The assessment of portfolio risk is often explicitly (e.g., the square root formula under Basel III) or implicitly (e.g., credit risk portfolio models) driven by the marginal distributions of the risky components and the correlations amongst them. We assess the extent by which such practice is...

We propose a novel model-free approach for extracting the risk-neutral quantile function of an asset using options written on this asset. We develop two applications. First, we show how for a given stochastic asset model our approach makes it possible to simulate the underlying terminal asset...

Leveraged exchange-traded funds (LETF) are newly introduced ETFs that have become increasingly popular. It closely tracks the value of an underlying index while allowing for additional leverage. In this paper, we consider the valuation of options written on leveraged exchange-traded funds under...