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What does the financial market pricing do? A simulation analysis with a view to systemic volatility, exuberance and vagary

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Abstract

Biondi et al. (Phys A 391(22):5532–5545, 2012) develop an analytical model to examine the emergent dynamic properties of share market price formation over time, capable to capture important stylized facts. These latter properties prove to be sensitive to regulatory regimes for fundamental information provision, as well as to market confidence conditions among actual and potential investors. We comparatively assess accounting models belonging to two main families: historical cost accounting and mark-to-market (fair value) accounting regimes. Regimes based upon mark-to-market measurement of traded security, while generating higher linear correlation between market prices and fundamental signals, also involve higher market instability and volatility. These regimes also incur more relevant episodes of market exuberance and vagary in some regions of the market confidence space, where lower market liquidity further occurs.

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Notes

  1. Nevertheless, the actual degree of fundamentalism (chartism) does not depend only on exogenous subjective attitudes or beliefs. Indeed, the actual degree is fixed by the matching process (discussed later in this section) between demand and supply sides that occurs at a certain degree of fundamentalism/chartism. This fundamentally endogenous settlement makes the collective dimension irreducible to individual dimensions that are aggregated over both sides of the market.

  2. As robustness check we also simulated our model with a pure historical cost approach without the trend: outcomes are extremely similar and relegated to appendix.

  3. As robustness check we also simulated our model on a signal that reverts toward a precise value: results are very similar and relegated to appendix.

  4. The presence of this random error turns out to be without material impact on simulation results as discussed in the next section.

  5. From our assumption that \(\phi _i\) is distributed uniformly among investors between 0 and 1, it follows that values of the market confidence \(m_{S,D}>0.5\) imply that investors tend to be speculative. At the opposite, when \(m_{S,D}<0.5\), investors tend to be fundamentalists.

  6. For the FVA this device is called from a minimum of \(0.11\,\%\) of the times up to a maximum of \(23.92\,\%\) of the steps. It is called in average \(7.9\,\%\) of the steps (median \(6.76\,\%\)). Further details on this variable are available upon request from the authors.

  7. Under FVA regime, the average minimum price is 997.43 (median 999.56) with a median value of minimum prices of 39.06.

  8. This peak point denotes the expected maximum value of volatility under that accounting regime at 75 % likelihood.

  9. Given this strict definition of dissociation we find relatively low percentages of time that fall into this category. This difference, however, shows significant differences across common knowledge regimes.

  10. The relationship between this hypothesis and an equilibrium approach is acknowledged but not investigated here.

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Acknowledgments

Yuri Biondi is Research Director and Member of the Executive Committee of the Labex ReFi (Financial Regulation Lab), ESCP Europe, 79 avenue de la Republique, Paris 75011, France, http://www.labex-refi.com/en/. The authors would like to thank ESCP-Europe Business School for the financial support to the project Effects of localized social and cognitive interactions under alternative financial regulation regimes on Financial Market Prices Dynamics: Numerical simulation and experimental analyses, granted through the ESCP Europe Research Funding (EERF) for a visiting professor position.

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Appendices

Appendix 1: Summary of common knowledge regimes

Together with the HRT, FVA and TRA-S common knowledge regimes (introduced in Eqs. 4, 5 and 6) we analyze here two further regimes as robustness check of the results for HRT and TRA-S respectively.

The Historical Cost Accounting (HCA) regime implies an evolving exogenous signal of fundamental performance that is orthogonal to market price dynamics and results from stochastic positive and negative flows (Biondi 2011c):

$$\begin{aligned} F_t=N[-1;+1] + \epsilon _t \,\,\,\, \forall t \end{aligned}$$
(15)

The Fixed Target Reverting Accounting (TRA-F) regime implies a reverting fundamental performance signal that targets a fixed core value of reference:

$$\begin{aligned} F_t = - (p_t - F_{t-1}) + \epsilon _t \,\, \forall t \end{aligned}$$
(16)

Again, for these two accounting regimes the same stochastic error (introduced in Eq. 7) is added to account for estimation errors, measurement errors and other random effects.

Overall, this article develops results for five different mechanisms (summarized in Table 7) generating common knowledge information. These mechanisms are consistent with distinctive accounting regimes: two belonging to the historical cost accounting model family; one belonging to the fair value (current value, mark-to-market) accounting model family; and two providing a theoretical benchmark derived from equilibrium approaches, involving target-based signalling provision. We refer to the first three regimes as actual regimes as they denote stylized existing modes of accounting, while referring to the last two regimes as theoretical regimes that are and can be only thought in a vacuum.

Table 7 Taxonomy of the common knowledge regimes discussed in this article

Appendix 2: Data tables (comparisons across common knowledge regimes)

In this appendix we reproduce the tables displayed in the main text including the omitted results for the theoretical Fixed Target Reverting Accounting (TRA-F) regime and for the actual Historical Cost Accounting (HCA) regime. Tables 10 and 13 are only reported here to confirm results further corroborated by other variables in the main text.

1.1 Market pricing

See Table 8.

Table 8 Market prices

1.2 Market volatility

The volatility width \(W_v\) around its median (\(Q2_v\)) further comforts the results regarding market volatility (Table 9). Let us define:

Table 9 First lines: mean volatility \(v\) for market price series. Second lines: volatility likelihood at \(75\,\%\) of the distribution (peak point)
$$\begin{aligned} W[v]=\frac{Q3[v]-Q1[v]}{Q2[v]} \,\, \forall t \end{aligned}$$
(17)

where Q1, Q2 and Q3 respectively represents the first quartile, the median value and the third quartile of the market volatility distribution. We can observe in Table 10 that historical cost regimes remain in line with performance by theoretical regimes while the fair value regime shows anomalously high values of volatility width.

Table 10 Volatility width \(W[v]\) of the signal around its median (see Eq. 17 for definition)

1.3 Market exuberance and vagary

See Tables 1112.

Table 11 First line: expected maximum distance \(d_t\) at 75 % likelihood (see Eq. 13 for definition). Second line: mean exuberance range (see Eq. 14 for definition)
Table 12 First lines: percentage of time in which the market price evolution is dissociated from the cumulated fundamental signal \(S_t\). Second lines: mean length of the dissociation duration

1.4 Market liquidity

See Table 13.

Table 13 Ratio between the agents that participate to the clearing process and the total of those willing to trade

1.5 Information quality

See Tables 1415.

Table 14 Cross-sectional correlation between cumulated fundamental signal \(S_{t}\) and market price \(p_t\)
Table 15 One-period lagged correlation between cumulated fundamental signal \(S_{t-1}\) and market price \(p_t\)

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Biondi, Y., Righi, S. What does the financial market pricing do? A simulation analysis with a view to systemic volatility, exuberance and vagary. J Econ Interact Coord 11, 175–203 (2016). https://doi.org/10.1007/s11403-015-0159-3

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