Bounds for the price of discrete arithmetic Asian options.

Abstract

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, Dhaene and Goovaerts (2000), and additionally, the ideas of Rogers and Shi (1995) and of Nielsen and Sandmann (2003). We are able to create a unifying framework for discrete 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 show that the hedging using these bounds is possible. Moreover, our methods are applicable to a wide range of (pricing) problems involving a sum of dependent random variables.Asian option; Choice; Efficiency; Framework; Hedging; Methods; Options; Premium; Pricing; Problems; Random variables; Research; Stop-loss premium; Variables;