| Although exotic options have been in existence for many years in the over-the-counter markets, it is only in recent years that their popularity has sky-rocketed. As the financial markets evolve, there is a greater demand for customized payoffs, increased flexibility, advanced hedging capacity and lower costs.; The Ordinal Optimization and Sampling-Selection algorithm (OOSS) presented in this thesis is a Monte Carlo simulation-based method for the pricing of American-style exotic options. It is shown that it is more efficient than most other alternative Monte Carlo methods. It is simple, easy to understand and implement and general, as it can be applied with few modifications to a wide variety of options.; The Monte Carlo simulation's inability to handle the early-exercise feature is overcome by introducing a boundary function B(t) such that, for any point in time the option will be exercised early if and only if its immediate payoff exceeds the boundary corresponding to time t. Thus the pricing of an American-style option becomes an optimization problem where the option value is maximized w.r.t. to the boundary function. In this optimization setting, Ordinal Optimization plays a key role in the algorithm's efficiency by significantly reducing the required computational cost.; In Ordinal Optimization, as opposed to conventional Cardinal Optimization, the question is not "what is the best value of the performance measure we are interested in" but "which design ranks first" or "among the best" w.r.t. to the above performance measure. Furthermore we are relaxing the goal of identifying the "best" to isolating a subset that contains a set of "good" with high probability. By doing this, we can distinguish the good alternatives early and thus save a great deal of simulation time, overcoming one of the major drawbacks of Monte Carlo, the long simulation times. The Sampling-Selection method goes one step further by using the Ordinal Optimization concepts to identify the search space with the highest probability of containing good designs, and then sample randomly from this space.; The OOSS algorithm is tested on a variety of different options with complicated structures, including regular puts, average-strike calls, lookback puts and calls on the maximum of two correlated stocks. It is also compared against alternative Monte Carlo simulation methods with very positive results. |
