Simulation methods for valuing Asian option prices in a hyperbolic asset price model

In this paper, we present a Quasi-Monte Carlo approach for pricing European-style Asian options, i.e. for options whose pay-off depends on the average price of the underlying asset where the average is extended over a fixed period up to the maturity date. Following a recent development in mathematical finance, we assume that the log returns of the asset are not normally but hyperbolically distributed. This hypothesis is approved by several authors with different statistic tests on real financial data. The aim of this paper is to advance the hyperbolic model to the pricing of Asian options, since there only exist pricing formulae for plain vanilla options and some types of exotic options (e.g. power call options, barrier options) so far. We show how one can obtain prices of general Asian options in such incomplete markets in an efficient way.