Modern quantitative finance must address the management of portfolio-level risk, whether computing capital requirements, measuring the cost of counterparty risk (CVA) or its mitigation via collateralization (FVA) or hedging. Such calculations rest on modeling a range of risk factors, across asset classes, in a coherent manner. This hybrid modeling problem presents considerable challenges, with the result that the state of the art is limited to a few special cases. Coupling between model parameters typically necessitates a bespoke calibration procedure and expensive, short-step Monte Carlo simulation. These issues can be side-stepped if the joint characteristic function is known, but the class of such models is small. In addition, treatment of correlation remains at the level of model parameters, and it seldom relates in a meaningful way to correlations between observable quantities.
We propose a new approach to hybrid modeling based on a careful definition of inter-process correlation, and a new technique, called Automatic Numeraire Corrections. With this approach, an arbitrary collection of models for an arbitrary set of underlyings can be combined at run-time to form a wide variety of hybrid models on-the-fly, in which correlation parameters can be calibrated to observable correlations between physical quantities.
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