Bounds For The Price Of An Asian Option Following A Generalized Geometric Brownian Motion

From the expression for the price of an arithmetic Asian call option, we see that the problem of pricing such options turns to be equivalent to calculating stop-loss premiums of a sum of dependent ran-dom variables. This means we can apply the concept of comonotonicity to find accurate lower and upper bounds for the price of Asian options. Though in J. Dhaene et al.(2002), applications in a black and scholes has been presented, the assumption of stochastic process following a geometric Brownian motion with constant drift and constant volatility sometimes is not realistic.So, using the concept of comonotonicity, this thesis derives express-ions for the upper and lower bound for the price of an Asian call option in a Black and Scholes model where the stochastic process follows a generalized geometric Brownian. In particular, we emphasize the choice of the conditioning random variable and consider two different forms of the conditioning random variable. At last, we numerically illustrate the bounds for the price of Asian options and compare the lower and upper bounds with Monte Carlo estimates. On the one hand, the lower and the upper bounds is very close to the Monte Carlo estimates. This might indicates that the bounds are very close to the real price. On the other hand, despite the quite large number of paths, the95%confidence interval of Monte Carlo estimates is wider than the [LB,UB]-interval in some cases. This indicates that sometimes the bounds should be preferred over simulation.