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Here is how I would approach such a calibration. Assuming we have the necessary market data one can easily construct the emprical distribution of the arrival rate. Let $\lambda_{emp}(\delta)$ be the empirical distribution. Then one can define a metric by $$ m(k,A,N)=\sum_{i=1}^N |\lambda_{emp}(i)-\lambda^a(i)| $$ After you have decided upon a suitable ...


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At long maturities, the real problem tends more to be model error than volatility estimation: over that kind of time period most companies undergo significant capital structure changes, for which there are very few models.



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