Double-exponential fast Gauss transform algorithms for pricing discrete lookback options

This paper presents fast and accurate algorithms for computing the prices of discretely sampled lookback options. Under the Black-Scholes framework, the pricing of a discrete lookback option can be reduced to a series of convolutions of a function with the Gaussian distribution. Using this fact, an efficient algorithm, which computes these convolutions by a combination of the double-exponential integration formula and the fast Gauss transform, has been proposed recently. We extend this algorithm to lookback options under Merton’s jump-diffusion model and American lookback options. Numerical experiments show that our method is much faster and more accurate than conventional methods for lookback options under Merton’s model. For American lookback options, our method outperforms conventional methods when required accuracy is relatively high. A lookback option is the right to sell an asset at the end of a time period at the highest price the asset took during the period (lookback put option)