This technical note serves to establish proofs for the list of statements in Bakshi, Crosby,and Gao (2019). We maintain their notation. Equation numbers not prefixed by letters refer to equations in Bakshi, Crosby, and Gao (2019). Section I studies the quantitative implications of the Vasicek...

If the evolution of equity index volatility and the pricing kernel were to be absent of risks unspanned by index futures, it would counterfactually imply that (i) the expected excess return of OTM calls on futures is positive, (ii) the expected excess return of straddles is approximately zero,...

In our approach, the conditional expectation of asset return quantities, under the real-world probability measure, can be expressed as a linear combination of the prices of the risk-free bond, the asset, and options on the asset. The method is free of distributional assumptions, and we use it to...

We develop an axiomatically consistent way of ranking and scoring funds that respects an industry benchmark. Our performance measure, termed MAP, accounts for the feature that investors may exhibit skepticism when evaluating investment strategies versus a benchmark. Linking developed theory to...