A Continuous-Time, Forward-Looking, Implied Ambiguity Index

This paper introduces a real-time, instantaneous, forward-looking, implied ambiguity index. Ambiguity — the uncertainty of probabilities — is measured by the expected volatility of probabilities. Using option prices, the dynamic and continuous snapshot of the expected (implied) ambiguity in the financial markets is extracted. The ambiguity of risk-neutral probabilities is extracted as well. Similarly to the VIX, the proposed ambiguity indices can be traded. The well-documented relation between ambiguity and rates of return suggests a diversification benefit from including an ambiguity instrument in an investment portfolio. Based upon the proposed ambiguity indices, futures and options can be designed to deliver and trade pure ambiguity exposure in a single efficient package.