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

TL;DR

This paper introduces three efficient algorithms for accurately pricing European Asian options, including single-stock and basket options, with provable error bounds and improved computational speed.

Contribution

It presents the first Monte Carlo algorithm with analytical error bounds for single-stock options, a recursive bucketing scheme for flexible accuracy-speed trade-offs, and a FFT-based method for basket options.

Findings

Monte Carlo algorithm with confidence bounds for single-stock options

Recursive bucketing scheme enabling accuracy-speed trade-offs

FFT-based polynomial-time pricing for basket options

Abstract

This paper develops three polynomial-time pricing techniques for 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 can use the Aingworth-Motwani-Oldham aggregation algorithm, Monte-Carlo simulation and possibly others as the base-case subroutine. This scheme enables robust trade-offs between accuracy and time over subtrees of different sizes. For long-term options or high frequency price averaging, it can price single-stock options with smaller errors in less time than the base-case algorithms themselves. The third technique combines Fast Fourier Transform with bucketing-based schemes for pricing basket options. This technique takes polynomial time in the number of days and the number of stocks, and does not add any errors to those already incurred in the companion bucketing scheme. This technique assumes that the price of each underlying stock moves independently.