Understanding the Numbers Game

Estimating Sensitivities in the Simulation of Complex Systems

Numbers can be a tricky business.

Michael C. Fu, the Smith Chair of Management Science and chair of the Decision, Operations and Information Technologies Department at the University of Maryland’s Robert H. Smith School of Business, understands just how tricky they can be.

Fu, who has a joint appointment with the Institute for Systems Research and an affiliate appointment with the Department of Electrical and Computer Engineering, both in the A. James Clark School of Engineering, recently co-authored a research article with Peking University’s Yijie Peng, Fudan University’s Jian-Qiang Hu, and Vrije Universiteit Amsterdam’s Bernd Heidergott, in which he examined some of the difficulties in getting the numbers right when simulating complex systems.

The paper, “A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances With Structural Parameters,” provides an efficient and accurate methodology for estimating sensitivities in complex systems that require simulation for performance evaluation, specifically, by introducing a new method that can handle discontinuous sample performance measures — an open research problem with various practical applications.

The estimator the researchers formulated is unbiased and has an analytical form, and the general framework addresses many derivative estimation problems, for example in settings of pricing financial derivatives, analyzing queueing systems, performing inventory control and management, doing statistical process control, or managing supply chains, manufacturing plants, transportation systems, communications networks, or service systems such as banks, amusement parks, retail stores.

Fu offers a quote from a book popular with practitioners in the financial services industry, “Monte Carlo Methods in Financial Engineering,” which says, “Whereas the prices themselves can often be observed in the market, their sensitivities cannot, so accurate calculation of sensitivities is arguably even more important than calculation of prices.” As examples, Fu says, consider how a finance professional might estimate the delta of an IBM stock option as compared to determining the price of the option itself.

An important statistical property of the estimator is that it be unbiased, the researchers explain, meaning that the expected value of the estimator equals the quantity that it is trying to estimate (for example, the price sensitivity of a stock option). The new methodology can handle both continuous and discontinuous settings. Continuous performance measures have been addressed by past research, whereas discontinuous performance measures are more challenging. Binary outcomes are the simplest examples of discontinuous performance measures. “In the context of finance, a digital option pays off a fixed value (e.g., $100) if above a certain threshold —the strike price — and zero otherwise,” Fu explains.

Instances of a structural parameter in the stock option example would be the strike price or expiration date, in contrast to a distributional parameter, which would affect the dynamics of the underlying asset.

Read more: A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances with Structural Parameters is featured in Operations Research.