Financial Engineering

Monte Carlo Methods are among the most broadly applicable and thus most powerful tools for valuing derivatives securities and measuring their risks. As computer speeds continue to increase and new research expands the scope and efficiency of these methods, their use is destined to grow. This book is devoted to the use of Monte Carlo methods in finance. Advances in Monte Carlo methods in financial engineering take place at the interface between academic research and industry practice. This book targets that interface developing theory closely tied to applications.

Bayesian learning implies decreasing weights on prior beliefs and increasing weights on the accuracy of the analyst?s past forecast record, as the number of forecast errors comprising her forecast record (its length) increases. Consistent with this model of investor learning, empirical tests show that investors? reactions to forecast news are increasing in the product of the accuracy and length of analysts? forecast records. Moreover, the Bayesian learning predicted by our model is more descriptive of investor reactions than is a static model which predicts that investors?

This paper develops algorithms for the pricing of discretely sampled barrier, lookback and hindsight options and discretely exercisable American options. Under the Black-Scholes framework, the pricing of these options can be reduced to evaluation of a series of convolutions of the Gaussian distribution and a known function. We compute these convolutions efficiently using the double-exponential integration formula and the fast Gauss transform.

In this chapter, I'll lay out the principal facts and controversies surrounding international flows of capital and their attendant risks. I'll review the perspectives of economic historians and economists on the implications of capital mobility, both during the first wave of globalization (prior to World War I) and during the recent wave (since 1980). I'll emphasize changes over time - especially political changes - that have weakened the case for unfettered capital mobility and have made capital flows more controversial among economists today than in the past.

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.

We investigate the ability of a tax-based fundamental –the ratio of tax-to-book income– to predict earnings growth and stock returns and to explain the earnings-price ratio. This tax fundamental reflects both temporary and permanent book-tax differences as well as tax accruals, such as changes in the tax valuation allowance. We find that the tax-to-book income ratio predicts subsequent five-year earnings changes, both before and after the implementation of Statement of Financial Accounting Standards (SFAS) No. 109 in 1993. For the pre-SFAS No.

This paper describes a practical algorithm based on Monte Carlo simulation for the pricing of multi-dimensional American (i.e., continuously exercisable) and Bermudan (i.e., discretely-exercisable) options. The method generates both lower and upper bounds for the Bermudan option price and hence gives valid confidence intervals for the true value. Lower bounds can be generated using any number of primal algorithms.

The Millennium Date Change (often referred to as Y2K) was anticipated to be a major liquidity event by many financial and corporate institutions as well as the central banks around the world. The timing of the event was foreseeable and thus satisfies the assumptions in the economic theory on public provision of private liquidity. We apply the theory to understand the liquidity premium in financial markets and the actions of the U.S. central bank in the period surrounding Y2K.