On the Pricing of Currency Options under Variance Gamma Process

TL;DR

This paper compares the variance gamma model to the Black-Scholes model for pricing USD-INR currency options, demonstrating the former's superior performance due to better handling of distribution skewness and kurtosis.

Contribution

It evaluates the effectiveness of the variance gamma process in currency option pricing across different volatility regimes, showing its advantages over traditional models.

Findings

Variance gamma model outperforms Black-Scholes in all tested scenarios.

The model effectively captures skewness and kurtosis in currency returns.

Variance gamma provides better risk management strategies.

Abstract

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.