Financial Engineering

Our results are broadly consistent with the predictions of a benign view of the role of investment banks in advising acquisition targets. Fees to investment banks are correlated with attributes of transactions and target firms in ways that make sense if banks are being paid for processing information. The more contingent (and, therefore, risky) the fees, the higher they tend to be, all else held constant. Variation in acquisition premia also can be explained by fundamental deal attributes.

We derive and analyze Monte Carlo estimators of price sensitivities ("Greeks") for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is to investigate connections between Malliavin estimators and the more traditional and elementary pathwise method and likelihood ratio method.

The measurement of portfolio credit risk focuses on rare but significant large-loss events. This paper investigates rare event asymptotics for the loss distribution in the widely used Gaussian copula model of portfolio credit risk. We establish logarithmic limits for the tail of the loss distribution in two limiting regimes. The first limit examines the tail of the loss distribution at increasingly high loss thresholds; the second limiting regime is based on letting the individual loss probabilities decrease toward zero.

Previous research concludes that options are mispriced based on the high average returns, CAPM alphas, and Sharpe ratios of various put selling strategies. One criticism of these conclusions is that these benchmarks are ill-suited to handle the extreme statistical nature of option returns generated by nonlinear payoffs. We propose an alternative way to evaluate the statistical significance of option returns by comparing historical statistics to those generated by well-accepted option pricing models.

This paper develops numerical approximations for pricing collateralized debt obligations (CDOs) and other portfolio credit derivatives in the multifactor Normal Copula model. A key aspect of pricing portfolio credit derivatives is capturing dependence between the defaults of the elements of the portfolio. But, compared with an independent-obligor model, pricing in a model with correlated defaults is more challenging. Our approach strikes a balance by reducing the problem of pricing in a model with correlated defaults to calculations involving only independent defaults.

Although the vast majority of real options models assume that investment opportunities are permanently available, many real-world investment opportunities are sporadic. Options to invest can suddenly become blacked-out, only to be followed by a re-opening in the future. For example, the option to develop real estate may open or close depending upon zoning and growth control decisions, competitive entry, or input (labor or material) availability. Similar factors influence complex R&D options. We term such randomly recurring investment opportunities as options on illiquid projects.

This paper lays out a decomposition of book-to-price (B/P) that derives from the accounting for book value and that articulates precisely how B/P "absorbs" leverage. The B/P ratio can be decomposed into an enterprise book-to-price (that pertains to operations and potentially reflects operating risk) and a leverage component (that reflects financing risk).

Both noncooperative and cooperative game theory have been applied to business strategy. We propose a hybrid noncooperative-cooperative game model, which we call a biform game. This is designed to formalize the notion of business strategy as making moves to try to shape the competitive environment in a favorable way. (The noncooperative component of a biform game models the strategic moves. The cooperative component models the resulting competitive environment.) We give biform models of various well-known business strategies.

This chapter provides an overview of modeling and computational issues associated with portfolio credit risk. We consider the problem of calculating the loss distribution in a portfolio of assets exposed to credit risk, such as corporate bonds or bank loans. We also discuss the pricing of portfolio credit derivatives, such as basket default swaps and collateralized debt obligations. A portfolio view of credit risk requires capturing dependence between the assets in the portfolio; we discuss models of dependence and associated computational techniques.