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This paper investigates jump risk and return characteristics of currency carry trades by employing both empirical approach and analytical method. With country-level stochastic discount factor, a mathematical model is proposed to describe carry trade return dynamics that capture jump risk. Carry trade returns are modeled as jump-diffusion processes where types of jumps involve global and idiosyncratic jumps. We derive the first four moments of return process on exchange rates and use the methoddoi:10.7936/05bb-5r14 fatcat:7sels7atv5a4fccq5mywqx5674