not 0
for (int i = 0; i < K.Length; ++i)
{
ssvi.T = T[i];
k = ssvi.Log_moneyness(K[i]);
sigma = ssvi.SSVI_Impliedvolatility(T[i], k);
double price;
if (i < 3) //call options
{
price = (BlackScholesFormula.CalculateCallOptionPrice(ssvi.S, ssvi.r, sigma, K[i], T[i]));
Console.WriteLine("For K = {0}, T = {1}, Call option price = {2}", K[i], T[i], Math.Round(price, 2));
}
else //put options
{
price = (BlackScholesFormula.CalculatePutOptionPrice(ssvi.S, ssvi.r, sigma, K[i], T[i]));
Console.WriteLine("For K = {0}, T = {1}, Put option price = {2}", K[i], T[i], Math.Round(price, 2));
}
}
}
//Use main to call other methods
static void Main(string[] args)
{
//Declare parameters
double S = 100;
double n = 0.2, rho = 0.3, gamma = 0.7, alpha = Math.Sqrt(0.1), beta = 1, r = 0.025; //constants given in assignment description
SSVIparametrisasion ssvi = new SSVIparametrisasion(n, gamma, rho, alpha, beta, r, S); //create the surface
int timesteps = 128, nrofpaths = 100000; //Change this to make code faster
//Use static methods to complete task in a organized way
//doTask21(ssvi);
Console.WriteLine("\nMonte Carlo methods using {0} different paths with {1} time steps", nrofpaths, timesteps);
doTask22(ssvi, timesteps, nrofpaths);
doTask24(ssvi, timesteps, nrofpaths);
doTask25(ssvi, timesteps, nrofpaths);
doTaskExtra(ssvi, timesteps, nrofpaths);
Console.WriteLine("\nProgram execution completed press any key to continue");
Console.ReadKey();
}
