Financial Engineering

High-dimensional problems frequently arise in the pricing of derivative securities—for example, in pricing options on multiple underlying assets and in pricing term structure derivatives. American versions of these options, i.e., where the owner has the right to exercise early, are particularly challenging to price. We introduce a stochastic mesh method for pricing high-dimensional American options when there is a finite, but possibly large, number of exercise dates.

This paper derives Monte Carlo simulation estimators to compute option price derivatives, i.e., the `Greeks,' under Heston's stochastic volatility model and some variants of it which include jumps in the price and variance processes. We use pathwise and likelihood ratio approaches together with the exact simulation method of Broadie and Kaya (2004) to generate unbiased estimates of option price derivatives in these models.

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence.

Any simulation procedure has difficulty achieving accuracy for rare events that lie in the tails of the probability distributions one is simulating from. But that is where the outcomes that produce defaults in a credit portfolio occur, making pricing and risk management for CDOs and similar instruments difficult and (computer) time-consuming. In this article, Glasserman introduces several approximation procedures for estimating the tails of the distribution of default risk exposure for a credit portfolio.

This paper analyzes the role of jumps in continuous-time short rate models. I first develop a test to detect jump-induced misspecification and, using Treasury bill rates, find evidence for the presence of jumps. Second, I specify and estimate a nonparametric jump-diffusion model. Results indicate that jumps play an important statistical role. Estimates of jump times and sizes indicate that unexpected news about the macroeconomy generates the jumps. Finally, I investigate the pricing implications of jumps.

This paper presents a financial statement analysis that distinguishes leverage that arises in financing activities from leverage that arises in operations. The analysis yields two leveraging equations, one for borrowing to finance operations and one for borrowing in the course of operations. These leveraging equations describe how the two types of leverage affect book rates of return on equity.

Monte Carlo simulation is widely used to measure the credit risk in portfolios of loans, corporate bonds, and other instruments subject to possible default. The accurate measurement of credit risk is often a rare-event simulation problem because default probabilities are low for highly rated obligors and because risk management is particularly concerned with rare but significant losses resulting from a large number of defaults. This makes importance sampling (IS) potentially attractive.

We assemble bank-level and other data for Fed member banks to model determinants of bank failure. Fundamentals explain bank failure risk well. The first two Friedman-Schwartz crises are not associated with positive unexplained residual failure risk, or increased importance of bank illiquidity for forecasting failure. The third Friedman-Schwartz crisis is more ambiguous, but increased residual failure risk is small in the aggregate. The final crisis (early 1933) saw a large unexplained increase in bank failure risk.

This paper considers the problem of sequential parameter and state estimation in stochastic volatility jump diffusion models. We describe the existing methods, the particle and practical filter, and then develop algorithms to apply these methods to the case of stochastic volatility models with jumps. We analyze the performance of both approaches using both simulated and S and P 500 index return data. On simulated data, we find that the algorithms are both effective in estimating jumps, volatility, and parameters.