public void TestCrankNicolson()
{
double spot = 385.5;
double epsilon = 0.0001;
double strike = 400;
double[] rt = { 0.0425,
0.0452,
0.0457,
0.0462 };
int[] tt = { 1, 32, 63, 93 };
int[] divdays = { 0, 48 };
double[] divs = { 20, 10 };
double vol = 0.2046;
int steps = 80;
double tStepSize = 0.01;
DateTime today = new DateTime(2010, 05, 07);
DateTime expiry = new DateTime(2010, 06, 24);
//string style = "European";
double t = expiry.Subtract(today).Days / 365.0 + epsilon; // For CN backwards propagation div time needs to be strictly less than expiry time
double fwd = EquityAnalytics.GetForwardCCLin365(spot, t, divdays, divs, tt, rt);
double df = EquityAnalytics.GetDFCCLin365(0, t, tt, rt);
BlackScholes bs = new BlackScholes(spot, strike, false, t, vol, tt, rt, divdays, divs);
CrankNicolson lhs = new CrankNicolson(false, false, spot, strike, t, vol, steps, tStepSize, 8.0, divdays, divs, tt, rt);
double[,] res0 = OptionAnalytics.BlackScholesWithGreeks(false, fwd, strike, vol, t);
double[] res_cn = lhs.GetPriceAndGreeks();
double pr_bs = bs.GetPrice();
double delta_bs = bs.GetDelta();
double gamma_bs = bs.GetGamma();
double theta_bs = bs.GetTheta();
double pr_cn = res_cn[0];
double delta_cn = res_cn[1];
double gamma_cn = res_cn[2];
double theta_cn = res_cn[3];
Assert.AreEqual(pr_cn, pr_bs, 0.50);
Assert.AreEqual(delta_cn, delta_bs, 0.03);
Assert.AreEqual(gamma_cn, 0.012931145370580023, 0.005);
Assert.AreEqual(bs.GetTheta(), theta_cn, 0.01);
}
public void FurtherCNTests()
{
int[] dt = { 448, 813, 1179, 1544, 1909, 2274, 2640, 3005, 3370, 3735 };
double[] divs = { 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2 };
int[] rtdt = { 74, 439 };
double[] rtam = { 0.03, 0.03 };
DateTime today = new DateTime(2009, 4, 13);
DateTime expiry = new DateTime(2010, 04, 13);
double tau = expiry.Subtract(today).Days / 365.0;
double spot = 26.4;
double strike = 30;
double vol = 0.20;
CrankNicolson cn_ep = new CrankNicolson(false, false, spot, strike, tau, vol, 800, 0.05, 8, dt, divs, rtdt, rtam);
CrankNicolson cn_ec = new CrankNicolson(true, false, spot, strike, tau, vol, 100, 0.05, 8, dt, divs, rtdt, rtam);
CrankNicolson cn_ac = new CrankNicolson(true, true, spot, strike, tau, vol, 100, 0.05, 8, dt, divs, rtdt, rtam);
CrankNicolson cn_ap = new CrankNicolson(false, true, spot, strike, tau, vol, 100, 0.05, 8, dt, divs, rtdt, rtam);
//CrankNicolson cn_ep = new CrankNicolson(ep, rc, dl, 8, 800, 0.05); //extra fine grid
//CrankNicolson cn_ec = new CrankNicolson(ec, rc, dl, 8, 100, 0.05);
//CrankNicolson cn_ac = new CrankNicolson(ac, rc, dl, 8, 100, 0.05);
//CrankNicolson cn_ap = new CrankNicolson(ap, rc, dl, 8, 100, 0.05);
double[] ep_pr = cn_ep.GetPriceAndGreeks();
double[] ec_pr = cn_ec.GetPriceAndGreeks();
double[] ac_pr = cn_ac.GetPriceAndGreeks();
double[] ap_pr = cn_ap.GetPriceAndGreeks();
Assert.AreEqual(ep_pr[0], 3.825991125, 0.001);
Assert.AreEqual(ec_pr[0], 1.121514221, 0.001);
Assert.AreEqual(ac_pr[0], 1.121514221, 0.001);
Assert.AreEqual(ap_pr[0], 4.065906254, 0.001);
}
public void FurtherCNTestsLongDated()
{
int[] dt = { 83,
2274,
2640,
3005,
3370,
3735 };
double[] divs = { 5, 0, 0, 0, 0, 0 };
int[] rtdt = { 74, 439 };
double[] rtam = { 0.05, 0.05 };
DateTime today = new DateTime(2009, 4, 13);
DateTime expiry = new DateTime(2014, 04, 13);
double spot = 26.4;
double strike = 30;
double vol = 0.30;
double tau = expiry.Subtract(today).Days / 365.0;
CrankNicolson cn_ep = new CrankNicolson(false, false, spot, strike, tau, vol, 200, 0.05, 8, dt, divs, rtdt, rtam);
CrankNicolson cn_ec = new CrankNicolson(true, false, spot, strike, tau, vol, 200, 0.05, 8, dt, divs, rtdt, rtam);
CrankNicolson cn_ac = new CrankNicolson(true, true, spot, strike, tau, vol, 200, 0.05, 8, dt, divs, rtdt, rtam);
CrankNicolson cn_ap = new CrankNicolson(false, true, spot, strike, tau, vol, 200, 0.05, 8, dt, divs, rtdt, rtam);
double[] ep = cn_ep.GetPriceAndGreeks();
double[] ec = cn_ec.GetPriceAndGreeks();
double[] ac = cn_ac.GetPriceAndGreeks();
double[] ap = cn_ap.GetPriceAndGreeks();
double volback = cn_ep.ImpVol(ep[0]);
Assert.AreEqual(vol, volback, 0.001);
double ep_delta = ep[1];
double ec_delta = ec[1];
double ac_delta = ac[1];
double ap_delta = ap[1];
double ep_gamma = ep[2];
double ec_gamma = ec[2];
double ac_gamma = ac[2];
double ap_gamma = ap[2];
double ep_theta = ep[3];
double ec_theta = ec[3];
double ac_theta = ac[3];
double ap_theta = ap[3];
Assert.AreEqual(ep[0], 6.9534149, 0.001);
Assert.AreEqual(ec[0], 5.0652783, 0.001);
Assert.AreEqual(ac[0], 5.0652783, 0.001);
Assert.AreEqual(ap[0], 9.3556003, 0.001);
Assert.AreEqual(ep_delta, -0.41851728556981282, 0.001);
Assert.AreEqual(ec_delta, 0.58178041660965252, 0.001);
Assert.AreEqual(ac_delta, 0.58178041660965252, 0.001);
Assert.AreEqual(ap_delta, -0.6687734186983475, 0.001);
Assert.AreEqual(ep_gamma, 0.026900894453080339, 0.001);
Assert.AreEqual(ec_gamma, 0.026899818384012897, 0.001);
Assert.AreEqual(ac_gamma, 0.026899818384012897, 0.001);
Assert.AreEqual(ap_gamma, 0.052277076176625865, 0.001);
//Assert.AreEqual(ep_theta, 0 , 0.001);
//Assert.AreEqual(ec_theta, 0.026899818384012897, 0.001);
//Assert.AreEqual(ac_theta, 0.026899818384012897, 0.001);
//Assert.AreEqual(ap_theta, 0.052277076176625865, 0.001);
}
