Fast Pricing of European Asian Options with Provable Accuracy: Single-Stock and Basket Options

This paper develops three polynomial-time techniques for pricing European Asian options with provably small errors, where the stock prices follow binomial trees or trees of higher-degree. The first technique is the first known Monte Carlo algorithm with analytical error bounds suitable for pricing single-stock options with meaningful confidence and speed. The second technique is a general recursive bucketing-based scheme that enables robust trade-offs between accuracy and run-time. The third technique combines the Fast Fourier Transform with bucketing-based schemes for pricing basket options. This technique is extremely fast, polynomial in the number of days and stocks, and does not add any errors to those already incurred in the companion bucketing scheme.

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