Extreme Risk Model Considerations
VaR is an accurate, intuitive and easy-to-operate risk measurement and management technology, which can more effectively predict the maximum value fluctuation and probability of the assets that provide liquidity in the future, but it needs to follow market efficiency assumptions and assumptions Market fluctuations are random (under normal market conditions), but for the phenomenon of peaks and thick tails, fluctuations are clustered. The prediction of (volatility clustering) and extreme risk situations (in fact, these situations will be more frequent) needs to be coordinated with other models or higher-order stochastic simulation methods (such as GARCH family models and Monte Carlo simulation methods) to further avoid underestimation The possibility of small probability events and more accurate assessment of loss probability. As shown in the figure, Cauchy Distribution (Cauchy Distribution) is a well-known type of fat-tailed distribution, which is suitable for the prediction of small probability events such as financial crises, which is different from normal distributed.
The CVaR model is often used to monitor "black swan" events (extreme events on the left), pointing out that losses exceed the conditional mean value of VaR, and are more sensitive to extreme risk assessments on the asset side.
The function f is the loss function, p represents the distribution function of the rate of return y, and β is the confidence level. Although the Centauri Finance contract framework tries to split the entire fund pool into three pools: fund pool, transaction pool, and savings pool. However, when risk control liquidation is triggered, in the face of such extreme risks, their tail correlation may suddenly increase, which cannot play the role of risk diversification. For the measurement of extreme tail risks, Centauri Finance will establish corresponding financial solutions suitable for chains. The core idea of the tail risk parity model of the system is to "share" the tail risk by rationally allocating the weight of the liquidity pool of portfolio assets. We still use VaR to reverse the tail correlation, that is, to calculate the combination VaR (VaR-implied tail correlation) through the respective VaR value of each asset and the combination weight:
ρ12 represents the correlation degree of price changes of various assets.
If the asset-side price changes follow a Gaussian distribution, the correlation coefficient is equivalent to the classic Pearson Correlation Coefficient. As mentioned before, VaR has limitations. In order to accurately describe the left fat tail of the return distribution, VaR can be further replaced by the ES (Expected Shortfall, same as CVaR) calculation method, which can more effectively describe the mean value of the left tail risk ( condition expectations).
Given the expectation that the expected shortfall is the worst α percentage, X ∈ Lp(F ) denote future returns. On the whole, the internal circulation of Centauri Finance and the risk measurement model when the liquidity is exhausted will fully consider the measurement of Convergent risks (can be modeled and quantified) and Divergent risks (can not be measured well), and will complete in order not to "default" ", the "default" can be quantified, the "default" can be predicted, and the progressive risk control model that reduces the "default" loss. It is worth emphasizing again that there is no right or wrong in models and theories, and they are not static. The key is to always grasp the most essential cognition and exploration of the encryption market and the future, establish a model and methodology, and develop a phenomenon into One direction, becoming a comprehensive field supported by more professionals and border industries, can continuously expand the financial border on the chain and bring the Centauri Finance mechanism to a new height.
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