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Fixed Income

Risk Management

Risk management is a process to identify and measure risk. The goal of risk management solution is to ensure that risk is under limit and there is no surprise in future. In capital markets, risk management is accountable for oversighting and monitoring the profit and loss, market risk, credit risk, liquidity risk and valuation risk activities of a firm.

1. Counterparty Credit Risk

Counterparty credit risk (CCR) refers to the risk that a counterparty to a bilateral financial derivative contract may fail to fulfill its contractual obligation causing financial loss to the non-defaulting party. It will be incurred in the event of default by a counterparty.

If one party of a contract defaults, the non-defaulting party will find a similar contract with another counterparty in the market to replace the default one. That is why counterparty credit risk sometimes is referred to as replacement risk.

Only over-the-counter (OTC) derivatives and financial security transactions (e.g., repo) are subject to counterparty risk. If one party of a contract defaults, the non-defaulting party will find a similar contract with another counterparty in the market to replace the default one. That is why counterparty credit risk sometimes is referred as replacement risk. The replacement risk is the MTM value of a counterparty portfolio at the time of the counterparty default.

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2. Counterparty Credit Risk Simulation Methodology

Counterparty credit risk (CCR) is the risk of loss that will be incurred in the event of default by a counterparty. It will be incurred in the event of default by a counterparty. Only over-the-counter (OTC) derivatives and financial security transactions (e.g., repo) are subject to counterparty risk. If one party of a contract defaults, the non-defaulting party will find a similar contract with another counterparty in the market to replace the default one. That is why counterparty credit risk sometimes is referred as replacement risk. The replacement risk is the MTM value of a counterparty portfolio at the time of the counterparty default.

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3. Collateral Management

Collateral is a property or an asset that a borrower offers as a way for a lender to secure the loan. Collateral arrangement is a risk reduction tool that mitigates risk by reducing credit exposure. Collateral doesn’t turn a bad counterparty into a good one and doesn’t eliminate credit risk. Instead, it just reduces the loss at the time of default. Collateral arrangement is an essential element in the plumbing of the financial system.

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4. Credit Valuation Adjustment

Credit valuation adjustment (CVA) is the market price of counterparty credit risk that has become a central part of counterparty credit risk management. By definition, CVA is the difference between the risk-free portfolio value and the true/risky portfolio value. In practice, CVA should be computed at portfolio level. That means calculation should take Master agreement and CSA agreement into account.

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5. Funding Valuation Adjustment

Funding Valuation Adjustment (FVA) is introduced to capture the incremental costs of funding uncollateralized derivatives. It can be referred to as the difference between the rate paid for the collateral to the bank’s treasury and rate paid by the clearinghouse. Also FVA can be thought of as a hedging cost or benefit arising from the mismatch between an uncollateralized client trade and a collateralized hedge in the interdealer market. FVA should be also calculated at portfolio level.

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6. Fundamental Review of the Trading Book

The Fundamental Review of the Trading Book (FRTB) is a new Basel committee framework for the next generation market risk regulatory capital rules. It is inspired by the undercapitalisation of trading book exposures witnessed during the financial crisis. FRTB aims to address shortcoming of the current Basel 2.5 market risk capital framework.

FRTB provides a clear definition of the boundary between the trading book and the banking book. It consists of an overhaul of the internal model approach (IMA) to focus on tail risk and an overhaul of the standardized approach (SA) to make it more risk sensitive. Each approach also explicitly captures default risk and other residual risks. Liquidity risk is explicitly included for different asset classes via liquidity horizons. This presentation provides an overview of the standardised approach.

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7. Historical VaR

Value at Risk (VaR) is the regulatory measurement for assessing market risk. It reports the maximum likely loss on a portfolio for a given probability defined as x% confidence level over N days. VaR is vital in market risk management and control. Also regulatory and economic capital computation is based on VaR results. Although VaR measure is objective and intuitive, it doesn’t capture tail risk. There are three commonly used methodologies to calculate VaR – parametric, historical simulation and Monte Carlo simulation. This section focuses on historical VaR.

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8. Standard Initial Margin Model

Initial Margin (IM) is the amount of collateral required to open a position with a broker or an exchange or a bank. The Standard Initial Margin Model (SIMM) is very likely to become the market standard. It is designed to provide a common methodology for calculating initial margin for uncleared OTC derivatives. Initial margin calculation is counterparty-portfolio-based. Given this standardized approach, counterparties can easily reconcile the results.

Initial margin calculation is counterparty-portfolio-based. It applies to non-cleared OTC derivatives only. Derivative trades belonging to a counterparty will be divided into cleared-trade portfolio and non-cleared-trade portfolio. The initial margin is computed for the non-cleared portfolio. This presentation provides many practical details of the SIMM.

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9. Incremental Risk Charge

The incremental risk charge (IRC) is a regulatory requirement from the Basel Committee in response to the financial crisis. It supplements existing Value-at-Risk (VaR) and captures the loss due to default and migration events at a 99.9% confidence level over a one-year capital horizon.

The liquidity of a position is explicitly modeled in IRC through liquidity horizon and constant level of risk. The constant level of risk is a new concept in IRC. It assumes banks hold portfolio constant over a liquidity horizon. At the beginning of the next horizon, they rebalance any default, downgraded, or upgraded positions and roll over any matured trades. This presentation describes methodology and implementation details of IRC.

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10. Financial Market

A financial market is a market where people trade financial products. Typical financial markets are the fixed income and interest rate market, the currency market, the equity market, the commodity market and the credit market.

One of the central tenets of financial economics is the necessity of some tradeoff between risk and expected return. This presentation gives an overview of financial market basics

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11. Market Risk Economic Capital

Financial business is exposed to many types of risks due to the nature of business. To guard against the risk, financial institutions must hold capital in proportion to the potential risk. Market risk economic capital is intended to capture the value change due to changes in market risk factors. It is an internal capital reserve to cover unexpected loss due to market movement.

Economic capital falls into the category of Value at Risk (VaR) measures as both try to capture value change due to market movement. Most institutions use the existing VaR system to compute economic capital. VaR captures the market risk of 1-day time period at 99% confidence level whereas Economic capital measures the market risk of 1-year time period at 99.95 confidence level. Therefore, scaling methodology is the key to compute economic capital, i.e., scaling 1-day to 1-year and 99% to 99.95%. This presentation is intended to answer several fundamental economic capital questions: what is economic capital? What is the difference between economic capital and regulatory capital? How to compute economic capital?

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12. Parametric VaR

Value at Risk (VaR) is the regulatory measurement for assessing market risk. It reports the maximum likely loss on a portfolio for a given probability defined as x% confidence level over N days. VaR is vital in market risk management and control. Also regulatory and economic capital computation is based on VaR results. Although VaR measure is objective and intuitive, it doesn’t capture tail risk. There are three commonly used methodologies to calculate VaR – parametric, historical simulation and Monte Carlo simulation. This section focuses on parametric VaR.

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13. Risk Sensitivity

Risk sensitivities, also referred to as Greeks, are the measure of a financial instrument’s value reaction to changes in underlying factors. The value of a financial instrument is impacted by many factors, such as interest rate, stock price, implied volatility, time, etc. Sensitivities are risk measures that are more important than fair values.

Risk sensitivities or Greeks are vital for risk management. They can help financial market participants isolating risk, hedging risk and explaining profit & loss. This presentation gives certain practical insights onto this topic.

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14. Monte Carlo VaR

Value at Risk (VaR) is the regulatory measurement for assessing market risk. It reports the maximum likely loss on a portfolio for a given probability defined as x% confidence level over N days. VaR is vital in market risk management and control. Also regulatory and economic capital computation is based on VaR results. Although VaR measure is objective and intuitive, it doesn’t capture tail risk. There are three commonly used methodologies to calculate VaR – parametric, historical simulation and Monte Carlo simulation. This section focuses on Monte Carlo VaR.

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15. Collateralized Derivatives

This paper presents a new model for pricing OTC derivatives subject to collateralization. It allows for collateral posting adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives. Using a unique dataset, we find empirical evidence that credit risk alone is not overly important in determining credit-related spreads. Only accounting for both collateral arrangement and credit risk can sufficiently explain unsecured credit costs. This finding suggests that failure to properly account for collateralization may result in significant mispricing of derivatives. We also empirically gauge the impact of collateral agreements on risk measurements. Our findings indicate that there are important interactions between market and credit risk.

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16. CVA and Wrong Way Risk

This paper presents a Least Square Monte Carlo approach for accurately calculating credit value adjustment (CVA). In contrast to previous studies, the model relies on the probability distribution of a default time/jump rather than the default time itself, as the default time is usually inaccessible. As such, the model can achieve a high order of accuracy with a relatively easy implementation. We find that the valuation of a defaultable derivative is normally determined via backward induction when their payoffs could be positive or negative. Moreover, the model can naturally capture wrong or right way risk.

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17. Convertible Bond

This paper presents a new model for valuing hybrid defaultable financial instruments, such as, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price.

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18. LIBOR Market Model

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround.

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19. Jump-Diffusion Model

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price.

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20. Collateralization

This paper attempts to assess the economic significance and implications of collateralization in different financial markets, which is essentially a matter of theoretical justification and empirical verification. We present a comprehensive theoretical framework that allows for collateralization adhering to bankruptcy laws. As such, the model can back out differences in asset prices due to collateralized counterparty risk. This framework is very useful for pricing outstanding defaultable financial contracts. By using a unique data set, we are able to achieve a clean decomposition of prices into their credit risk factors. We find empirical evidence that counterparty risk is not overly important in credit-related spreads. Only the joint effects of collateralization and credit risk can sufficiently explain unsecured credit costs. This finding suggests that failure to properly account for collateralization may result in significant mispricing of financial contracts. We also analyze the difference between cleared and OTC markets.

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21. Default Dependency

This article presents a comprehensive framework for valuing financial instruments subject to credit risk. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats in financial markets. We analyze how swap rates are affected by bilateral counterparty credit risk, and how CDS spreads depend on the trilateral credit risk of the buyer, seller, and reference entity in a contract. Moreover, we study the effect of collateralization on valuation, since the majority of OTC derivatives are collateralized. The model shows that a fully collateralized swap is risk-free, whereas a fully collateralized CDS is not equivalent to a risk-free one.

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22. IRC Calculation

The incremental risk charge (IRC) is a new regulatory requirement from the Basel Committee in response to the recent financial crisis. Notably few models for IRC have been developed in the literature. This paper proposes a methodology consisting of two Monte Carlo simulations. The first Monte Carlo simulation simulates default, migration, and concentration in an integrated way. Combining with full re-valuation, the loss distribution at the first liquidity horizon for a subportfolio can be generated. The second Monte Carlo simulation is the random draws based on the constant level of risk assumption. It convolutes the copies of the single loss distribution to produce one year loss distribution. The aggregation of different subportfolios with different liquidity horizons is addressed. Moreover, the methodology for equity is also included, even though it is optional in IRC.

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23. Multilateral Credit Risk

This article presents a new model for valuing financial contracts subject to credit risk and collateralization. Examples include the valuation of a credit default swap (CDS) contract that is affected by the trilateral credit risk of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.

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24. Bilateral Credit Risk

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

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25. Defaultable Swap

This paper presents an analytical model for valuing interest rate swaps, subject to bilateral counterparty credit risk. The counterparty defaults are modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

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26. Defaultable CDS

This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.

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27. Defaultable Derivatives

This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the literature, we emphasize that the market value of a defaultable derivative is actually a risky value rather than a risk-free value. Credit value adjustment (CVA) is also elaborated. A practical framework is developed for pricing defaultable derivatives and calculating their CVAs at a portfolio level.

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References:

https://finpricing.com/FinPricing-ProductBrochure.pdf