Using Bessel processes, one can solve several open problems involving the integral of an exponential of Brownian motion. This point will be illustrated with three examples. "The first one" is a formula for the Laplace transform of an Asian option which is "out of the money.""The second example"...

Barrier options have become increasingly popular over the last few years. Less expensive than standard options, they may provide the appropriate hedge in a number of risk management strategies. In the case of a single-barrier option, the valuation problem is not very difficult (see Merton 1973...