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# Valuation of Credit Default Options

Posted 10 years ago
 Credit default swap options which are better known by the term CDS Swaptions are useful instrument to trade future expectation of the credit worthiness of a reference entity in the option format. As the name suggest, they are similar to their interest rate counterparts, but differ in terms of knock out feature which makes the option worthless if the reference entity defaults before the option expiry. We review the standard European option pricing and suggest few alternatives from the Levy class models that provide tractable treatment for the jumps-enriched intensity processes in the credit markets. Attachments:
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Posted 10 years ago
 IgorThank you very much for your fascinating series on the application of Mathematica to finance, but is it possible to get the notebook behind this and the other PDF files?Regards Michael
Posted 10 years ago
 Hi Igor, thanks for the explanation. I understand now what's going on. Regards, Ruben
Posted 10 years ago
 Hi Igor, great post again. I've been trying to replicate your results but I have run into difficulties with the last example of valuation under a Gamma process with non-deterministic volatility. The result I get is a complex number. This is the code: pm1 = ParameterMixtureDistribution[GammaDistribution[a, b], b \[Distributed] ExponentialDistribution[\[Lambda]]]; sol3 = Solve[{Mean[pm1] == x0 + \[Mu]*t, StandardDeviation[pm1] == \[Sigma] Sqrt[t]}, {a, \[Lambda]}] sol3vals = {a /. sol3[[1]], \[Lambda] /. sol3[[1]]}; evpm1 = Subscript[A, 0] Expectation[If[x > k, x - k, 0], x \[Distributed] pm1, Assumptions -> k > 0 && t > 0] // Simplify evpmcal = evpm1 /. {a -> sol3vals[[1]], \[Lambda] -> sol3vals[[2]]}; evpmcal /. {t -> 3, x0 -> 0.014, k -> 0.014, \[Sigma] -> 0.004, \[Mu] -> 0, Subscript[A, 0] -> 45.598} 0.133831 - 0.116303 I May I know what I'm doing wrong? Many thanks in advance, Ruben
Posted 10 years ago
 Hello Ruben The problem with Gamma mixture resides in the parameter definition. For Gamma process, both parameters have to be positive. This is ensured when sigma (in the context of other parameters defined in this example) is at least 80 bp In[79]:= pm1 = ParameterMixtureDistribution[GammaDistribution[a, b], b \[Distributed] ExponentialDistribution[\[Lambda]]]; In[80]:= sl5 = Solve[{Mean[pm1] == x0 + \[Mu]*t, StandardDeviation[pm1] == \[Sigma] Sqrt[t]}, {a, \[Lambda]}]; In[81]:= sl5vals = {a /. sl5[[1]], \[Lambda] /. sl5[[1]]}; In[82]:= evpm1 = Subscript[A, 0] Expectation[If[x > k, x - k, 0], x \[Distributed] pm1, Assumptions -> k > 0 && t > 0] // Simplify In[69]:= evpmcal = evpm1 /. {a -> sl5vals[[1]], \[Lambda] -> sl5vals[[2]]}; In[78]:= evpmcal /. {t -> 5, x0 -> 0.014, k -> 0.014, \[Sigma] -> 0.008, \[Mu] -> 0, Subscript[A, 0] -> rann} Out[78]= 0.0269472 Hope this answers your question. If not, please let me know. Kind regards Igor