Efficient pricing of discrete Asian options

Asian options are popular path-dependent financial derivatives. This paper uses lattices to price fixed-strike European-style Asian options that are discretely monitored. The algorithm proposed can also be applied to floating-strike Asian options as well because fixed-strike and floating-strike Asia...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 217; no. 24; pp. 9875 - 9894
Main Authors: Hsu, William W.Y., Lyuu, Yuh-Dauh
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.08.2011
Elsevier
Subjects:
Algorithms
Asian
Combinatorics. Ordered structures
Convergence
Derivatives
Discrete Asian options
Exact sciences and technology
Lattices
Mathematical analysis
Mathematics
Multinomial lattice model
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Option pricing
Order, lattices, ordered algebraic structures
Pricing
Sciences and techniques of general use
Vanilla
Discrete Asian options
Option pricing
Multinomial lattice model
Complexity class
Lagrange multiplier
Numerical analysis
Applied mathematics
Pricing
Numerical method
Stochastic method
Algorithm
Convergence
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:Asian options are popular path-dependent financial derivatives. This paper uses lattices to price fixed-strike European-style Asian options that are discretely monitored. The algorithm proposed can also be applied to floating-strike Asian options as well because fixed-strike and floating-strike Asian options are related through an equation. The discretely monitored version is usually found in practice instead of the continuously monitored version usually encountered in the literature. This paper presents the first provably quadratic-time convergent lattice algorithm for pricing fixed-strike European-style discretely monitored Asian options. It is the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to choose the number of states for each node of the lattice. Extensive numerical experiments and comparisons with many existing numerical methods confirm the performance claims and the competitiveness of our algorithm. This result places fixed-strike European-style discretely monitored Asian options in the same complexity class as vanilla options.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.01.015