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Credit Default Swap (or CDS) refers to an insurance contract based on a pre-specified Notional Amount (e.g., US$10 Million) between two counterparties, whereby, in exchange for an agreed Premium payment (which can be paid upfront or by periodic installments), the seller commits to protect the buyer against the default-related losses arisen from the underlying Reference Obligation such as a defaultable bond for an agreed period of time (which is also called Maturity). During the 2007-2009 financial cirsis, it is widely recognized that proper valuation adjustments (collectively, called XVA) were lacking during the mark-to-market for Over-the-counter derivatives (or OTC), where mark-to-market for credit-risky financial assets is based on deriving risk-neutral default probabilities from liquid CDS Curves.

However, according to ECB's survey, over 75% of the counterparties for Internal Model Method (or IMM) banks do not have liquid CDS quotes, thus, have to be based on so-called CDS Proxy Method (or CDS Rate Construction Method ), which refers to a methodology used to derive risk-neutral default probabilities (or risk-neutral PD) for a counterparty when liquid CDS quotes are not available. When liquid CDS quotes are not available, proxy CDS rates are required for credit derivative pricing (such Single-name CDS, Index CDS, CDO, etc.), XVA pricing as well as CVA Charge. The absence of liquid CDS quotes is referred to as Shortage of Liquidity problem .

Hereunder we describe the uses of CDS Proxy Methods in the context of calculating CVA, CVA charge and four current CDS Proxy Methods in public domain.

CDS Proxy Rates used in CVA Calculation
For the purpose of brevity, we explain the calcualtion of CVA in the context of Unilateral default; as a result, CVA is given by the risk-neutral expectation of the discounted loss written as


 * $$ \mathrm{CVA(t, T)} =(1-R)\int_t^T E^Q\left[\frac{B_s}{B_t} E(t)|\tau=t\right] d\mathrm{PD}(t,s) $$

where $$T$$ stands for the longest maturity among all the transactions contained in a credit-risky portfolio, $$ B_t $$ is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity $$t$$, $$R$$ stands for the Expected Recovery Rate, i.e., the fraction of the portfolio value that can be recovered in event of a counterparty default, $$\tau$$ is the time of default, $$E(t)$$ is the Exposure at time $$t$$, and importantly, $$ \mathrm{PD}(s,t)$$ is the risk-neutral probability of counterparty default between times $$t$$ and $$s$$.
 * In case of liquid counterparties, these probabilities can be obtained from the term structure of CDS spreads;
 * in case of illiquid counterparties, which is applicable to vast majority of banks' counterparties, a CDS Proxy Method has to be applied.

CDS Proxy Rates used in CVA Capital and CVA Charge Calculation
In practice, CDS Proxy Rates are used beyond XVA calculations:
 * A part of the regulatory Capital and RWA (Risk-weighted asset) calculation introduced under Basel 3;
 * The CVA desk of an investment bank, whose purpose is to:
 * hedge for possible losses due to counterparty default;
 * hedge to reduce the amount of capital required under the CVA calculation of Basel 3;
 * The "CVA charge". The hedging of the CVA desk has a cost associated to it, i.e. the bank has to buy the hedging instrument. This cost is then allocated to each business line of an investment bank (usually as a contra revenue). This allocated cost is called the "CVA Charge".

Rating-implied Method
Some banks derive risk-neutral default probabilities from either internal ratings or credit agency's ratings, which is clearly not appropriate: both internal ratings and credit agency's ratings are based on long-term credit history and the PDs implied from ratings are so-called real-world measures, thus, are inappropriate for any of the purposes mentioned above. On March 15, 2016, Risk Magazine reported US$712 million CVA-losses due to the use of rating-implied PD in the CVA calculation in one British bank. In practice, the real-world PDs tend to be much lower than risk-neutral world, which leads to underestimation of default risks; thus, using Rating-implied PDs tends to underestimate CVA and inflates reported PnL. Clearly, once the bank switched away from Rating-implied Method, the masked losses resurfaced.

Curve Mapping Method and Cross-sectional Regression Method
Curve Mapping Method is based on the Mean or Median with or without ad-hoc adjustments from the CDS rates within a bucket consisting of CDS rates from the same Region, Sector and Rating. It assumes default-risk homogeneous within the bank, thus, neglecting the idiosyncrasies across the bucket among counterparties, which is clearly not appropriate and not consistent with regulation requirements.

Cross-sectional Regression Method is based on, which unfortunately, makes the same bucket-homogeneity for counterparty default risks, thus, has the same shortcomings as described above for Curve Mapping Method.

In addition, both the above methods can introduce arbitrage opportunity as highlighted in.

Machine Learning Technique-based Method
Brummelhuis and Luo (2017) introduced a novel methodology that is based on some of the most popular Machine Learning, in particular, classification techniques and achieved superior performances with the top 3 classifiers being: Neural Network, Support Vector Machine and Ensemble techniques based on K-fold (out-of-sample) cross validation with the following characteristics.
 * Counterparty-specific component of default risk is captured; the volatility within each Region/Sector/Rating bucket is accounted for.
 * No arbitrage introduced by a model.
 * The classification results are directly based on inputs from CDS market; for example, an illiquid Counterparty A is proxied by a liquid counterparty B, A would inherit the whole CDS curve (which, in principle, should be free of arbitrage across different CDS rates/spreads) from B. However, any of the above three methods would have one proxy rate derived for each maturity; thus, arbitrage opportunities (in case of inversion) can be introduced unless an assumption is imposed on the shape of CDS curve.
 * Established K-fold cross validation, which is out-of-sample, can be conducted to avoid model overfitting.
 * A wide range of classification techniques are used to achieve the best performing outcome.