Analogy Based Valuation of Currency Options
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The two most intriguing anomalies in currency markets are: 1) the implied volatility smile in currency options, and 2) the forward discount bias in currency exchange rates. I show that if currency options are valued in analogy with the underlying currency and beliefs are heterogeneous, then the forward discount bias causes the smile. The analogy based currency option pricing formula is put forward, which converges to Garman-Kohlhagen formula if there is no forward discount bias. In the presence of the forward discount bias, an increase in belief dispersion increases the slope as well as the curvature of the smile.