Pricing Lookback Options under Normal Inverse Gaussian Model by Variance Reduction and Randomized Quasi-Monte Carlo Methods

In this paper, we investigate the lookback option pricing problem under the exponential normal inverse Gaussian model for the underlying asset price by antithetic variate and control variate methods combined with the quasi-Monte Carlo methods. The payoff of the geometric Asian option and a random variate conditional on the geometric mean of asset prices are used as the control vartiates. Numerical results with various model parameters and strike prices show that variances are reduced by both the antithetic variate and control variate methods. The variance reduction ratios are significantly improved when quasi-Monte Carlo methods are combined. For example, the variance reduction ratios are more than 10⁵ for the discrete fixed strike lookback options with 32 monitoring points.