Bounds for the price of discretely sampled arithmetic Asian options

Bounds for the price of discretely sampled arithmetic Asian options In this paper the pricing of discretely sampled European-style arithmetic Asian options with fixed and floating strike is studied by deriving accurate lower and upper bounds. For a lower bound, we adapt the idea of Rogers and Shi (1995) and we use in addition results based on comonotonic risks. For an upper bound we first 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 we further use the ideas of Rogers and Shi (1995) and Nielsen and Sandmann (2002). We obtain analytical and easily computable bounds. We also study the hedging problem. Several sets of numerical results are included.