The Detection of Asset Price Bubbles in the Cryptocurrency Markets with an Application to Risk Management and the Measurement of Model Risk
Bibliographic record
Abstract
This study presents an analysis of the impact of asset price bubbles on the markets for cryptocurrencies and con-siders the standard risk management measure Value-at-Risk (“VaR”). We apply the theory of local martingales, present a styled model of asset price bubbles in continuous time and perform a simulation experiment featuring one- and two-dimensional Stochastic Differential Equation (“SDE”) systems for asset value through a Constant Elasticity of Variance (“CEV”) process that can detect bubble behavior. In an empirical analysis across several widely traded cryptocurrencies, we find that the estimated parameters of one-dimensional SDE systems do not show evidence of bubble behavior. However, if we estimate a two-dimensional system jointly with an equity market index, we do detect a bubble, and comparing bubble to non-bubble economies it is shown that asset price bubbles result in materially inflated VaR measures. The implication of this finding for portfolio and risk management is that rather than acting as a diversifying asset class, cryptocurrencies may not only be highly correlated with other assets but have anti-diversification properties that materially inflate the downside risks in portfolios combining these asset types. We also measure the model risk arising from mispecifying the process driving cryptocurrencies by ignoring the relationship to another representative risk asset through applying the principle of relative entropy, where we find that across all cryptocurrencies studied that the distributions of a distance measure between the simulated distributions of VaR are almost all highly skewed to the right and very heavy-tailed. We find that in the majority of cases that the model risk “multipliers” range in about two to five across cryptocurrencies, estimates which could be applied to establish a model risk reserve as part of an economic capital calculation for risk management of cryptocurrencies.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.020 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".