Exotic options, including lookback options with fixed and floating strike prices, offer investors high flexibility in managing risk and return. Models based on L ́evy processes, such as the inverse Gaussian model, have gained attention due to their better alignment with real market data. This paper explores efficient numerical methods, particularly the biased control variable method, for pricing lookback options with fixed strike prices under the inverse Gaussian model. By combining Monte Carlo, quasi-Monte Carlo, and randomized quasi-Monte Carlo simulation methods, it aims to overcome computational challenges posed by the high dimensionality of the problem and the lack of closed-form solutions for random variables. The results of this study will lead to improvements in the accuracy and efficiency of pricing exotic options.
