Path integral pricing of outside barrier Asian options

Using the path-integral framework to cast the pricing problem of the outside barrier Asian option into a Wiener functional integral form, we show that, after the introduction of a law-equivalent process and transformation of the new system, the deviation from the Monte Carlo price is seen to be wide...

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Bibliographic Details
Published in:Physica A 2014-01, Vol.394, p.266-276
Main Authors: Cassagnes, Aurelien, Chen, Yu, Ohashi, Hirotada
Format: Article
Language:English
Subjects:
Asian
Asian option
Barriers
Deviation
Integrals
Monte Carlo methods
Outside barrier option
Pricing
Statistical mechanics
Transformations
Wiener integral
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Summary:Using the path-integral framework to cast the pricing problem of the outside barrier Asian option into a Wiener functional integral form, we show that, after the introduction of a law-equivalent process and transformation of the new system, the deviation from the Monte Carlo price is seen to be widely reduced. Bypassing the path-partitioning step, we show that our results behave nicely with respect to increasing correlation. After putting forward empirical evidence of this improvement, we extend the scope to a double knock-out outside barrier, and derive there an original formula. In the latter setting, we propose a simple scheme to reduce the relative error due to a nearby knock-out barrier. •We propose an alternative to usual path-partitioning methods by transforming the system.•Error is reduced with increasing correlation.•We propose a novel formula for double outside barrier Asian options.•Error is reduced by use of a smooth interpolation when the barrier proximity increases.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2013.09.067