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Using model-independent lower bounds to improve pricing of Asian style options in Lévy markets. (English) Zbl 1290.91159

Summary: H. Albrecher et al. [Appl. Math. Finance 15, No. 2, 123–149 (2008; Zbl 1134.91394)] have proposed model-independent lower bounds for arithmetic Asian options. In this paper we provide an alternative and more elementary derivation of their results. We use the bounds as control variates to develop a simple Monte Carlo method for pricing contracts with Asian-style features. The conditioning idea that is inherent in our approach also inspires us to propose a new semi-analytic pricing approach. We compare both approaches and conclude that these both have their merits and are useful in practice. In particular, we point out that our newly proposed Monte Carlo method allows to deal with Asian-style products that appear in insurance (e.g., unit-linked contracts) in a very efficient way, and outperforms other known Monte Carlo methods that are based on control variates.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)

Citations:

Zbl 1134.91394
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