Financial Engineering

A general approach to improving simulation accuracy uses information about auxiliary control variables with known expected values to improve the estimation of unknown quantities. We analyze weighted Monte Carlo estimators that implement this idea by applying weights to independent replications. The weights are chosen to constrain the weighted averages of the control variables. We distinguish two cases (unbiased and biased) depending on whether the weighted averages of the controls are constrained to equal their expected values or some other values.

This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates.

This paper examines continuous-time stochastic volatility models incorporating jumps in returns and volatility. We develop a likelihood-based estimation strategy and provide estimates of parameters, spot volatility, jump times, and jump sizes using S&P 500 and Nasdaq 100 index returns. Estimates of jump times, jump sizes, and volatility are particularly useful for identifying the effects of these factors during periods of market stress, such as those in 1987, 1997, and 1998. Using formal and informal diagnostics, we find strong evidence for jumps in volatility and jumps in returns.

Interest rate swap pricing theory traditionally views swaps as portfolios of forward contracts with net swap payments discounted using the LIBOR curve. Current market practices of marking-to-market and collateralization question this view. Collateralization and marking-to-market affects discounting of swap payments (through altered default characteristics) and introduces intermediate cash-flows. This paper provides a theory of swap valuation under collateralization and we find evidence supporting the presence of costly collateral.

This paper develops formulas for pricing caps and swaptions in LIBOR market models with jumps. The arbitrage-free dynamics of this class of models were characterized in Glasserman and Kou [9] in a framework allowing for very general jump processes. For computational purposes, it is convenient to model jump times as Poisson processes; however, the Poisson property is not preserved under the changes of measure commonly used to derive prices in the LIBOR market model framework.

We consider a setting where a firm delegates an investment decision and, subsequently, a sales decision to a privately informed manager. For both decisions corporate income taxes have real effects. We show that compensating the manager based on pre-tax residual income can ensure after-tax NPV-maximization ("goal congruence") for each decision problem in isolation. However, this metric fails if both decisions are nontrivial, since it requires asset-specific hurdle rates and hence precludes asset aggregation.

This paper studies the capital budgeting process in a setting where a manager is privately informed about the profitability of an investment project and enjoys nonpecuniary benefits of control ("empire benefits"). I characterize the optimal required rate of return and show that a delegation scheme with residual income-based compensation can replicate the benchmark performance achieved under centralization. The main result of the paper is that the optimal capital charge rate for computing residual income always exceeds the required rate of return as a result of empire benefits.

The article examines the price implications of corporate disclosures as well as other information releases. Corporate disclosures are an important source of information for investors. For dividend announcements, the price implications appear straightforward: price is the present value of expected future dividends. Hence, to the extent that future dividends are related to current dividends, dividend changes should trigger price responses. Other corporate disclosures, such as earnings, may also be viewed as proxies for future dividends.

Simulation is widely used to estimate losses due to default and other credit events in financial portfolios. The challenge in doing this efficiently results from (i) rareevent aspects of large losses and (ii) complex dependence between defaults of multiple obligors. We discuss importance sampling techniques to address this problem in two portfolio credit risk models developed in the financial industry, with particular emphasis on a mixed Poisson model. We give conditions for asymptotic optimality of the estimators as the portfolio size grows.