There are well developed techniques to infer the risk neutral distribution of an asset return when a wide range of options prices written on this asset is available (Ait-Sahalia and Lo (1998), Breeden and Litzenberger (1978), Bodarenko (2003), Ross (2014)). In this paper, we develop a new algorithm to infer the “implied” dependence among assets (i.e. the dependence under the risk neutral probability) by using the information on basket options or spread options. Specifically, we are able to describe all possible dependence structures among stock prices that are consistent with prices of options written on individual stocks as well as options written on the corresponding index. This dependence information is a forward looking view of the interaction among assets in the market.
We apply this idea to infer possible implied dependence structures among the 30 stocks that form the Dow Jones 30 index. In particular, we look for measures that are consistent across the different candidate dependence structures to propose an implied systemic risk index that is driven by changes in the implied dependence among asset returns.
We then explain how the implied dependence that we find using our methodology improves upon the implied correlation index that was recently introduced by the CBOE. Our method is inspired by the rearrangement algorithm (RA) of Puccetti and Rueschendorf (2012) that was originally used to minimize the variance of a portfolio in which the distributions of the components are known but their interdependence is not.