This paper proposes methods for computing multivariate risk-neutral distributions from option prices. We illustrate the differences between the risk-neutral pdfs obtained from multivariate estimation and those from the use of univariate techniques. The estimation of multivariate distributions has important useful applications for financial hedging, derivative pricing, and the evaluation of correlation, contagion, and other measurements of comovement among the underlying securitires. We use an example with options on the dollar-mark, dollar-streling and mark-sterling exchange rates to highlight the differences in the estimated measures of comovement from the multivariate distribution and those obtained from historical estimation and univariate techniques. In general, the risk-neutral measures imply fatter distribution tails and higher correlations of large movements of the underlying securities than those suggested by historical prices.

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We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the stochastic process for a given portfolio. In particular, and as an example, we were able to identify mean reversion effect in our portfolio. Finally, we briefly discuss the potential practical effect of the virtual volatility on an investor asset allocation strategy.