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文件名:  Pribor3M.rar
资料下载链接地址: https://bbs.pinggu.org/a-1827470.html
本附件包括：
  • Pribor3M.mat
附件大小:
本贴主要参考Kladıvko, K. (2007). Maximum likelihood estimation of the Cox-Ingersoll-Ross process: the Matlab implementation. Technical Computing Prague.

CIR 利率期限结构模型


\[d{{r}_{t}}=\alpha (\mu -{{r}_{t}})dt+\sqrt{{{r}_{t}}}\sigma d{{W}_{t}}\]



论文及数据集Pribor3M见附件：


  1. clc
  2. clear all
  3. close all

  5. load Pribor3M

  7. Model.Data = Pribor3M; %此处即是文中Model.Data
  8. Model.TimeStep = 1/250; % recommended: 1/250 for daily data, 1/12 for monthly data, etc
  9. Model.Disp = 'y'; % 'y' | 'n' (default: y)
  10. Model.MatlabDisp = 'iter'; % 'off'|'iter'|'notify'|'final' (default: off)
  11. Model.Method = 'besseli'; % 'besseli' | 'ncx2pdf' (default: besseli)

  13. Results = CIRestimation(Model);
  14. % 使用OLS估计alpha mu sigma
  15. Nobs = length(Model.Data);
  16. x = Model.Data(1:end-1);
  17. dx = diff(Model.Data);
  18. dx = dx./x.^0.5;
  19. regressors = [Model.TimeStep./x.^0.5, Model.TimeStep*x.^0.5];
  20. drift = regressors\dx;
  21. res = regressors*drift - dx;
  22. alpha = -drift(2);
  23. mu = -drift(1)/drift(2);
  24. sigma = sqrt(var(res, 1)/Model.TimeStep);
  25. InitialParams = [alpha mu sigma];
  26. if ~isfield(Model, 'Disp'), Model.Disp = 'y'; end;
  27. if strcmp(Model.Disp, 'y')
  28. fprintf('\n initial alpha = %+3.6f\n initial mu = %+3.6f\n initial sigma = %+3.6f\n', alpha, mu, sigma);
  29. end

  31. % Optimization using fminsearch优化过程
  32. if ~isfield(Model, 'MatlabDisp'), Model.MatlabDisp = 'off'; end;
  33. options = optimset('LargeScale', 'off', 'MaxIter', 300, 'MaxFunEvals', 300, 'Display', Model.MatlabDisp, 'TolFun', 1e-4, 'TolX', 1e-4, 'TolCon', 1e-4);
  34. if ~isfield(Model, 'Method'), Model.Method = 'besseli'; end;
  35. if strcmp(Model.Method, 'ncx2pdf')
  36. [Params, Fval, Exitflag] =fminsearch(@(Params) CIRobjective2(Params, Model), InitialParams, options);
  37. else
  38. [Params, Fval, Exitflag] =fminsearch(@(Params) CIRobjective1(Params, Model), InitialParams, options);
  39. end

  41. Results.Params = Params;
  42. Results.Fval = -Fval/Nobs;
  43. Results.Exitflag = Exitflag;

  45. if strcmp(Model.Disp, 'y')
  46. fprintf('\n alpha = %+3.6f\n mu = %+3.6f\n sigma = %+3.6f\n', Params(1), Params(2), Params(3));
  47. fprintf(' log-likelihood = %+3.6f\n', -Fval/Nobs);
  48. end
  49. %最大似然估计方法之一：贝塞尔函数
  50. Data = Model.Data;
  51. DataF = Data(2:end);
  52. DataL = Data(1:end-1);
  53. Nobs = length(Data);
  54. TimeStep = Model.TimeStep;
  55. alpha = Params(1);
  56. mu = Params(2);
  57. sigma = Params(3);

  59. c = 2*alpha/(sigma^2*(1-exp(-alpha*TimeStep)));
  60. q = 2*alpha*mu/sigma^2-1;
  61. u = c*exp(-alpha*TimeStep)*DataL;
  62. v = c*DataF;
  63. z = 2*sqrt(u.*v);
  64. bf = besseli(q,z,1);
  65. lnL= -(Nobs-1)*log(c) + sum(u + v - 0.5*q*log(v./u) - log(bf) - z);
  66. %最大似然估计之二：非中心卡方分布函数
  67. Data = Model.Data;
  68. DataF = Data(2:end);
  69. DataL = Data(1:end-1);
  70. TimeStep = Model.TimeStep;
  71. alpha = Params(1);
  72. mu = Params(2);
  73. sigma = Params(3);

  75. c = 2*alpha/(sigma^2*(1-exp(-alpha*TimeStep)));
  76. q = 2*alpha*mu/sigma^2-1;
  77. u = c*exp(-alpha*TimeStep)*DataL;
  78. v = c*DataF;
  79. nc = 2*u;
  80. df = 2*q+2;
  81. s = 2*v;

  83. gpdf = ncx2pdf(s, df, nc);
  84. ppdf = 2*c*gpdf;
  85. lnL = sum(-log(ppdf));
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