Fast Pricing of European Asian Options with Provable Accuracy

Title: Fast Pricing of European Asian Options with Provable Accuracy

Abstract: This research aims to develop fast and accurate pricing techniques for European Asian options, which are financial instruments that pay off based on the average stock price over a specific period. The study focuses on single-stock and basket options and presents three pricing techniques with provable accuracy.

1. Introduction European Asian options are a type of option where the payoff depends on the average stock price over a specific period. This research aims to develop fast and accurate pricing techniques for these options, focusing on single-stock and basket options. The study presents three pricing techniques with provable accuracy:

1. Monte Carlo algorithm with analytical error bounds 2. General recursive bucketing-based scheme with Aingworth-Motwani -Oldham aggregation algorithm, Monte-Carlo simulation, and possibly others as base-case subroutines 3. Fast Fourier Transform (FFT) combined with bucketing-based schemes for pricing basket options

These techniques take polynomial time in the number of days and the number of stocks, and do not add any errors to those already incurred in the base-case algorithms.

2. Monte Carlo Algorithm with Analytical Error Bounds The first technique is a Monte Carlo algorithm with analytical error bounds, suitable for pricing single-stock options with meaningful confidence and speed. It is the first known Monte Carlo algorithm with analytical error bounds, making it a significant contribution to the field.

3. General Recursive Bucketing-Based Scheme The second technique is a general recursive bucketing-based scheme that uses Aingworth-Motwani -Oldham aggregation algorithm, Monte-Carlo simulation, and possibly others as base-case subroutines. This scheme enables robust trade-offs between accuracy and time over subtrees of different sizes. It is particularly useful for long-term options or high-frequency price averaging, allowing for smaller errors in less time than the base-case algorithms themselves.

4. Fast Fourier Transform (FFT) Combined with Bucketing-Based Schemes The third technique combines Fast Fourier Transform (FFT) 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 base-case algorithms.

5. Conclusion In conclusion, this research presents three fast and accurate pricing techniques for European Asian options, focusing on single-stock and basket options. These techniques provide valuable tools for traders and financial analysts in the field of options pricing.

Implications: The main implications of this research are:

1. The development of fast and accurate pricing techniques for European Asian options, which are valuable tools for traders and financial analysts. 2. The contribution of the Monte Carlo algorithm with analytical error bounds, which is the first known Monte Carlo algorithm with analytical error bounds. 3. The general recursive bucketing-based scheme, which enables robust trade-offs between accuracy and time over subtrees of different sizes. 4. The combination of Fast Fourier Transform (FFT) with bucketing-based schemes for pricing basket options, which takes polynomial time in the number of days and the number of stocks.

Link to Article: https://arxiv.org/abs/0102003v1 Authors: arXiv ID: 0102003v1