BFS 2002

Poster Presentation

Bounds for the price of discretely sampled arithmetic Asian options

Michèle Vanmaele, Jan Dhaene, Griselda Deelstra, Jan Liinev, Marc Goovaerts

We derive accurate, analytical and easy computable lower and upper bounds for the price of discretely sampled European-style arithmetic Asian options with fixed and floating strike. Adapting the idea of Rogers and Shi (1995) to the case of discrete averaging and using results based on comonotonic risks, we obtain a closed form expression for a lower bound which generalizes the lower bound of Nielsen and Sandmann (2002). For an upper bound we follow two different approaches, one that is based on a general technique for deriving bounds for stop-loss premiums of sums of dependent random variables from Kaas, Dhaene and Goovaerts (2000) and another that follows again the ideas of Rogers and Shi and of Nielsen and Sandmann. We compare our approaches and compare our results to those in literature. We also study the hedging Greeks of the lower and upper bounds. Several sets of numerical results are included.