Semiparametric method in predicting loss given default

shiyiming

From Dapangmao's blog on sas-analysis

<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-oNlKv_Qd2fY/TfeRUSBJL6I/AAAAAAAAAnQ/ybEMTESyueU/s1600/plot1.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="300" width="400" src="http://4.bp.blogspot.com/-oNlKv_Qd2fY/TfeRUSBJL6I/AAAAAAAAAnQ/ybEMTESyueU/s400/plot1.jpg" /></a></div><br />
Sparse data is a big concern in building models for loss given default (LGD) for corporate risk. For LGD, most predictors are instrument-related, firm-specific, macroeconomic and industry-specific variables, while the costs to collect such data may be relatively high. In one example of Gunter and Peter’s book, industry-wise average default rate, yearly average default rate, firm-wise leverage rate were applied to predict LGD. To increase the predictability, the painful transformation of LGD was conducted [Ref. 1]. Actually some non-linear models could be considered. <br />
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In a conference paper about consumer risk scoring, Wensui mentioned that generalized additive model (GAM) provides the ability to detect the nonlinear relationship between risk behavior and predictors [Ref. 2]. In this example, we are possibly more interested in estimating the parameter of firm-specific leverage (lev). Thus I used Proc GAM to estimate this variable’s parameter while smoothing other predictors by LOESS functions. In addition, I used Proc LOESS to realize the nonparametric regression.  Comparing the two methods in a series plot, their predictions of LGD are pretty close. As the result, Proc GAM may provide us an insightful tool to construct meaningful semiparametric regression to predict LGD. <br />
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References:<br />
1. Gunter Loeffler and Peter Posch. ‘Credit Risk Modeling using Excel and VBA’. The 2nd edition. Wiley. 2011 <br />
2. Wensui Liu, Chuck Vu, Jimmy Cela.‘Generalizations of Generalized Additive Model (GAM): A Case of Credit Risk Modeling’. SAS Global 2009<br />
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<pre style="background-color: #ebebeb; border: 1px dashed rgb(153, 153, 153); color: #000001; font-size: 14px; line-height: 14px; overflow: auto; padding: 5px; width: 100%;"><code>data _tmp01;
  infile "h:\raw_data.txt" delimiter = '09'x missover dsd firstobs=2;
  informat lgd   lev   lgd_a i_def 8.3;
  label lgd   = 'Real loss given default'
      lev   = 'Leverage coefficient by firm'
      lgd_a = 'Mean default rate by year'
      i_def = 'Mean default rate by industry';
  input lgd   lev   lgd_a i_def;
run;

ods html gpath = 'h:\' style = money;
ods graphics on;
proc loess data=_tmp01;
   model lgd = lev lgd_a i_def / scale = sd select = gcv degree = 2;
   score;
   ods output scoreresults = predloess;
run;

proc gam data= _tmp01 plots = components(clm);
   model lgd = loess(i_def) loess(lgd_a) param(lev) / method = gcv;
   output out = predgam p = pbygam;
run;
ods graphics off;

data _tmp02;
   merge predloess predgam;
   keep p_LGD LGD pbygamLGD obs;
   label p_LGD = 'Prediction by Proc LOESS'
      pbygamLGD = 'Prediction by Proc GAM';
run;

proc sgplot data = _tmp02;
   series x = obs y = lgd ;
   series x = obs y = p_lgd;
   series x = obs y = pbygamlgd;
   yaxis label = 'loss given default';
run;
ods html close;</code></pre><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/3256159328630041416-1684032422675976774?l=www.sasanalysis.com' alt='' /></div><img src="http://feeds.feedburner.com/~r/SasAnalysis/~4/QAPr8DGlF90" height="1" width="1"/>