Black Was Right: Price Is Within a Factor 2 of Value

Bouchaud, Jean‐Philippe; Ciliberti, Stefano; Lempérière, Yves; Majewski, Adam Aleksander; Seager, Philip; Ronia, K. Sin

doi:10.2139/ssrn.3070850

Cited by 22 publications

(27 citation statements)

References 27 publications

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“…This is consistent with the findings of Bouchaud et alii in a recent paper [3], in which they show empirically that returns are predictable at small scales and not at higher scales, at least on their dataset, which consists in daily prices of commodities, stocks, and currencies. In addition, they define a model to describe this effect: an Ornstein-Uhlenbeck process with a positively autocorrelated noise.…”

Section: Resultssupporting

confidence: 92%

“…As a consequence, we computed the empirical autocorrelation R(l) for each FX rate series, 2 with a lag l ranging from 1 to 1,000 time steps. 3 We want to determine which of the two following models best fits the empirical autocorrelation:…”

Section: Relevance Of the Delampertized Fbmmentioning

confidence: 99%

“…We worked directly with the rate series, not with the series of the variations of the rate 3. In other words, the lag is between 15 minutes and more than 10 days 4.…”

mentioning

confidence: 99%

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Hurst Exponents and Delampertized Fractional Brownian Motions

Garcin

2019

Int. J. Theor. Appl. Finan.

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The inverse Lamperti transform of a fractional Brownian motion (fBm) is a stationary process. We determine the empirical Hurst exponent of such a composite process with the help of a regression of the log absolute moments of its increments, at various scales, on the corresponding log scales. This perceived Hurst exponent underestimates the Hurst exponent of the underlying fBm. We thus encounter some time series having a perceived Hurst exponent lower than [Formula: see text], but an underlying Hurst exponent higher than [Formula: see text]. This paves the way for short- and medium-term forecasting. Indeed, in such series, mean reversion predominates at high scales, whereas persistence is overriding at lower scales. We propose a way to characterize the Hurst horizon, namely a limit scale between these opposite behaviors. We show that the delampertized fBm, which mixes persistence and mean reversion, is relevant for financial time series, in particular for high-frequency foreign exchange rates. In our sample, the empirical Hurst horizon is always above 1[Formula: see text]h and 23[Formula: see text]min.

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Section: Resultssupporting

confidence: 92%

Section: Relevance Of the Delampertized Fbmmentioning

confidence: 99%

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Hurst Exponents and Delampertized Fractional Brownian Motions

Garcin

2019

Int. J. Theor. Appl. Finan.

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“…As can be seen, simulated stock prices oscillate around their constant fundamental value, given by exp [ ] = 1. Theamplitude of the boom-bust dynamics suggests that simulated stock prices tend to be "a factor 2" away from the fundamental value, a relation that is reported byBlack (1986),Bouchaud et al (2017) andMajewski et al (2020) for actual stock markets, along with evidence that a self-correction of mispricing in stock markets can take several years. 8Note that mispricing in the simulated stock market is also quite persistent.…”

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confidence: 75%

Heterogeneous speculators and stock market dynamics: a simple agent-based computational model

Schmitt

Schwartz

Westerhoff

2020

The European Journal of Finance

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We propose a simple agent-based computational model in which speculators' trading behavior may cause bubbles and crashes, excess volatility, serially uncorrelated returns, fat-tailed return distributions and volatility clustering, thereby replicating five important stylized facts of stock markets. Since each speculator bets on his own (technical and fundamental) trading signals, stock prices are excessively volatile and oscillate erratically around their fundamental value. However, speculators' heterogeneity occasionally vanishes, e.g. due to panic-induced herding behavior, yielding extreme returns. Lasting regimes with high volatility originate from the fact that speculators extract stronger trading signals out of past stock price movements when stock prices fluctuate strongly. Simulations furthermore suggest that circuit breakers may be an effective tool to combat financial market turbulences.

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“…This linearity is a generic feature of material response for small enough stimuli, as it requires only that the constitutive relation be analytic and nonvanishing to first order. Linear constitutive relations have proven useful for characterizing a broad range of physical systems, including dielectric materials 3 , diffusion 4 , friction 5 , geomaterials 6 , Newtonian fluids 7 , piezoelectric materials 8 , thermoelectric materials 9 , and even abstract entities such as financial markets 10,11 .…”

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confidence: 99%

Physical limits to sensing material properties

et al. 2020

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All materials respond heterogeneously at small scales, which limits what a sensor can learn. Although previous studies have characterized measurement noise arising from thermal fluctuations, the limits imposed by structural heterogeneity have remained unclear. In this paper, we find that the least fractional uncertainty with which a sensor can determine a material constant λ0 of an elastic medium is approximately $$\delta {\lambda }_{0}/{\lambda }_{0} \sim ({\Delta }_{\lambda }^{1/2}/{\lambda }_{0}){(d/a)}^{D/2}{(\xi /a)}^{D/2}$$ δ λ 0 / λ 0 ~ ( Δ λ 1 / 2 / λ 0 ) ( d / a ) D / 2 ( ξ / a ) D / 2 for a ≫ d ≫ ξ, $${\lambda }_{0}\gg {\Delta }_{\lambda }^{1/2}$$ λ 0 ≫ Δ λ 1 / 2 , and D > 1, where a is the size of the sensor, d is its spatial resolution, ξ is the correlation length of fluctuations in λ0, Δλ is the local variability of λ0, and D is the dimension of the medium. Our results reveal how one can construct devices capable of sensing near these limits, e.g. for medical diagnostics. We use our theoretical framework to estimate the limits of mechanosensing in a biopolymer network, a sensory process involved in cellular behavior, medical diagnostics, and material fabrication.

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Black Was Right: Price Is Within a Factor 2 of Value

Cited by 22 publications

References 27 publications

Hurst Exponents and Delampertized Fractional Brownian Motions

Hurst Exponents and Delampertized Fractional Brownian Motions

Heterogeneous speculators and stock market dynamics: a simple agent-based computational model

Physical limits to sensing material properties

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