The distribution of modelled risk factors should account for the possible non-normality of the distribution of exposures, including the existence of leptokurtosis, where appropriate.
60 An AI should apply the same netting recognition as in its accounting CVA calculations.
In particular, the AI can model the netting uncertainty.
10.2 Qualitative Standards
61 An AI should meet the qualitative criteria set out below on an ongoing basis. The HKMA should be satisfied that the AI has met the qualitative criteria before granting an SA-CVA approval.
62 Exposure models used for calculating regulatory CVA should be part of a CVA risk management framework that includes the identification, measurement, management, approval and internal reporting of CVA risk. An AI should have a credible track record in using these exposure models for calculating CVA and CVA sensitivities to market risk factors.
63 Senior management should be actively involved in the risk control process and regard CVA risk control as an essential aspect of the business to which significant resources need to be devoted.
64 An AI should have a process in place for ensuring compliance with a documented set of internal policies, controls and procedures concerning the operation of the exposure system used for accounting CVA calculations.
65 An AI should have an independent control unit that is responsible for the effective initial and ongoing validation of the exposure models. This unit should be independent from business credit and trading units (including the CVA desk), be adequately staffed and report directly to senior management of the AI.
66 An AI should document the process for initial and ongoing validation of its exposure models to a level of detail that would enable a third party to understand how the models operate, their limitations, and their key assumptions; and recreate the analysis.
This documentation should set out the minimum frequency with which ongoing validation will be conducted as well as other circumstances (such as a sudden change in market behaviour) under which additional validation should be conducted. In addition, the documentation should describe how the validation is conducted with respect to data flows and portfolios, what analyses are used and how representative counterparty portfolios are constructed.
67 The pricing models used to calculate exposure for a given path of market risk factors should be tested against appropriate independent benchmarks for a wide range of market states as part of the initial and ongoing model validation process. Pricing models for options should account for the non-linearity of option value with respect to market risk factors.
68 An AI should carry out an independent review of the overall CVA risk management process regularly in the its internal auditing process. This review should include both the activities of the CVA desk and of the independent risk control unit.
69 An AI should define criteria on which to assess the exposure models and their inputs and have a written policy in place to describe the process to assess the performance of exposure models and remedy unacceptable performance.
70 Exposure models should capture transaction-specific information in order to aggregate exposures at the level of the netting set. An AI should verify that transactions are assigned to the appropriate netting set within the model.
71 Exposure models should reflect transaction terms and specifications in a timely, complete, and conservative fashion. The terms and specifications should reside in a secure database that is subject to formal and periodic audit. The transmission of transaction terms and specifications data to the exposure model should also be subject to internal audit, and formal reconciliation processes should be in place between the internal model and source data systems to verify on an ongoing basis that transaction terms and specifications are being reflected in the exposure system correctly or at least conservatively.
72 The current and historical market data should be acquired independently of the lines of business and be compliant with accounting. They should be fed into the exposure models in a timely and complete fashion, and maintained in a secure database subject to formal and periodic audit. An AI should also have a well-developed data integrity process to handle the data of erroneous and/or anomalous observations. In the case where an exposure model relies on proxy market data, an AI should set internal policies to identify suitable proxies and the AI should demonstrate empirically on an ongoing basis that the proxy provides a conservative representation of the underlying risk under adverse market conditions.
11 Components of the SA-CVA
73 The SA-CVA capital charge is calculated as the sum of the capital charges for delta and vega risks calculated for the entire CVA portfolio (including eligible hedges).
74 The capital charge for delta risk is calculated as the simple sum of delta risk capital charges calculated independently for the following six risk classes:
interest rate risk;
foreign exchange (FX) risk;
counterparty credit spread risk;
reference credit spread risk (i.e. credit spreads that drive the CVA exposure component);
equity risk; and
commodity risk.
75 If an instrument is deemed as an eligible hedge for credit spread delta risk under paragraph 42, an AI should assign it entirely either to the counterparty credit spread or to the reference credit spread risk class. The AI should not split the instrument between the two risk classes.
76 The capital charge for vega risk is calculated as the simple sum of vega risk capital charges calculated independently for five of the six risk classes as set out in paragraph 74. There is no vega risk capital charge for counterparty credit spread risk.
77 The capital charges for delta and vega risks are calculated in the same manner using the same procedures set out in paragraphs 78 to 84.
78 For each risk class, (i) the sensitivity of the aggregate CVA, 𝑠𝑘𝐶𝑉𝐴, and (ii) the sensitivity of the market value of all eligible hedging instruments in the CVA portfolio, 𝑠𝑘𝐻𝑑𝑔, to each risk factor k in the risk class are calculated. The sensitivities are defined as the ratio of the change in the market value of (i) aggregate CVA or (ii) market value of all CVA hedges caused by a small change of the risk factor’s current value to the size of the change. Specific definitions for each risk class are set out in subsections 12 to 14.
These definitions include specific values of changes or shifts in risk factors. However, an AI may use smaller values of risk factor shifts if doing so is consistent with internal risk management calculations.
79 An AI should calculate CVA sensitivities for vega risk regardless of whether or not the portfolio includes options. When calculating those CVA sensitivities, the AI should apply the volatility shift to both types of volatilities that appear in exposure models:
volatilities used for generating risk factor paths; and
volatilities used for pricing options.
80 If a hedging instrument is an index, an AI should calculate the sensitivities to all risk factors upon which the value of the index depends. The index sensitivity to risk factor k is calculated by applying the shift of risk factor k to all index constituents that depend on this risk factor and recalculating the changed value of the index. For example, to calculate delta sensitivity of the Hang Seng Index to large12 financial companies, an AI should apply the relevant shift to equity prices of all large financial companies that are constituents of the Hang Seng Index and re-compute the index.
81 An AI may choose to introduce a set of additional risk factors that directly correspond to qualified credit and equity indices for the following risk classes:
counterparty credit spread risk;
reference credit spread risk; and
equity risk.
82 For delta risk, a credit or equity index is qualified if it satisfies liquidity and diversification conditions specified in paragraph 132 of CP 19.01; and for vega risks, any credit or equity index is qualified.
83 For a covered transaction or an eligible hedging instrument whose underlying is a qualified index, an AI may replace its contribution to sensitivities to the index constituents with its contribution to a single sensitivity to the underlying index. For example, for a portfolio consisting only of equity derivatives referencing only qualified equity indices, the AI may not need to calculate the CVA sensitivities to non-index equity risk factors. If more than 75% of constituents of a qualified index (taking into account the weightings of the constituents) are mapped to the same sector, the entire index must be mapped to that sector and treated as a single-name sensitivity in that bucket. In all other cases, the sensitivity must be mapped to the applicable index bucket.
12 Please refer to paragraph 130 for the definition of large market capitalisation.
84 For each risk class, an AI should determine the sensitivities 𝑠𝑘𝐶𝑉𝐴 and 𝑠𝑘𝐻𝑑𝑔 to a set of prescribed risk factors, risk-weight those sensitivities, and aggregate the resulting net risk-weighted sensitivities separately for delta and vega risk using the following step-by-step approach.
Step 1: For each risk factor k, the sensitivities 𝑠𝑘𝐶𝑉𝐴 and 𝑠𝑘𝐻𝑑𝑔 are determined as set out in paragraph 78. The weighted sensitivities 𝑊𝑆𝑘𝐶𝑉𝐴 and 𝑊𝑆𝑘𝐻𝑑𝑔 are calculated by multiplying the net sensitivities 𝑠𝑘𝐶𝑉𝐴 and 𝑠𝑘𝐻𝑑𝑔 , respectively, by the corresponding risk weight RWk as set out in subsections 13 and 14.
Step 2: The net weighted sensitivity of the CVA portfolio 𝑊𝑆𝑘 to risk factor k is obtained by13:
𝑊𝑆𝑘= 𝑊𝑆𝑘𝐶𝑉𝐴 − 𝑊𝑆𝑘𝐻𝑑𝑔
Step 3: The net weighted sensitivities should be aggregated into a capital charge Kb
within each bucket b as set out in the formula below:
𝐾𝑏= √(∑ 𝑊𝑆𝑘2+ specified in subsections 13 and 14; and
R is the hedging disallowance parameter, set at 0.01, that prevents the possibility of recognising perfect hedging of CVA risk.
Step 4: Bucket-level capital charges should then be aggregated across buckets within each risk class as set out in the formula below:
𝐾 = 𝑚𝐶𝑉𝐴∙ √∑ 𝐾𝑏2+ ∑ ∑ 𝛾𝑏𝑐∙ 𝑠𝑏∙ 𝑠𝑐
𝑚𝐶𝑉𝐴 is the multiplier as set out in paragraph 43; and
𝑠𝑏 is the sum of the weighted sensitivities WSk for all risk factors k within bucket b, floored by –Kb and capped by Kb, and 𝑠𝑐 is defined in the same way for all risk factors k in bucket c:
𝑆𝑏 = 𝑚𝑎𝑥 {−𝐾𝑏; 𝑚𝑖𝑛 (∑ 𝑊𝑆𝑘; 𝐾𝑏
𝑘∈𝑏
)}
𝑆𝑐 = 𝑚𝑎𝑥 {−𝐾𝑐; 𝑚𝑖𝑛 (∑ 𝑊𝑆𝑘; 𝐾𝑐
𝑘∈𝑐
)}