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Many recent papers have investigated the role played by volatility in determining the cross-section of currency returns. This paper employs two time-varying factor models: a threshold model and a Markov-switching model to price the excess returns from the currency carry trade. We show that the importance of volatility depends on whether the currency markets are unexpectedly volatile. Volatility innovations during relatively tranquil periods are largely unrewarded in the market, whereas during the unexpected volatile period, this risk has a substantial impact on currency returns. The empirical results show that the two time-varying factor models fit the data better and generate a smaller pricing error than the linear model, while the Markov-switching model outperforms the threshold factor models not only by generating lower pricing errors but also distinguishes two regimes endogenously and without any predetermined state variables.

The pricing of unexpected volatility in the currency market