Financial Engineering

This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts.

We provide a comprehensive treatment of option pricing with particular emphasis on the valuation of American options on dividend-paying assets. We begin by reviewing principles for European contingent claims in a financial market in which the underlying asset price follows an Ito process and the interest rate is stochastic. Then this analysis is extended to the valuation of American contingent claims. In particular, the early exercise premium and the delayed exercise premium representations of the American option price are presented.

We analyze the performance of a splitting technique for the estimation of rare event probabilities by simulation. A straightforward estimator of the probability of an event evaluates the proportion of simulated paths on which the event occurs. If the event is rare, even a large number of paths may produce little information about its probability using this approach. The method we study reinforces promising paths at intermediate thresholds by splitting them into subpaths which then evolve independently.

The bottleneck in a production-inventory network is commonly taken to be the facility that most limits flow through the network and thus the most highly utilized facility. A further connotation of "bottleneck," however, is the facility that most constrains system-wide performance or the facility at which additional resources would have the greatest impact.

This paper develops methods for fast estimation of option price sensitivities in Monte Carlo simulation of term structure models. The models considered are based on discretely compounded forward rates with proportional volatilities. The efficient estimation of option deltas, gammas, and vegas are investigated in this setting.

The increased complexity of modern manufacturing has led to uncertainties in production processes. Factors such as unplanned machine maintenance, tool unavailability, and complex process adjustments make it difficult to maintain a predictable level of output. To be effective, an appropriate production model must incorporate these uncertainties into the representation of the production process. This paper considers a one-time production of an application-specific product which must follow a fixed routing through the manufacturing system.

To improve the efficiency of product distribution for a centralized bakery, I first performed each person's tasks and discovered that constructing optimal minimum-distance routes would not significantly reduce costs but replacing the physical validation of new routes with a manual mathematical computation or simulation would. The trick was getting management to trust the simulation enough to use it.

A major problem in forecasting is estimating the time of some future event. Traditionally, forecasts are designed to minimize an error cost function that is evaluated once, possibly when the event occurs and forecast accuracy can be determined. However, in many applications forecast error costs accumulate over time, and the forecasts themselves may be updated with information that is collected as the expected time of the event approaches. This paper examines one such application, in which flow control managers in the U.S.

We determine the minimum cost of super-replicating a nonnegative contingent claim when there are convex constraints on portfolio weights. We show that the optimal cost with constraints is equal to the price of a related claim without constraints. The related claim is a dominating claim, that is, a claim whose payoffs are increased in an appropriate way relative to the original claim. The results hold for a variety of options, including some path-dependent options.