Proxy Risk Factors Under Basel Market Risk Rules

# Dummy time series to be considered


# Dummy time series to be considered












When estimating various risk measure like `VaR` a good amount of times series data is required. Somethings it happens that sufficient data may not available of identified risk factor. In that case some dummy/proxy time series is used.

I wonder if there is any regulatory mandate which defines a floor on estimated correlation coefficient between actual time series and it's dummy/proxy? Any reference of such regulatory framework/mandate would be really helpful

## Answer by Dimitri Vulis (score 1, accepted)

https://quant.stackexchange.com/a/76928

VaR is so Basel II! :)

https://www.fdic.gov/news/speeches/2023/spjun2223.html

> many of the Value at Risk models used proxy risk factors from other more widely traded products as approximations. The heavy use of proxies on less liquid trading positions materially underestimated the risk in these products and contributed to the undercapitalization of many banking organizations during the global financial crisis.

> To deal with the most pressing deficiencies in the market risk capital framework, the Basel Committee introduced a limited set of revisions in July 2009 and then set out to address a number of other issues to improve the overall design and coherence of the capital standard for market risk.2 This led to the so-called fundamental review of the trading book (or FRTB) as part of this final round of Basel III.3

In the newer framework, the Fundamental Review of the Trading Book (FRTB), not having good historical data (real price observations (RPOs) for 12 months) is one of the reasons a factor may fail the Risk Factor Eligibility Test (RFET), which renders this factor a "non-modelable risk factor" (NMRF), which you'd rather try to avoid by using proxy data, and by decomposing the factor into components, some of which would be "modelable". Using proxies may allow you to include the problematic factor in the internal model calculaion of the extended shortfall (ES), which replaces VaR.

The BCBS FRTB guidance is in chapter 31 "Internal models approach: model requirements" on the web site of the Basel Committee for Banking Supervision (BSBS) / Bank for International Settlements: https://www.bis.org/basel_framework/chapter/MAR/31.htm . You should read the entire framework. Your local regulator may have some guidance that may differ a little from BCBS, e.g. https://www.federalregister.gov/documents/2023/09/18/2023-19200/regulatory-capital-rule-large-banking-organizations-and-banking-organizations-with-significant

> (10) A [BANKING ORGANIZATION] must acquire current and historical market data that are either independent of the lines of business or validated independently from the lines of business and be compliant with applicable accounting standards. The data must be input into the exposure models in a timely and complete fashion, and maintained in a secure database subject to formal and periodic audit. A [BANKING ORGANIZATION] must also have a well-developed data integrity process to handle the data of erroneous and anomalous observations. In the case where an exposure model relies on proxy market data, a [BANKING ORGANIZATION] must set internal policies to identify suitable proxies and the [BANKING ORGANIZATION] must demonstrate empirically on an ongoing basis that the proxy provides a conservative representation of the underlying risk under adverse market conditions.

If you google FRTB proxy data and the above-mentioned abbreviations, you will find many of "explain like I'm 5" discussions of data proxies, e.g. https://www.fintegral.com/storage/app/media/blog/FRTB/20211118_FRTB_The%20usage%20of%20proxies%20under%20FRTB.pdf

but if you must look at the old Basel II guidance https://www.bis.org/publ/bcbs193.pdf

> 718a the supervisor has to be satisfied that proxies are used which show a good track record for the actual position held (i.e. an equity index for a position in an individual stock). ... 718xc... In addition, the model must meet minimum data standards. Proxies may be used only where available data is insufficient or is not reflective of the true volatility of a position or portfolio, and only where they are appropriately conservative. ... Where data histories for a particular instrument do not meet the quantitative standards in paragraph 718(Lxxvi) and where the bank has to map these positions to proxies, then the bank must ensure that the proxies produce conservative results under relevant market scenarios

I would interpet this guidance as - the correlation under normal market conditions is not as important as what happens in the tail that matters for VaR.