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 factor representing systematic risk. We derive approximated pricing formulas for the future factor values and their proxies, when the size n of the class is large. Up to order 1/n, these closed-form approximations involve well-chosen summary statistics of the basic asset returns but not the current and lagged 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 corporate bonds, and for longevity risk analysis, which involves large portfolios of life insurance contracts.