Implied ICA: Factor Extraction and Multiasset
Derivative Pricing

Abstract

This article presents a different approach to modeling the return dynamics for a portfolio. The component stocks are all assumed to be exposed to shocks from a small number of independent factors, each of which follows a Heston-type square root diffusion process. To illustrate the model, the authors construct a portfolio of the three biotech stocks that have the largest weightings among the twelve stocks in the BBH ETF portfolio, assuming there are only two independent factors. The estimated variance equations show that the more important factor, Factor 1, has high volatility and is rapidly mean reverting, while Factor 2 reverts more slowly and steadily toward a low value. Theoretical values for options on the three-stock portfolio obtained by simulation should be approximately the same as traded option contracts on the BBH index. The fitted volatility smiles under the model are similar to those observed for BBH, but with some notable discrepancies.