Accurate approximations for European-style Asian options

Abstract

In the binomial tree model, we provide efficient algorithms for computing an accurate lower bound for the value of a European-style Asian option with either a fixed or a floating strike. These algorithms are inspired by the continuous-time analysis of Rogers and Shi [10]. Specifically we consider lower bounds on the option value that are given by the expectation of the conditional expectation of the payoff conditioned on some random variable Z. For a specific Z, Rogers and Shi estimate this conditional expectation numerically in continuous time, and show experimentally that their lower bound is very accurate. We consider a modified random variable Z that gives a strictly better lower bound. In addition, we show that this lower bound can be computed exactly in the n-step binomial tree model in time proportional to n 7 . We show that computing the approximation is equivalent to counting paths of various types, and that this can be done efficiently by a dynamic programming technique. We...

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