Bounds for the price of discrete arithmetic Asian options

In this paper the pricing of European-style discrete arithmetic Asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds. In our approach we use a general technique for deriving upper (and lower) bounds for stop-loss premiums of sums of dependent random v...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2006, Vol.185 (1), p.51-90
Main Authors: Vanmaele, M., Deelstra, G., Liinev, J., Dhaene, J., Goovaerts, M.J.
Format: Article
Language:English
Subjects:
Analytical bounds
Applications
Asian option
Black and Scholes setting
Comonotonicity
Exact sciences and technology
Insurance, economics, finance
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic analysis
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Summary:In this paper the pricing of European-style discrete arithmetic Asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds. In our approach we use a general technique for deriving upper (and lower) bounds for stop-loss premiums of sums of dependent random variables, as explained in Kaas et al. (Ins. Math. Econom. 27 (2000) 151–168), and additionally, the ideas of Rogers and Shi (J. Appl. Probab. 32 (1995) 1077–1088) and of Nielsen and Sandmann (J. Financial Quant. Anal. 38(2) (2003) 449–473). We are able to create a unifying framework for European-style discrete arithmetic Asian options through these bounds, that generalizes several approaches in the literature as well as improves the existing results. We obtain analytical and easily computable bounds. The aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters, investigate the effect of different conditioning variables and compare their efficiency numerically. Several sets of numerical results are included. We also discuss hedging using these bounds. Moreover, our methods are applicable to a wide range of (pricing) problems involving a sum of dependent random variables.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.01.027