金融代写|量化风险管理代写Quantitative Risk Management代考|Internal Ratings-Based Approach

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• 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|Internal Ratings-Based Approach

Both foundation internal ratings-based approach (FIRB) and advanced internal ratings-based approach (AIRB) refer to sets of credit risk measurement approaches under Basel II/III capital assessment rules for banks underpinning the fact that these are allowed to develop their own empirical model to evaluate the required capital to cover credit risk exposure. The financial institutions considered are only allowed to use this approach following a thorough review and the approval from the adequate regulatory and/or supervisory authority.

FIRB banks are allowed to develop their own model to estimate the probability of default (PD) for individual clients or groups of clients while other parameters are provided by the regulators. FIRB banks are required to use regulator’s prescribed loss given default (LGD) and other parameters required for calculating the riskweighted asset (RWA) for non-retail portfolios while for retail exposures banks are required to use their own IRB parameters, for instance, the probability of default, the loss given default, and the credit conversion factor. Then total required capital is calculated as a fixed percentage of the estimated RWA. Banks can use this approach after they received an approval from their local regulators.

AIRB banks are entitled to use their own quantitative models to estimate the PD, the exposure at default (EAD), the LGD as well as any other parameter required for calculating the RWA. The regulatory capital is then calculated as a fixed percentage of the estimated RWA. Credit risk being an element of core banking it follows, that banks are expected to be capable of adopting more sophisticated techniques in credit risk measurement and management.

The credit valuation adjustment (CVA) (BCBS 2015; Gregory 2012) is the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA is the market value of counterparty credit risk. This price depends on counterparty credit spreads as well as on the market-risk factors that drive derivatives’ values and, therefore, exposure. CVA belongs to the family of related valuation adjustments, collectively

known as XVA for $X$-value adjustment. Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation can be written as
$$\mathrm{CVA}(\mathrm{T})=E^{Q}\left[L^{*}\right]=(1-R) \int_{0}^{T} E^{Q}\left[\frac{B_{0}}{B_{t}} E(t) \mid \tau=t\right] d \operatorname{PD}(0, t)$$
where $T$ is the maturity of the longest transaction in the portfolio, $B_{t}$ is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity $t, R$ is the fraction of the portfolio value that can be recovered in case of a default, $\tau$ is the time of default, $E(t)$ is the exposure at time $t$, and $\operatorname{PD}(s, t)$ is the risk-neutral probability of counterparty default between times $s$ and $t$. These probabilities can be obtained from the term structure of credit default swap (CDS) spreads. More generally CVA can refer to a few different concepts:

• The mathematical concept as defined above;
• 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 with it, i.e., the bank has to buy the hedging instrument. This cost is then allocated to each business line of an investment bank. This allocated cost is called the “CVA Charge”.

Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to
$$\mathrm{CVA}=(1-R) \int_{0}^{T} \mathrm{EE}^{}(t) d \mathrm{PD}(0, t)$$ where $\mathrm{EE}^{}$ is the risk-neutral discounted expected exposure (EE)

金融代写|量化风险管理代写Quantitative Risk Management代考|Basic Indicator Approach

Operational risk capital allocation is done using a single indicator: the gross income. The allocation is a fixed percentage (denoted $\alpha$ in what follows) multiplied by its individual amount of gross income. This approach is easy to implement and universally applicable. Nevertheless its simplicity limits responsiveness to firmspecific needs and characteristics. While the basic indicator approach might be suitable for smaller banks with a simple range of business activities, the Basel Committee expects internationally active banks and banks with significant operational risk to use a more sophisticated approach within the overall framework. The Basel Committee provides incentives to move towards more sophisticated approaches: they actually proposed to set $\alpha$ at a higher level, to use the second pillar or to make the standardised approach the entry point for internationally active banks. It is also worth noticing that a sample of internationally active banks has formed the basis of this calibration. As it is anticipated that the basic indicator approach will mainly be used by smaller, domestic banks, a wider sample base may be more appropriate. Formally, the capital allocation (CA) is given by,
$$C A=\alpha \times G I$$
where, GI represents the gross income.

金融代写|量化风险管理代写Quantitative Risk Management代考|Internal Ratings-Based Approach

FIRB 银行可以开发自己的模型来估计个别客户或客户群体的违约概率 (PD)，而其他参数由监管机构提供。FIRB 银行必须使用监管机构规定的违约损失 (LGD) 和其他参数来计算非零售投资组合的风险加权资产 (RWA)，而对于零售风险敞口，银行则需要使用自己的 IRB 参数，例如概率违约损失、违约损失和信用转换因子。然后将所需资本总额计算为估计 RWA 的固定百分比。银行在获得当地监管机构的批准后可以使用这种方法。

AIRB 银行有权使用自己的量化模型来估计 PD、违约风险敞口 (EAD)、LGD 以及计算 RWA 所需的任何其他参数。然后将监管资本计算为估计 RWA 的固定百分比。信用风险是核心银行业务的一个要素，因此银行有望在信用风险计量和管理中采用更复杂的技术。

C在一个(吨)=和问[大号∗]=(1−R)∫0吨和问[乙0乙吨和(吨)∣τ=吨]dPD⁡(0,吨)

• 上述定义的数学概念；
• 巴塞尔协议 3 下引入的监管资本和 RWA（风险加权资产）计算的一部分；
• 投资银行的 CVA 服务台，其目的是：
• 对冲交易对手违约可能造成的损失；
• 对冲以减少根据巴塞尔协议 3 计算 CVA 所需的资本金额；
• “CVA 费用”。CVA 柜台的套期保值有与之相关的成本，即银行必须购买套期保值工具。然后将此成本分配给投资银行的每个业务线。这种分配的成本称为“CVA 费用”。

C在一个=(1−R)∫0吨和和(吨)d磷D(0,吨)在哪里和和是风险中性贴现预期敞口 (EE)

C一个=一个×G我

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