Financial Engineering

This articles studies the design and valuation of debt contracts in a general dynamic setting under uncertainty. We incorporate some insights of the recent corporate finance literature into a valuation framework. The basic framework is an extensive form game determined by the terms of a debt contract and applicable bankruptcy laws. Debtholders and equityholders behave noncooperatively. The firm's reorganization boundary is determined endogenously. Strategic debt service results in significantly higher default premia at even small liquidation costs.

We develop lower and upper bounds on the prices of American call and put options written on a dividend-paying asset. We provide two option price approximations one based on the lower bound (termed LBA) and one based on both bounds (termed LUBA). The LUBA approximation has an average accuracy comparable to a l,000-step binomial tree. We introduce a modification of the binomial method (termed BBSR) that is very simple to implement and performs remarkably well. We also conduct a careful large-scale evaluation of many recent methods for computing American option prices.

Simulation has proved to be a valuable tool for estimating security prices for which simple closed form solutions do not exist. In this paper we present two direct methods, a pathwise method and a likelihood ratio method, for estimating derivatives of security prices using simulation. With the direct methods, the information from a single simulation can be used to estimate multiple derivatives along with a security's price. The main advantage of the direct methods over re-simulation is increased computational speed.

We study the effect of changing buffer sizes in serial lines withgeneral blocking, a mechanism that incorporates limited intermediate finished goods inventory at each stage, as well as limited intermediate raw material inventory. This model includes ordinarymanufacturing, communication, andkanban blocking as special cases. We present conditions under which increasing buffer sizes or re-allocating buffer capacity increases throughput, and in some cases characterize optimal allocations.

We consider the problem of allocating production capacity among multiple items, assuming that a fixed proportion of overall capacity can be dedicated exclusively to the production of each item. Given a capacity allocation, production of each item follows a base-stock policy, i.e., each demand triggers a replenishment order to restore safety stocks to target levels. We present procedures for choosing base-stock levels and capacity allocations that are asymptotically optimal.

We give a unified presentation of stability results for stochastic vector difference equations Yn+1 = An ⊗ Yn ⊕ Bn based on various choices of binary operations ⊕ and ⊗, assuming that {(An, Bn), n ≥ 0} are stationary and ergodic. In the scalar case, under standard addition and multiplication, the key condition for stability is E[log |A0|]<0. In the generalizations, the condition takes the form γ <0, where γ is the limit of a subadditive process associated with {A(n), n≥0}.

Theoretical work on financing costs under asymmetric information has linked shifts in firms' internal funds and investment spending, holding constant investment opportunities. An impediment to convincing tests of these models is the lack of firm-level data on the relative cost of internal and external funds. We use a tax experiment, the surtax on undistributed profits in the 1930s, to identify firms' relative cost of internal and external funds by calculating surtax margins.

Bundling of products is very prevalent in the marketplace. For example, travel packages include airfare, lodging, and a rental car. Considerable economic research has focused on the change in profits and consumer surplus that ensues if bundles are offered. There is relatively little research in marketing that deals with bundling, however. In this article we concentrate on some tactical issues of bundling, such as which types of products should be bundled, what price one can charge for the bundle, and how the price of the bundle should be presented to consumers to improve purchase intent.

We consider limits of first passage times to indexed families of nested sets in regenerative processes. The sets are exponentially rare, in the sense that the probability that the process reaches an indexed set in a cycle vanishes exponentially fast in the indexing parameter. Under appropriate formulations of this hypothesis, we prove strong laws, iterated logarithm laws and limits in distribution, both for the index of the rarest set reached in a cycle and for the time to reach a set.