### 金融代写|量化风险管理代写Quantitative Risk Management代考| Market Risk

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|量化风险管理代写Quantitative Risk Management代考|The Fundamental Review of the Trading Book

The fundamental review of the trading book or FRTB regulations (BCBS 2014) is a response to a pre-crisis framework that has been deemed inadequate and weak in many areas. This is particularly true for the definition of the boundary of the trading book. Indeed, internal model approach was not sufficient and many issues were to be dealt with for a better regulatory capital framework.

For instance, tail risk was something that the VaR approach did not capture adequately along with illiquidity. Most IMA-based approaches also allow for generous diversification effects as they are based on historic parameters which definitely do not hold in a crisis situation (correlation largely become relevant in very stressed markets).

The current standardised approach is highly inadequate as the linkage between the internal model and the standardised approach is inappropriate. Besides, the current standardised approach lacks risk sensitivity. This issue needs to be dealt with along with constraining the diversification benefits and hedging.

The FRTB addresses the boundary issue between the banking and the trading book in order to reduce regulatory arbitrage between the two books limiting the will to transfer from one book to the other and introducing reporting guidelines and regulatory oversight that should allow for a much better framework that governs the boundary between the two books.

The FRTB also aims at capturing the effect of tail risk more effectively as well as capturing liquidity effects. Tail risk is captured moving from a VaR to an expected shortfall approach for various horizon depending on asset/risk classes.

Under FRTB internal models have to be approved at the desk level. If desks are not approved, these will be moved back to the standardised approach. Trading desks will have to show that their models are compliant by showing that they have adequate $P \& L$ attribution and backtesting procedures in place. It is important to note that $P \& L$ attribution (i.e. model-based $P \& L$ by opposition to risk-based theoretical $\mathrm{P} \& \mathrm{~L}$ ) will be under scrutiny to ensure that risk models properly capture the risk associated with the models themselves. Besides, hedging and diversification benefits will be constrained and an additional charge will come to cover non-modellable risk factors.

The revised standardised approach (RSA) will be considered for banks willing to use simple approaches. This approach will also be the fallback for banks not gaining approval for there internal models. The main methodological modification is that the approach is now based on risk sensitivities across asset classes. The RSA aims at providing a consistent way to measure risks across geographic areas, giving authorities a better way to compare IMA and SA banks as the two approaches are sharing a common framework. Furthermore, a standardised default risk charge will be added along an add-on for residual risk, clearly harder to model. Therefore, following the FRTB and from a capital calculations standpoint, two possibilities are offered to banks to perform them. These are presented in the following.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Standardised Approach

As presented in the standardised approach capital requirement (BCBS 2016a) is the simple sum of three components: the risk charges under the sensitivities-based method, the default risk charge, and the residual risk add-on.

The risk charge under the sensitivities-based method must be calculated by aggregating the following risk measures:

• Delta: A risk measure based on sensitivities of a bank’s trading book to regulatory delta risk factors. Delta sensitivities are to be used as inputs into the aggregation formula which delivers the capital requirement for the sensitivities-based method.
• Vega: A risk measure that is also based on sensitivities to regulatory vega risk factors to be used as inputs to a similar aggregation formula as for delta risks.
• Curvature: A risk measure which captures the incremental risk not captured by the delta risk of price changes in the value of an option. Curvature risk is based on two stress scenarii involving an upward shock and a downward shock to a given risk factor. The worst loss of the two scenarii is the risk position to be used as an input into the aggregation formula which delivers the capital charge.

In order to address the risk that correlations may increase or decrease in periods of financial stress, three risk charge figures must be calculated for each risk class defined under the sensitivities-based method, based on three different scenarios on the specified values for the correlation parameter $\rho_{k l}$ (i.e. correlation between risk factors within a bucket) and $\gamma_{b c}$ (i.e. correlation across buckets within a risk class). There must be no diversification benefit recognised between individual risk classes. We refer to BCBS (2016a) for more details on the parameters.

The bank must determine each delta and vega sensitivity and curvature scenario based on instrument prices or pricing models that an independent risk control unit within a bank uses to report market risks or actual profits and losses to senior management.

The default risk charge captures the jump-to -default risk in three independent capital charge computations for default risk of non-securitisations, securitisations (non-correlation trading portfolio), and securitisation correlation trading portfolio. It is calibrated based on the credit risk treatment in the banking book in order to reduce the potential discrepancy in capital requirements for similar risk exposures across the bank. Some hedging recognition is allowed within a risk weight bucket. There must be no diversification benefit recognised between different buckets.
Additionally, the Committee acknowledges that not all market risks can be captured in the standardised approach, as this might necessitate an unduly complex regime. A residual risk add-on is thus introduced to ensure sufficient coverage of market risks.

Supervisory authorities will be able to insist on a period of initial monitoring and live testing of a bank’s internal model before it is used for supervisory capital purposes. In addition to these general criteria, banks using internal models for capital purposes will be subject to the additional requirements detailed below.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Internal Models Approach

The use of an internal model for the purposes of regulatory capital determination will be conditional upon the explicit approval of the bank’s supervisory authority. Home and host country supervisory authorities of banks that carry out material trading activities in multiple jurisdictions intend to work cooperatively to ensure an efficient approval process.

1. It is satisfied that the bank’s risk management system is conceptually sound and is implemented with integrity;
2. The bank has, in the supervisory authority’s view, sufficient numbers of staff skilled in the use of sophisticated models not only in the trading area but also in the risk control, audit and, if necessary, back office areas;
3. The bank’s models have, in the supervisory authority’s judgement, a proven track record of reasonable accuracy in measuring risk;
4. The bank regularly conducts stress tests along the lines discussed in BCBS (2016a); and
5. The positions included in the internal model for regulatory capital determination are held in approved trading desks that have passed the required tests.

From a quantitative standpoint, the document states the following: Banks will have flexibility in devising the precise nature of their models, but the following minimum standards will apply for the purpose of calculating their capital charge. Individual banks or their supervisory authorities will have discretion to apply stricter standards. “Expected shortfall” must be computed on a daily basis for the bankwide internal model for regulatory capital purposes. Expected shortfall must also be computed on a daily basis for each trading desk that a bank wishes to include within the scope for the internal model for regulatory capital purposes.

In calculating the expected shortfall, a $97.5$ th percentile, one-tailed confidence level is to be used. In calculating the expected shortfall, the liquidity horizons described in BCBS (2016a) (see Table 2.2) must be reflected by scaling an expected shortfall calculated on a base horizon. The expected shortfall for a liquidity horizon must be calculated from an expected shortfall at a base liquidity horizon of 10 days with scaling applied to this base horizon result as follows:
$$E S=\sqrt{\left(E S_{T}(P)\right)^{2}+\sum_{j \leq 2}\left(E S_{T}(P, j) \sqrt{\frac{\left(L H_{j}-L H_{j-1}\right)}{T}}\right)^{2}}$$
where,

• $E S$ is the regulatory liquidity-adjusted expected shortfall;
• $T$ is the length of the base horizon, i.e., 10 days;

## 金融代写|量化风险管理代写Quantitative Risk Management代考|The Fundamental Review of the Trading Book

FRTB 解决了银行业务和交易账簿之间的边界问题，以减少两账簿之间的监管套利，限制从一账簿转移到另一账簿的意愿，并引入报告指南和监管监督，以建立一个更好的框架，支配着两本书之间的界限。

FRTB 还旨在更有效地捕捉尾部风险的影响以及捕捉流动性效应。尾部风险是根据资产/风险类别从 VaR 转移到不同期限的预期缺口方法来捕获的。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Standardised Approach

• Delta：基于银行交易账户对监管 delta 风险因素的敏感性的风险度量。Delta 敏感度将用作聚合公式的输入，该公式为基于敏感度的方法提供资本要求。
• Vega：一种风险度量，也基于对监管 vega 风险因素的敏感性，用作与 delta 风险类似的聚合公式的输入。
• 曲率：一种风险度量，它捕捉期权价值的价格变化的增量风险未捕捉到的增量风险。曲率风险基于两种压力情景，包括对给定风险因素的向上冲击和向下冲击。这两种情况中最严重的损失是风险头寸被用作提供资本费用的聚合公式的输入。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Internal Models Approach

1. 对本行风险管理体系概念健全、执行健全的情况感到满意；
2. 监管机构认为，银行拥有足够数量的员工，他们不仅在交易领域，而且在风险控制、审计以及必要时的后台办公领域，都能够熟练使用复杂的模型；
3. 根据监管机构的判断，银行的模型在衡量风险方面具有合理准确的可靠记录；
4. 银行按照 BCBS (2016a) 中讨论的思路定期进行压力测试；和
5. 包含在监管资本确定内部模型中的头寸在已通过所需测试的经批准的交易平台中持有。

• 和小号是监管流动性调整后的预期缺口；
• 吨是基准层的长度，即10天；

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