  The pricing of currency options is largely dependent on the dynamic
relationship between a pair of currencies. Typically, the pricing of options
with payoffs dependent on multi-assets becomes tricky for reasons such as the
non-Gaussian distribution of financial variable and non-linear macroeconomic
relations between these markets. We study the options based on the currency
pair US dollar and Indian rupee (USD-INR) and test several pricing formulas to
evaluate the performance under different volatility regimes. We show the
performance of the variance gamma and the symmetric variance gamma models
during different volatility periods as well as for different moneyness, in
comparison to the modified Black-Scholes model. In all cases, variance gamma
model outperforms Black-Scholes. This can be attributed to the control of
kurtosis and skewness of the distribution that is possible using the variance
gamma model. Our findings support the superiority of variance gamma process of
currency option pricing in better risk management strategies.
