Chap 24 - Credit Risk and Credit Derivatives Flashcards
In fact, the non–U.S. Treasury fixed-income market is often referred to as the spread product market. This is because all other U.S.-dollar-denominated fixed-income products (e.g., bank loans, high-yield bonds, investment-grade corporate bonds, and emerging markets debt) trade at a credit spread relative to U.S. Treasury securities. Similarly, risky debt denominated in other currencies trades at a credit spread over the bonds of the dominant sovereign issuer in that currency
What is a Structural model ?
Structural models directly relate the valuation of debt securities to the financial characteristics of the economic entity that has issued the credit security. These factors usually include firm-level variables, such as the debt-to-equity ratio and the volatility of asset values or cash flows. The key is that structural credit models describe credit risk in terms of the risks of the underlying assets and the financial structures that have claims to the underlying assets (i.e., degree of leverage).
What is a Reduced-form credit model ?
Reduced-form credit models, in contrast, do not attempt to look at the structural reasons for default risk. Therefore, reduced-form credit models do not rely extensively on asset volatility or underlying structural details, such as the degree of leverage, to analyze credit risk. Instead, reduced-form credit models focus on default
probabilities based on observations of market data of similar-risk securities. In other words, reduced-form approaches typically model the observed relationships among yield spreads, default rates, recovery rates, and frequencies of rating changes throughout the market. The key feature of reduced-form credit models is that credit risk is understood through analysis and observation of market data from similar credit risks rather than through the underlying structural details of the entities, such as the amount of leverage.
What are the 3 factors that can determine an expected credit loss of a credit exposure ?
- Probability of default (PD), which specifies the probability that the counterparty fails to meet its obligations.
- Exposure at default (EAD), which specifies the nominal value of the position that is exposed to default at the time of default.
- Loss given default (LGD), which specifies the economic loss in case of default. The converse of LGD is the economic proceeds given default—that is, the recovery rate (RR). The recovery rate is the percentage of the credit exposure that the lender ultimately receives through the bankruptcy process and all available remedies. Therefore, LGD =(1− RR), and RR =(1−LGD).
THEREFORE: Expected Credit Loss =
PD × EAD × (1 − RR)
A risk-neutral approach to pricing a bond with credit risk: A risk-neutral approach models financial characteristics, such as asset prices, within a framework that assumes that investors are risk neutral. A risk-neutral investor is an investor that requires the same rate of return on all investments, regardless of levels and types of risk because the investor is indifferent with regard to how much risk is borne. Economic theory associates investor risk neutrality with investors whose utility or happiness is a linear function of their wealth.
Although the assumption of risk neutrality by investors is unrealistic, the power of risk-neutral modeling emanates from two key characteristics: (1) the risk-neutral modeling approach provides highly simplified and easily tractable modeling.
(2) in some cases, it can be shown that the prices generated by risk-neutral modeling must be the same as the prices in an economy where investors are risk averse.
When applicable, risk-neutral pricing provides extremely simplified
frameworks to price assets in a risk-averse world.
A risk-neutral probability is a probability-like value that adjusts the statistical probability of default to account for risk premiums. A risk-neutral probability is equal to the statistical probability of default only when investors are risk neutral; it should not be interpreted as the probability of default that would occur if investors were risk averse. Of course, investors are not risk neutral, and they demand a premium for investing in risky investments. To account for the risk premium, risk-neutral probabilities can be used rather than statistical probabilities. Other approaches to risk adjustment include use of higher discount rates and reduction of expected cash flows (the certainty-equivalent approach).
The risk-neutral probability of default is equal to the credit spread divided by the expected loss given default, or (1− RR). In the simple case of a risk-neutral world and a bond with no recovery (RR =0), the credit spread of a bond will equal its annual probability of default!
λ ≈ s / (1 − RR) and s ≈ λ * (1 − RR)
Where λ is a probability of default. It should not be interpreted as predicting an actual probability of default. Rather, λ should be viewed as a modeling tool. The actual probability of default will be less than λ to the extent that investors
demand a risk premium.
How to find it:
Given the bond’s forecasted cash flows, the current value (time 0) of the one-period bond, B(0,1):
B(0, 1) = K / (1 + r) (RR ×λ+ [1 − λ])
We then can also find the same answer with a credit spread ; expresses the current price (time zero) of this debt due in one year, B(0,1), using a credit spread:
B(0, 1) = K / (1 + r + s)
–> The risk premium required to hold a risky bond is expressed through the use of a higher discount rate: the addition of the credit spread, s, to the
riskless rate, r.
Equalizing both formulas gives the first equation ( to find lambda with a credit spread)
Explain : s ≈ λ * (1 − RR)
It indicates that s, the credit spread (the excess of a risky bond’s yield above the riskless yield), is equal to the expected percentage loss of the one-year bond over the remaining year under the assumption of risk neutrality. The expected annual loss is the product of the risk-neutral probability of default (λ) and the proportion of loss given default (1− RR).
What does it mean “to calibrate a model “ ?
To calibrate a model means to establish values for the key parameters in a model, such as a default probability or an asset volatility, typically using an analysis of market prices of highly liquid assets. For example, the volatility of short-term interest rates might be calibrated in a model by using the implied volatility of highly liquid options on short-term bonds.
What are the 2 advantages from using Reduced-form models ?
- They can be calibrated using derivatives such as credit default swap spreads, which are highly liquid.
- They are extremely tractable and are well suited for pricing derivatives and portfolio products. The models can rapidly incorporate credit rating changes and can be used in the absence of balance sheet information (e.g., for sovereign issuers).
What are the 4 disadvantages from using Reduced-form models ?
- There may be limited reliable market data with which to calibrate a model.
- They can be sensitive to assumptions, particularly chose regarding the recovery rate.
- Information on actual historical default rates can be problematic. That is, few observations are available for defaults by major firms or sovereign states.
- Historical default rates on classes of borrowers (e.g., borrowers of a particular ratings class) may have limited value in the prediction of future default rates to the extent that economies undergo major fundamental changes.
What is hazard rate ?
Hazard rate is a term often used in the context of reduced-form models to denote the default rate. The number is usually annualized and may be based on historical analysis of similar bonds or on expectations. Thus, an asset with a hazard rate of 2% is believed to have a 2% actual (i.e., statistical rather than risk-neutral) probability of default on an annual basis.
The primary way that credit derivatives contribute to the economy and its participants is by facilitating risk management in general and diversification
Derivatives are cost-effective vehicles for the transfer of risk, with values driven by an underlying asset. Credit derivatives transfer credit risk from one party to another such that both parties view themselves as having an improved position as a result of
the derivative. Roughly, most credit derivative transactions transfer the risk of default from a buyer of credit protection to a seller of credit protection.
What is Price revelation (price discovery) ?
Price revelation, or price discovery, is the process of observing prices being used or offered by informed buyers and sellers. Prices are the mechanism through which values of resources are communicated in a large economy.
What are the 3 major methods for grouping credit derivatives ?
1- Single-name versus multi-name instruments:
Single-name credit derivatives transfer the credit risk associated with a single entity. Most single-name credit derivatives are credit default swaps (CDSs).
Multi-name instruments, in contrast to single-name instruments, make
payoffs that are contingent on one or more credit events (e.g., defaults)
affecting two or more reference entities. Credit indices are examples of multi-name credit instruments. CDSs on baskets of credit risk offer specified pay-outs based on specified numbers of defaults in the underlying credit risks. In the most common form of a basket CDS, a first-to-default CDS, the protection seller compensates the buyer for losses associated with the first entity in the basket to default, after which the swap terminates and provides no further protection.
2- Unfunded versus funded instruments:
Unfunded credit derivatives involve exchanges of payments that are tied to a notional amount, but the notional amount does not change hands until a default occurs. An unfunded credit derivative is similar to an interest rate swap in which there is no initial
cash purchase of a promise to receive principal but rather an agreement to exchange future cash flows. The most common unfunded credit derivative is the CDS.
Funded credit derivatives require cash outlays and create exposures similar to those gained from traditional investing in corporate bonds through the cash market. Credit-linked notes, are a common type of funded instrument. They can be thought of as a riskless debt instrument with an embedded credit derivative.
3- Sovereign versus nonsovereign entities: The reference entities of credit
derivatives can be sovereign nations or corporate entities. Credit derivatives
on sovereign nations tend to be more complex because their analysis has to
consider not only the possible inability of the entity to meet its obligations
but also the potential unwillingness of the nation to meet its obligations. The
modeling of the credit risk associated with sovereign risk involves political
and macroeconomic risks that are normally not present in modeling corporate credit risk. Finally, the market for credit derivatives on sovereign nations is smaller than the market for other credit derivatives.
Both Smithson and Mengle have observed four stages in the evolution of credit derivatives activity. The first, or defensive, stage, which started in the late 1980s and ended in the early 1990s, was characterized by ad hoc attempts by banks to lay off some of their credit exposures. The second stage, which began about 1991 and lasted through the mid- to late 1990s, was the emergence of an intermediated market in which dealers applied derivatives technology to the transfer of credit risk, and investors entered the market to seek exposure to credit risk. Further, in 1999, the International Swaps and Derivatives Association (ISDA) issued a set of standard definitions for credit derivatives to be used in connection with the ISDA master agreement, as discussed in more detail later in the chapter. Finally, dealers began
warehousing risks and running hedged and diversified portfolios of credit derivatives. During this stage, the market encountered a series of challenges, ranging from credit events associated with restructuring to renegotiation of emerging market debts. The fourth stage centered on the development of a liquid market. With new ISDA credit derivative definitions in place in 2003, dealers began to trade according to standardized practices (e.g., standard settlement dates) that went beyond those adopted for other over-the-counter (OTC) derivatives.
What is a plain vanilla interest rate swap ?
In a plain vanilla interest rate swap, party A agrees to pay party B cash flows based on a fixed interest rate in exchange for receiving from B cash flows in accordance with a specified floating interest rate. Both payments are based on a notional principal and
a specified number of years, which typically range from two to 15 years.
In a plain vanilla interest rate swap, who is the payer and the reciever ?
The payer in a vanilla swap is the party that agrees to pay a fixed rate in exchange for receiving a floating rate. The receiver (i.e., the buyer of the fixed rate) is the party that agrees to pay a floating rate in exchange for receiving a fixed rate.
Credit risk and interest rate risk interact in fine ways. These interactions can be
examined by estimating the MTM value of swaps for a range of term-structure scenarios and credit-risk assumptions. These estimations can be performed using Monte Carlo simulation or other techniques.
Ferrara and Ali (2013) simulate many forward yield curves (using an arbitrage-free interest rate model), and evaluate the potential exposure of vanilla interest rate swaps under the most familiar yield curve shapes and under different volatility assumptions. The authors highlight that unanticipated changing interest rates can, on one hand, create substantial mark-to-market (MTM) or counterparty exposure, which may cause significant MTM losses and require substantial collateral posting. On the other hand, they also find that unanticipated changing interest rates can generate considerable MTM gains, which can lead to counterparty exposure if the swap contract is not collateralized.
What are the two key assumptions under which the traditional approach to pricing and valuing standard interest rate swaps is based ?
LIBOR discount factors are :
(1) reasonable proxies for the credit quality of the counterparty when the contract is uncollateralized.
(2) suitable measures for the risk-free term structure when the contract is collateralized.
What is a credit default swap (CDS) ?
A credit default swap (CDS) is an insurance-like bilateral contract in which the buyer pays a periodic fee (analogous to an insurance premium) to the seller in exchange for a contingent payment from the seller if a credit event occurs with respect to an underlying credit-risky asset. A CDS may be negotiated on any of a variety of credit-risky investments, primarily corporate bonds.
In a CDS, the credit protection buyer pays a periodic premium on a predetermined amount (the notional amount) in exchange for a contingent payment from the credit protection seller if a specified credit event occurs. The credit protection seller receives a periodic premium in exchange for delivering a contingent payment to the credit protection buyer if a specified credit event occurs.
How does a Total return swap works ?
Total return swap, the credit protection buyer, typically the owner of the credit
risky asset, passes on the total return of the asset to the credit protection seller in return for a certain payment. Thus, the credit protection buyer gives up the uncertain returns of the credit-risky asset in return for a certain payment from the credit protection seller. The credit protection seller now receives both the upside and the downside of the return associated with the credit-risky asset. The credit protection seller takes on all of the economic risk of the underlying asset, just as if that asset were on the balance sheet or in the investment portfolio.
