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This paper develops distribution-specific theoretical constraints on relative prices of out-of-the-money European call and put options that, are also valid for American options on futures. Systematic violations of these constraints by prices of American options on Deutschemark futures are found, indicating that distributions more asymmetric than those of standard models are necessary. An American option pricing model for jump-diffusion processes with asymmetric jumps is developed. Estimates of parameters implicit in prices of options on Deutschemark futures indicate that throughout 1984–87, market participants perceived a remote chance of a substantial crash in the dollar,