Derivative contracts on multiple foreign exchange rates must be priced to avoid arbitrage by contracts on the cross-rates. Given the triangle of smiles for two underlyings and their cross, we provide an analytic formula for a joint probability density such that all three vanilla markets are...

To properly value a basket option, one should construct a joint probability density correctly repricing all asset smiles and correlation smiles. At first sight, the task seems formidable. However, by reformulating the problem, we can develop a model that is simple and fast, admitting analytic or...