Approaches to Asian Option Pricing with Discrete Dividends

TL;DR

This paper compares various methods for pricing Asian options with discrete dividends, emphasizing practical accuracy and performance, and introduces hybrid and Monte Carlo techniques for improved results.

Contribution

It evaluates the performance of hybrid analytical-finite difference and Monte Carlo methods for Asian option pricing with discrete dividends, highlighting their strengths and limitations.

Findings

Hybrid approach performs well for equidistant monitoring tails.

Finite difference method is highly accurate but slow for long intervals.

Quasi-Monte Carlo method is effective for long monitoring intervals.

Abstract

The method and characteristics of several approaches to the pricing of discretely monitored arithmetic Asian options on stocks with discrete, absolute dividends are described. The contrast between method behaviors for options with an Asian tail and those with monitoring throughout their lifespan is emphasized. Rates of convergence are confirmed, but greater focus is put on actual performance in regions of accuracy which are realistic for use by practitioners. A hybrid approach combining Curran's analytical approximation with a two-dimensional finite difference method is examined with respect to the errors caused by the approximating assumptions. For Asian tails of equidistant monitoring dates, this method performs very well, but as the scenario deviates from the method's ideal conditions, the errors in the approximation grow unfeasible. For general monitoring straightforward solution of the full three-dimensional partial differential equation by finite differences is highly accurate but suffers from rapid degradation in performance as the monitoring interval increases. For options with long monitoring intervals a randomized quasi-Monte Carlo method with control variate variance reduction stands out as a powerful alternative.

Full text

Approaches to Asian Option Pricing with Discrete Dividends333This

work relies in part on work done by one of the authors (Lundgren) for a thesis project in collaboration with Uppsala University

Jacob Lundgren111ITIVITI, www.itiviti.com, Yuri Shpolyanskiy222ITIVITI, www.itiviti.com; ITMO University, St.Petersburg, Russia

(February 6, 2017)

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Declaration of Interest

This work has been done largely as part of normal operations at Itiviti. The authors would argue that this affiliation is of no detriment to the objectivity of the exposition, but the fact should be mentioned. The authors alone are responsible for the content and writing of the paper.