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The Econometrics of Learning in Financial Markets
- Peter Bossaerts
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- Journal:
- Econometric Theory / Volume 11 / Issue 1 / February 1995
- Published online by Cambridge University Press:
- 11 February 2009, pp. 151-189
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The asymptotic behavior of the sample paths of two popular statistics that test market efficiency are investigated when markets learn to have rational expectations. Two cases are investigated, where, should markets start out at a rational expectations equilibrium, both statistics would asymptotically generate standard Brownian motions. In a first case, where agents are Bayesian and payoffs exogenous, the statistics have identical sample paths, but they are not standard Brownian motions. Whereas the finite-dimensional distributions are Gaussian, there may be a bias if agents' initial beliefs differ. A second case is considered, where payoffs are in part endogenous, yet agents consider them to be drawn from a stationary, exogenous distribution, which they attempt to learn in a frequentist way. In that case, one statistic behaves as if the economy were at a rational expectations equilibrium from the beginning on. The other statistic has sample paths with substantially non-Gaussian finite-dimensional distributions. Moreover, there is a negative bias. The behavior of the two statistics in the second case matches remarkably well the empirical results in an investigation of the prices of six foreign currency contracts over the period 1973–1990.
3 - Experiments with Financial Markets: Implications for Asset Pricing Theory
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- By Peter Bossaerts, Professor of Economics and Management, California Institute of Technology
- Edited by Michael Szenberg, Pace University, New York, Lall Ramrattan, University of California, Berkeley
- Foreword by Paul A. Samuelson
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- Book:
- New Frontiers in Economics
- Published online:
- 06 July 2010
- Print publication:
- 06 September 2004, pp 103-127
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Summary
INTRODUCTION
This essay surveys experiments of financial markets that were designed with the competitive paradigm in mind. The results will be analyzed from a particular theoretical angle, namely, asset pricing theory. That is, we discuss to what extent a given financial markets experiment can shed light on the validity of asset pricing theory.
Modern asset pricing theory has strong roots in economics and probability theory. Its models are logically compelling, and the derivations elegant. Many models are widely used in industry and government, in applications of capital budgeting, industry rate regulation, and performance evaluation, among others. Yet, there is surprisingly little evidence in support of the theory, and what has come forth is controversial. But tests of asset pricing models have almost exclusively been based on econometric analysis of historical data from naturally occurring markets. That type of empirical analysis is very difficult, because many auxiliary assumptions (homogeneous, correct ex ante beliefs, stationarity, unbiased samples, and so on) have to be added to the theory for it to become testable.
Experimentation would provide an alternative means to verify the principles of asset pricing theory, because many auxiliary assumptions are under the control of the experimenter. That is, experimentation provides one way to gauge the validity of what would otherwise remain mere elegant mathematics. This essay reports on what has been accomplished so far.
Not all experiments on financial markets were designed with the idea that they should verify theoretical principles. Often, the link with the theory is vague.
Martingale-Based Hedge Error Control
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- By Peter Bossaerts, California Institute of Technology, Bas Werker, Tilburg University
- Edited by L. C. G. Rogers, University of Bath, D. Talay, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt
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- Book:
- Numerical Methods in Finance
- Published online:
- 05 June 2012
- Print publication:
- 26 June 1997, pp 290-304
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Summary
Introduction
In the seminal paper of Black & Scholes (1973), the payoff on a European option is replicated perfectly by a dynamic strategy in the underlying security and a zero-coupon bond. Hence, the price of the replicating portfolio determines the no-arbitrage value for the option. Since that work of Black and Scholes, option pricing has been following this standard pattern of first specifying a perfect dynamic hedge, followed by an exploration of the pricing implications of the absence of arbitrage.
In Black–Scholes model, markets are complete in the sense that the payoff on the option is attainable through a dynamic trading strategy in the underlying stock and a money account. In practice, however, some of their assumptions can be proven wrong. Foremost, volatility is stochastic. In the absence of an asset that is instantaneously perfectly correlated with the volatility of the stock, market completeness is thereby invalidated. Likewise, actual rebalancing necessarily occurs over discrete intervals of time, in contrast with Black-Scholes continuous rebalancing.
If markets are incomplete, a blind application of complete-markets hedging strategies seems inappropriate. Most importantly, such policies do not self-correct even if a significant deviation from the target payoff is apparent. That immediately raises the question of whether there are hedging strategies that continuously correct in a way that facilitates error control. In other words, are there policies that adjust to past tracking errors such that the stochastic characteristics of the total tracking error become wellspecified?