Market microstructure

Why Does the Stock Market Crash? Learning from Historical Volatility in Markets (1988)

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• published: 17 Jun 2015
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Areas of research attempting to explain (or at least model) these phenomena include noise trading, market microstructure, and Heterogeneous agent models. The latter is extended to Agent-based computational economics, where price is treated as an emergent phenomenon, resulting from the interaction of the various market participants (agents). The Noisy market hypothesis argues that prices can be influenced by speculators and momentum traders, as well as by insiders and institutions that often buy and sell stocks for reasons unrelated to fundamental value; see Noise (economic). The adaptive market hypothesis is an attempt to reconcile the efficient market hypothesis with behavioral economics, by applying the principles of evolution to financial interactions. An information cascade, alternatively, shows market participants engaging in the same acts as others ("Herd behavior"), despite contradictions with their private information. See also George Soros' approach: #Reflexivity, financial markets, and economic theory. On the obverse, various studies have shown that despite these departures from efficiency, asset prices do typically exhibit a random walk and that one cannot therefore consistently outperform market averages.[18] The practical implication, therefore, is that passive investing (e.g. via low-cost index funds) should, on average, serve better than any other active strategy.[19] Burton Malkiel's A Random Walk Down Wall Street - first published in 1973, and in its 12th edition as of 2015 - is a widely read popularization of these arguments. Note also that institutionally inherent limits to arbitrage — as opposed to factors directly contradictory to the theory — are sometimes proposed as an explanation for these departures from efficiency. As above, the assumptions that market prices follow a random walk and / or that asset returns are normally distributed are fundamental. Empirical evidence, however, suggests that these assumptions may not hold (see Kurtosis risk, Skewness risk, Long tail) and that in practice, traders, analysts and particularly risk managers frequently modify the "standard models" (see Model risk). In fact, Benoît Mandelbrot had discovered already in the 1960s that changes in financial prices do not follow a Gaussian distribution, the basis for much option pricing theory, although this observation was slow to find its way into mainstream financial economics. Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models; jump diffusion models allow for (option) pricing incorporating "jumps" in the spot price. Risk managers, similarly, complement (or substitute) the standard value at risk models with Historical simulations, volatility clustering, mixture models, Principal component analysis and extreme value theory.[20] For further discussion see Fat-tailed distribution#Applications in economics. Closely related is the Volatility smile, where implied volatility is observed to differ as a function of strike price (i.e. moneyness). The term structure of volatility describes how (implied) volatility differs for related options with different maturities; an implied volatility surface is a three-dimensional surface plot of volatility smile and term structure. These empirical phenomena negate the assumption of constant volatility — and log-normality— upon which Black-Scholes is built. See Black–Scholes model#The volatility smile. Approaches developed here in response include Local volatility and Stochastic volatility (the Heston, SABR and CEV models, amongst others). Alternatively, implied-binomial and -trinomial trees instead of directly modelling volatility, return a lattice consistent with — in an arbitrage-free sense — (all) observed prices, facilitating the pricing of other, i.e. non-quoted, strike/maturity combinations. Edgeworth binomial trees allow for a specified (i.e. non-Gaussian) skew and kurtosis in the spot price. Priced here, options with differing strikes will return differing implied volatilities, and the tree can thus be calibrated to the smile if required.[21] Similarly purposed closed-form models include: Jarrow and Rudd (1982); Corrado and Su (1996); Backus, Foresi, and Wu (2004). https://en.wikipedia.org/wiki/Financial_economics