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 method

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... f moments to estimate parameters, which show the model matches excess carry trade returns in data quite well. Empirical findings show that carry trade returns exhibit an asymmetric leptokurtic feature. We also conduct asset pricing model testing and obtain results suggest that the skewness factor is a driving force to carry trade returns.