HW2Q2 code: Convergence of Stock Price SDE solutions
sizeN = [6,1]; a size larger than in Ques#2;
N = [100,1000,10000,100000,1000000,10000000];
T = 2.000;
sizedt = [6,1];
dt = [2.000e-02,2.000e-03,2.000e-04,2.000e-05,2.000e-06,2.000e-07];

1: Compute the Reference Maximum Sample Results, i.e., i = m.

sizetm = [1,10000001];
m = 6; Nm = 10000000 = 1.0e+07; only Test:
std(SSDEm-SEXPm) = 2.549e-03;

2: Compute Standard Deviation Results:

Standard Deviation Convergence Test:
 	 	     a)		     b.1)	        b.2)
  i	 N	 std(SSDE-SEXP)	 std(SSDE-SEXACT)   std(SEXP-SEXACT)
  1	1.0e+02	 1.355e+00	 2.192e+01	    2.250e+01
  2	1.0e+03	 1.514e-01	 4.318e+01	    4.316e+01
  3	1.0e+04	 8.907e-02	 3.487e+01	    3.487e+01
  4	1.0e+05	 6.899e-02	 1.290e+02	    1.291e+02
  5	1.0e+06	 9.629e-03	 3.296e+01	    3.296e+01
  6	1.0e+07	 2.549e-03	 2.549e-03	    0.000e+00

3:  Extra Computation of the Convergence Rates.

 Assuming asymptotically, std(Delta[S]) ~ C*(dt(i,1))^beta;
   or log(std(Delta[S])) ~ -beta*log(N(1,i)/T)+log(C).

Local Convergence Rates by Linear Interpolation:
 	 	   a)		     b.1)
  i	 N	 Beta(i)	 Beta(i)
  2	1.0e+03	 9.518e-01	 -2.945e-01
  3	1.0e+04	 2.303e-01	 9.278e-02
  4	1.0e+05	 1.110e-01	 -5.682e-01
  5	1.0e+06	 8.552e-01	 5.928e-01
  6	1.0e+07	 5.771e-01	 4.112e+00
Note: Only Part a) convergence is Useful.

Convergence Rate Fit by Ordinary Least Squares for Part a) Results:
Cov[-log(N),log(Stda)] = 7.656e+00; Var[-log(N)] = 1.546e+01;
Conv. Rate Power: beta_a = Cov/Var = 4.951e-01; Approx. 0.5;
Note: Approximately, convergence is O(1/sqrt(N(i,1))),
      which is very appropriate for a Normal Distribution
      and simple Monte Carlo simulations.
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