Abstract
Abstract The calculation of the Asian option value has posed a great challenge to financial mathematicians as well as practitioners for the last two decades. Since there exists no analytical valuation formula to date, one has to resort to other methods to price this commonly used derivative product. One possibility is the usage of simulation approaches, which however are especially inefficient for Asian options, due to their dependence on the entire stock price trajectory. Another alternative is resorting to semi-analytical methods, based on the inversion of the option price’s Laplace transform, which however are prone to severe numerical difficulties. In this paper, we seek answer to the question whether it is possible to improve on the efficiency of the semi-analytical approach, implementing and comparing different numerical algorithms, so that they could be applied in real-life situations. We look into whether today’s superior computer environment has changed the relative strength of numerical and simulation approaches with regards to Asian option pricing. Based on a comprehensive analysis of speed and reliability, we find that the Laplace transform inversion method can be further enhanced, pushing down the prior critical value from 0.01 to 0.005 and the calculation time from 20 - 30 seconds to 3 - 4 seconds. This renders the numerical approach readily applicable for practitioners; however, we conclude that the simulation approach is a more efficient option when σ2<0.01.
Highlights
Asian options are popular hedging instruments in the hands of financial risk managers, owing to their special payout structure and cost-effectiveness
Another alternative is resorting to semi-analytical methods, based on the inversion of the option price’s Laplace transform, which are prone to severe numerical difficulties
Based on a comprehensive analysis of speed and reliability, we find that the Laplace transform inversion method can be further enhanced, pushing down the prior critical value from 0.01 to 0.005 and the calculation time from 20 - 30 seconds to 3 - 4 seconds
Summary
Asian options are popular hedging instruments in the hands of financial risk managers, owing to their special payout structure and cost-effectiveness. Medvegyev behavior, these options are “European”, in the sense that they can be exercised only at a pre-agreed (maturity) date; as opposed to (plain) vanilla products, Asian options have an “exotic” payout at maturity ( ) = f (T,S (T )). Where K stands for the pre-agreed strike price and Avg[0,T] (S ) stands for the time average of the underlying asset’s prices from time 0 to time T (i.e. during the lifetime of the option). As a result, according to a survey including 200 derivative-using non-financial U.S firms conducted by Bodnar et al [1], Asian options are the most popular exotic payout options chosen by non-financial firms for risk management
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