Robust price bounds for the forward starting straddle

In this article we consider the problem of giving a robust, model-independent, lower bound on the price of a forward starting straddle with payoff $|F_{T_1} - F_{T_0}|$ where $0<T_0<T_1$. Rather than assuming a model for the underlying forward price $(F_t)_{t \geq 0}$, we assume that call prices for maturities $T_0<T_1$ are given and hence that the marginal laws of the underlying are known. The primal problem is to find the model which is consistent with the observed call prices, and for which t...