Deconstructing correlation
To properly value a basket option, one should construct a joint probability density, correctly repricing all asset smiles and correlation smiles. At first sight the task seems formidable, but by reformulating the problem, Peter Austing develops a model that is simple and fast, admitting analytic or semi-analytic valuation
When markets are stressed, assets become more strongly correlated. Just as there is an implied volatility smile, there is also a correlation smile. However, though it is known to exist, the correlation smile has been largely ignored in multi-asset derivatives pricing for reasons of practicality: there may not be liquid instruments to determine the smile, and even if it is known, practical pricing algorithms taking account of the smile may not exist.
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