• Dependence and Risk Management

    Copula-regression for the risk-neutral distribution of two highly-correlated assets

    We seek to model the multivariate distribution of two financial indices (X,Y) at some future time point, with the following partial information given. From derivatives prices on financial markets we can infer information about (the market’s opinion of) the univariate distribution functions of X and of Y. Empirical evidence and experts’ opinions further justify the assumption that Y=g(X) for some monotone function g. Consequently, a reasonable model for the multivariate law of (X,Y) is to join the retrieved marginal laws with a parametric copula function, whose parameter controls the level of deviation from the base “regression” model Y = g(X). The present article clarifies in which situations such a model can be helpful and discusses desirable properties of the applied copula function.