Hi Igor, I'm trying to replicate your examples in "Credit Valuation Adjustment with Mathematica 10" but I'm having difficulties with the swap expected positive exposure and mean hazard rate functions. Mathematica complains regarding the window specification using Max[dt, x] since dt has not been defined. May I know how to define dt?

Hi Igor, thanks a lot for the answer! I'm now able to generate the graphs related to the swap expected positive exposure and the mean hazard rate. I also have no problems replicating the survival probability plot and the conditional probabilities as a function of time graph. Unfortunately, when I evaluate the CVAS formula, Mathematica returns a series of errors:

CVAS[n_, fr_, r_] :=
 Module[{f, g, s}, 
   f = TemporalData[Table[{i, survfunc[i]}, {i, 0, n, fr}]];
   g = MovingMap[First[#] - Last[#] &, f, {2}];
   s = (1 - r)*
     Sum[DF[i]*epe[i]*g["PathFunction"][i], {i, fr, n, fr}];
   s];
CVAS[5, 1/2, 0.4]*10^4

InterpolatingFunction::dmval: Input value {-(1/2)} lies outside the range of data in the interpolating function. Extrapolation will be used.

InterpolatingFunction::dmval: Input value {-1} lies outside the range of data in the interpolating function. Extrapolation will be used.

InterpolatingFunction::dmval: Input value {-(3/2)} lies outside the range of data in the interpolating function. Extrapolation will be used.

General::stop: Further output of InterpolatingFunction::dmval will be suppressed during this calculation.

16.7952

May I know how to solve this issue? I'm attaching the notebook as well for further reference. Many thanks in advance

Attachments:

Hi Igor, thanks a lot for the code, unfortunately, using Mathematica 11.1.1 that's not what I get:

In[1]:= zrates = {0.012, 0.015, 0.0167, 0.0176, 0.019, 0.0201, 0.0223,
    0.0235};
times = {0.25, 0.5, 1, 1.5, 2, 3, 4, 5};
zrobj = TemporalData[zrates, {times}];

In[4]:= intrate = Interpolation[zrobj["Path"], Method -> "Spline"];

In[5]:= DF[x_] := Exp[-intrate[x]*x];
{dt, y, R} = {0.005, 5, 0.4};

In[8]:= cW[\[Rho]_] := 
  Refine[ItoProcess[{{0, 0}, IdentityMatrix[2]}, {{n1, n2}, {0, 0}}, 
    t, {{1, \[Rho]}, {\[Rho], 1}}], -1 < \[Rho] < 1];

In[9]:= combprc = 
  ItoProcess[{\[DifferentialD]s[
       t] == \[Mu] s[t] \[DifferentialD]t + \[Sigma]1*
       s[t] \[DifferentialD]n1[t], \[DifferentialD]c[
       t] == \[Theta] (\[Beta] - c[t]) \[DifferentialD]t + \[Sigma]2*
       Sqrt[Abs[c[t]]] \[DifferentialD]n2[t]}, {s[t], 
    c[t]}, {{s, c}, {s0, c0}}, t, {n1, n2} \[Distributed] cW[\[Rho]]];

In[10]:= simproc = 
  RandomFunction[
   combprc /. {\[Mu] -> 0.022, \[Sigma]1 -> 0.2, \[Theta] -> 
      0.005, \[Beta] -> 0.015, \[Sigma]2 -> 0.05, \[Rho] -> 0.5, 
     s0 -> 0.025, c0 -> 0.0125}, {0, y, dt}, 1000, 
   Method -> "StochasticRungeKutta"];

In[11]:= Exposure[T_, S_, t_, v_] := (T - t)*Max[v - S, 0];

In[12]:= swapproc = simproc["PathComponent", 1];

In[13]:= expswap = 
  TimeSeriesMapThread[Exposure[5, 0.025, #1, #2] &, swapproc];

In[14]:= cdsproc = simproc["PathComponent", 2];

In[15]:= hazrate = TimeSeriesMap[#/(1 - R) &, cdsproc];

In[16]:= eeswap = 
  TimeSeriesThread[Mean, expswap, ResamplingMethod -> Interpolation];
eehaz = TimeSeriesThread[Mean, hazrate, 
   ResamplingMethod -> Interpolation];

In[18]:= epe[x_] := 
  Mean[TimeSeriesWindow[eeswap, {0, Max[dt, x]}, 
    ResamplingMethod -> Interpolation]];

In[19]:= exphazrate[x_] := 
  Mean[TimeSeriesWindow[eehaz, {0, Max[dt, x]}, 
    ResamplingMethod -> Interpolation]];

In[20]:= survfunc[x_] := Exp[-exphazrate[x]*x];

In[21]:= CVAS[n_, fr_, r_] := 
  Module[{f, g, s}, 
   f = TemporalData[Table[{i, survfunc[i]}, {i, 0, n, fr}]];
   g = MovingMap[First[#] - Last[#] &, f, {2}];
   s = (1 - r)*
     Sum[DF[i]*epe[i]*g["PathFunction"][i], {i, fr, n, fr}];
   s];

In[22]:= CVAS[5, 1/2, 0.4]*10^4

During evaluation of In[22]:= InterpolatingFunction::dmval: Input value {-(1/2)} lies outside the range of data in the interpolating function. Extrapolation will be used.

During evaluation of In[22]:= InterpolatingFunction::dmval: Input value {-1} lies outside the range of data in the interpolating function. Extrapolation will be used.

During evaluation of In[22]:= InterpolatingFunction::dmval: Input value {-(3/2)} lies outside the range of data in the interpolating function. Extrapolation will be used.

During evaluation of In[22]:= General::stop: Further output of InterpolatingFunction::dmval will be suppressed during this calculation.

Out[22]= 16.5418

Any ideas why is still not working?

Hi Igor, yes, that took care of the problem. Thanks a lot! By the way, do you have any idea why Mathematica returns the error message?