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Market Simulation

Copyright 2004, Institutional Investor Journals.

Copyright 2010, CFA Institute. Reproduced and republished from Financial Analysts Journal with permission from CFA Institute. All rights reserved.

Financial Market Simulation
by Bruce I. Jacobs, Kenneth N. Levy, and Harry M. Markowitz, The Journal of Portfolio Management, 30th Anniversary Issue, September 2004

Simulating Security Markets in Dynamic and Equilibrium Modes
by Bruce I. Jacobs, Kenneth N. Levy, and Harry M. Markowitz, Financial Analysts Journal, September/October 2010

Most financial models today assume security prices follow a continuous-time, random process. This is true of most option pricing models, beginning with the original Black-Scholes-Merton model. For some purposes, it may be sufficient to assume that prices follow a continuous-time process. Often, however, it is necessary to look more closely to determine how prices actually evolve.

Investment actions themselves may change the price process. Certain investment strategies, for example, can have feedback effects. Consider momentum trading, which tends to exacerbate trends in prices. Momentum traders helped to fuel the stock market's rise in the late 1990s, changing the price process in ways that a continuous-time model would have had difficulty predicting. By contrast, a model that incorporated the actual trading rules of major market participants at that time might have been able to forecast the growing technology stock bubble. (For a description of momentum trading’s effects on markets, see Bruce Jacobs, “Momentum Trading: The New Alchemy.”)

The Jacobs Levy Markowitz Simulator (“JLMSim”), developed by Bruce Jacobs, Ken Levy, and Harry Markowitz, is an asynchronous, discrete-time model that allows its users to model financial markets, employing their own inputs about the numbers and types of investors, traders, and securities. It does not assume that a process changes continuously over time. Instead, it assumes that changes reflect events, which unfold in an irregular fashion. Prices may thus be discontinuous, gapping up or down. The JLMSim can be used to detect how prices might change as the result of changes in financial market regulations or even something more subtle, such as a change in the composition of market participants.

Asynchronous models may also be superior when the question to be analyzed is whether micro-theories about the behavior of investors add up to the observed macro-phenomena of the market. From time to time, the market manifests liquidity “black holes,” which seem to defy rational investor behavior. Consider the stock market crash on October 19, 1987. That day, prices fell precipitously and discontinuously. While one might have expected rational value investors to step in to pick up bargain stocks, few did. Similar black holes developed in connection with the collapse of the hedge fund Long-Term Capital Management in 1998 and, more recently, during the 2008-09 credit crisis. In these and other less extreme cases, the price process was not fixed. Continuous-time modeling that assumes a fixed price process would have provided misleading results, whereas asynchronous models may be able to explain both the abundance of sellers and the dearth of buyers. (For detailed descriptions of such events, see Bruce I. Jacobs, Capital Ideas and Market Realities: Option Replication, Investor Behavior, and Stock Market Crashes; “Risk Avoidance and Market Fragility;” and “Tumbling Tower of Babel: Subprime Securitization and the Credit Crisis.”) 

It is important to recognize that large traders may not be mere price-takers; they can affect prices. We believe an asynchronous-time market simulator such as JLMSim, which is capable of modeling the agents and market mechanisms behind observed prices, is much better equipped than continuous-time models to capture this reality of markets. For this reason, we believe the JLMSim will stimulate much future research. 

Key Articles:

· “Simulating Security Markets in Dynamic and Equilibrium Modes,” by Bruce I. Jacobs, Kenneth N. Levy, and Harry M. Markowitz, Financial Analysts Journal, September/October 2010.
Asynchronous discrete-time models, whose clocks advance in irregular intervals from one event to the next, can provide information that the more commonly used continuous-time models cannot. They can be used, for example, to test the effects on security prices of real-world events such as changes in investors’ strategies, modifications in overall leverage, or switches in regulatory regimes. The present paper uses an asynchronous discrete-time model to demonstrate the effects on market prices of different ways of estimating security returns and of different trading rules. In particular, it shows how variations in the ratio of momentum-type investors to value-type investors can have dramatic effects on security prices. When the ratio of momentum to value investors is large, security prices tend to “explode”; when the ratio is low, prices fluctuate rather realistically, but do not destabilize. Security prices can also become unstable when traders in a thin market do not use trading rules that “anchor” their bids and asks to recent market prices. Finally, this paper demonstrates that an asynchronous discrete-time model can be used to arrive at equilibrium expected returns for a variety of realistic financial markets; it does not require the kind of unrealistic assumptions that some analytical models require.

· “Financial Market Simulation,” by Bruce I. Jacobs, Kenneth N. Levy, and Harry M. Markowitz, The Journal of Portfolio Management, 30th Anniversary Issue, September 2004.(1)
When they want to see how complex systems work, scientists often turn to asynchronous-time simulation, which allows processes to change sporadically over time, typically at irregular intervals. While rarely used in finance today, such models may turn out to be valuable tools for understanding how markets respond to changes in the participation rates of different types of investors, for example, or to changes in regulatory or investment policies. The asynchronous, discrete-event, stock market simulator described here allows users to create a model of the market, using their own inputs. Users can vary the numbers of investors, traders, portfolio analysts, and securities, as well as their investing and trading decision rules. Such a simulation may be able to provide a more realistic picture of complex markets.

For information on the availability of the JLM Simulator, go to http://www.jacobslevy.com/jlm_simulator.htm

Other Research Categories:

Security Selection

Plan Architecture and Portfolio Engineering

Long-Short Investing

Portfolio Optimization, Short Sales, and Leverage Aversion

Market Crises


(1)Presented at Carnegie Mellon University and Princeton University, September 2005.

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