public void C9_9_6_TwoFactor_Spread_European()
{
// Declare and initialise the parameters
var myData = new TwoFactorBinomialParameters
{
sigma1 = 0.2,
sigma2 = 0.3,
T = 1.0,
r = 0.06,
K = 1.0,
div1 = 0.03,
div2 = 0.04,
rho = 0.5,
exercise = false
};
// Clewlow and Strickland p. 47
// false;
var S1 = 100.0;
var S2 = 100.0;
var w1 = 1.0;
var w2 = -1.0;
var cp = 1;
myData.pay = new SpreadStrategy(cp, myData.K, w1, w2);
var myTree = new TwoFactorBinomial(myData, numberOfSteps, S1, S2);
var price = myTree.Price();
Assert.AreEqual(price, 10.13757, 0.001);
}
public void C9_9_6_TwoFactor_Basket_European()
{
double Price(double T, double sig1, double sig2)
{
var myData = new TwoFactorBinomialParameters
{
sigma1 = sig1,
sigma2 = sig2,
T = T,
r = 0.1,
K = 40.0,
div1 = 0.0,
div2 = 0.0,
rho = 0.5,
exercise = false
};
var S1 = 18.0;
var S2 = 20.0;
var w1 = 1.0;
var w2 = 1.0;
var cp = -1; // Weights; put option
myData.pay = new BasketStrategy(myData.K, cp, w1, w2);
var myTree = new TwoFactorBinomial(myData, 500, S1, S2);
return(myTree.Price());
}
Assert.AreEqual(Price(0.95, 0.1, 0.1), 0.6032, 0.001);
Assert.AreEqual(Price(0.95, 0.1, 0.2), 1.2402, 0.001);
Assert.AreEqual(Price(0.95, 0.1, 0.3), 1.9266, 0.001);
Assert.AreEqual(Price(0.95, 0.2, 0.1), 1.1597, 0.001);
Assert.AreEqual(Price(0.95, 0.2, 0.2), 1.7749, 0.001);
Assert.AreEqual(Price(0.95, 0.2, 0.3), 2.4383, 0.001);
Assert.AreEqual(Price(0.95, 0.3, 0.1), 1.7639, 0.001);
Assert.AreEqual(Price(0.95, 0.3, 0.2), 2.355, 0.001);
Assert.AreEqual(Price(0.95, 0.3, 0.3), 2.9976, 0.001);
Assert.AreEqual(Price(0.05, 0.1, 0.1), 1.8025, 0.001);
Assert.AreEqual(Price(0.05, 0.1, 0.2), 1.8332, 0.001);
Assert.AreEqual(Price(0.05, 0.1, 0.3), 1.9117, 0.001);
Assert.AreEqual(Price(0.05, 0.2, 0.1), 1.8270, 0.001);
Assert.AreEqual(Price(0.05, 0.2, 0.2), 1.8859, 0.001);
Assert.AreEqual(Price(0.05, 0.2, 0.3), 1.9817, 0.001);
Assert.AreEqual(Price(0.05, 0.3, 0.1), 1.8906, 0.001);
Assert.AreEqual(Price(0.05, 0.3, 0.2), 1.9682, 0.001);
Assert.AreEqual(Price(0.05, 0.3, 0.3), 2.0737, 0.001);
}
// Accuracy of price on number of steps
public static Vector <double> Prices(TwoFactorBinomialParameters optionData, Vector <int> meshSizes, double S1,
double S2)
{
// Caculates the price for a number of step sizes (usually increasing)
Vector <double> result = new Vector <double> (meshSizes.Size);
//print (result);
// TwoFactorBinomial(TwoFactorBinomialParameters optinData,long NSteps,
// double S1, double S2);
TwoFactorBinomial local;
for (int j = result.MinIndex; j <= result.MaxIndex; j++)
{
local = new TwoFactorBinomial(optionData, meshSizes[j], S1, S2);
result[j] = local.Price();
//cout << local.Price() << ";;";
}
return(result);
}
public static void Main()
{
// Declare and initialise the parameters
TwoFactorBinomialParameters myData = new TwoFactorBinomialParameters();
// Clewlow and Strickland p. 47
myData.sigma1 = 0.2; myData.sigma2 = 0.3;
myData.T = 1.0; myData.r = 0.06; myData.K = 1.0;
myData.div1 = 0.03; myData.div2 = 0.04;
myData.rho = 0.5; myData.exercise = true; // false;
double S1 = 100.0;
double S2 = 100.0;
double w1 = 1.0; double w2 = -1.0; int cp = 1;
myData.pay = new SpreadStrategy(cp, myData.K, w1, w2);
// Min-max option
/* myData.sigma1 = 0.3;
* myData.sigma2 = 0.3;
*
* myData.T = 10.0;
* myData.r = 0.1;
* myData.K = 40.0;
* myData.div1 = 0.0;
* myData.div2 = 0.0;
* myData.rho = 0.5;
* myData.exercise = true;
* double S1 = 40.0;
* double S2 = 40.0;
*
*
* int cp = 1;
* int dMinMax = 1; // 1 == Max, else Min
* myData.pay = new RainbowStrategy(cp, myData.K, dMinMax);*/
// Topper 2005 page 198
/* myData.sigma1 = 0.1; myData.sigma2 = 0.1;
* myData.T = 0.05; myData.r = 0.1; myData.K = 40.0;
* myData.div1 = 0.0; myData.div2 = 0.0;
* myData.rho = 0.5; myData.exercise = false;
*
* double S1 = 18.0; double S2 = 20.0;
* double w1 = 1.0; double w2 = 1.0; int cp = -1; // Weights; put option
* myData.pay = new BasketStrategy(myData.K, cp, w1, w2);*/
/* myData.sigma1 = 0.2; myData.sigma2 = 0.2;
* myData.T = 0.5; myData.r = 0.1; myData.K = 10.0;
* myData.div1 = 0.0; myData.div2 = 0.0;
* myData.rho = 0.5; myData.exercise = false;*/
// double S1 = 122.0; double S2 = 120.0;
// int a = 1; int b = -1; int pp = 1;
// myData.pay = new BasketStrategy(myData.K, pp, a, b);
// myData.pay = new BestofTwoStrategy(myData.K, pp);
// myData.pay = new WorstofTwoStrategy(myData.K, -1);
// myData.pay = new SpreadStrategy(-pp, myData.K, 1,-1);
// cout << "How many timesteps: ";
int NumberOfSteps = 50;
// cin >> NumberOfSteps;
// myData.sigma1 = 0.3; myData.sigma2 = 0.2;
// myData.T = 0.95; myData.r = Math.Log(1.1);
// myData.div1 = Math.Log(1.05); myData.div2 = Math.Log(1.05);
//// myData.div1 = 0; myData.div2 = 0;
// myData.rho = 0.99; myData.exercise = false;
// double S1 = 100; double S2 = 100;
// double w1 = 1.0; double w2 = 1.0; int cp = -1; // Weights; put option
// myData.pay = new BasketStrategy(myData.K, cp, w1, w2); //double strike, int cp,double weight1, double weight2)
// myData.pay = new WorstofTwoStrategy(myData.K, cp);
//myData.pay = new RainbowStrategy(cp, myData.K, 1); //(int cp, double strike, int DMinDMax)
// myData.pay = new DualStrikeStrategy(110, 100, +1, -1); //(int cp, double strike, int DMinDMax)
//myData.pay = new ExchangeStrategy();
// int n1 = 1; int n2 = 1; myData.K = 40.0;
// myData.pay = new PortfolioStrategy(n1, n2, myData.K, -1);
Console.WriteLine("Computing...");
TwoFactorBinomial myTree = new TwoFactorBinomial(myData, NumberOfSteps, S1, S2);
Console.WriteLine("Price is now: {0}", myTree.Price());
// Console.WriteLine(myTree.Price());
// Now examine the convergence of 2-factor Binomial method
/* int size = 12;
* Vector<int> meshSizes = new Vector<int>(size);
* int N = 2;
* for (int j = meshSizes.MinIndex; j <= meshSizes.MaxIndex; j++)
* {
* meshSizes[j] = N;
* N *= 2;
*
* }
* //print(meshSizes);
*
* Vector<double> result = TwoFactorBinomial.Prices(myData, meshSizes, S1, S2);
* for (int j = meshSizes.MinIndex ; j <= meshSizes.MaxIndex; j++)
* {
* Console.WriteLine(result[j]);
* }
*/
}
public TwoFactorBinomial(TwoFactorBinomialParameters optionData, int NSteps,
double S1, double S2)
{ // The most important constuctor
par = optionData;
N = NSteps;
// Mesh sizes, Clewlow (2.43)-(2.44)
delta_T = par.T / N; // DeltaT
h1 = par.sigma1 * Math.Sqrt(delta_T); // DeltaX1
h2 = par.sigma2 * Math.Sqrt(delta_T); // DeltaX2
//cout << "deltas t, S... " << k << ", " << h1 << ", " << h2 << endl;
// Parameters (prob)
double nu1 = par.r - par.div1 - (0.5 * par.sigma1 * par.sigma1);
double nu2 = par.r - par.div2 - (0.5 * par.sigma2 * par.sigma2);
//cout << "nu1... " << nu1 << ", " << nu2 << endl;
double a = h1 * h2; double b = h2 * nu1 * delta_T; double c = h1 * nu2 * delta_T;
double d = par.rho * par.sigma1 * par.sigma2 * delta_T;
//cout << "a ..." << a << ", " << b << ", " << c << ", " << d << endl;
double disc = Math.Exp(-(par.r) * delta_T);
puu = disc * 0.25 * (a + b + c + d) / a; // eq. (2.45)
pud = disc * 0.25 * (a + b - c - d) / a;
pdu = disc * 0.25 * (a - b + c - d) / a;
pdd = disc * 0.25 * (a - b - c + d) / a;
//cout << "puu ..." << puu << ", " << pud << ", " << pdu << ", " << pdd << endl;
// Asset arrays
// Initialise asset prices at *maturity*. Norice that the start index is a negative number
asset1 = new Vector <double>(2 * N + 1, -N);
asset2 = new Vector <double>(2 * N + 1, -N);
asset1[-N] = S1 * Math.Exp(-N * h1);
asset2[-N] = S2 * Math.Exp(-N * h2);
double edx1 = Math.Exp(h1);
double edx2 = Math.Exp(h2);
//cout << "edx1... disc " << edx1 << ", " << edx2 << ", " << disc << endl;
for (int n = -N + 1; n <= N; n++)
{
asset1[n] = asset1[n - 1] * edx1;
asset2[n] = asset2[n - 1] * edx2;
}
//print(asset1);
//print(asset2);
option = new NumericMatrix <double>(2 * N + 1, 2 * N + 1, -N, -N);
// Calculate option price at the expiry date
for (int j = option.MinRowIndex; j <= option.MaxRowIndex; j += 2)
{
//cout << j << ", ";
for (int k = option.MinColumnIndex; k <= option.MaxColumnIndex; k += 2)
{
option[j, k] = Payoff(asset1[j], asset2[k]);
}
}
}
