Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk
We consider a homogeneous class of assets, whose returns are driven by an unobservable factorrepresenting systematic risk. We derive approximated pricing formulas for the future factor valuesand their proxies, when the size n of the class is large. Up to order 1=n, these closed form approximationsinvolve well-chosen summary statistics of the basic asset returns, but not the current andlagged factor values. The potential of the closed form approximation formulas seems quite large,especially for credit risk analysis, which considers large portfolios of individual loans or corporatebonds, and for longevity risk analysis, which involves large portfolios of life insurance contracts.
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