Overview Overview

Overview Overview

Decentralized derivatives product Opium has launched the first credit default swap (CDS) product built on DeFi. This feature was first used by DeversiFi with a 20 BTC credit line, allowing efficient trading of credit risk on Aave entrusted loans. Specifically, the CDS seller needs to lock up collateral as a guarantee for the CDS buyer, and the buyer pays the seller an advance payment. The buyer can use it to cover potential losses on the actual loan.

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credit default swap

credit default swap

In short, a CDS is used to transfer the credit risk of a reference entity (corporate or sovereign) from one party to another. In a standard CDS contract, one party purchases credit insurance from the other party to cover the loss of the face value of the asset following a credit event. Credit events are legally defined events that typically include bankruptcies, defaults and restructurings. This insurance continues until a specific maturity date. To pay for this insurance, the insurance buyer makes periodic payments to the insurance seller, called a premium leg. The amount of these premium payments is calculated based on a quoted default swap spread, which is paid against the face value of the insurance. These payments are until a credit event occurs or are due, whichever occurs first.

Figure 1: premium legs

If the credit event does occur before the contract's due date, the insurance seller will make a payment called the protection leg. The payment is equal to the difference between the face value of the reference entity's fair value delivery asset (CTD) and compensates the insurance buyer for losses. It can be in the form of cash or physical settlement.

Figure 2: protection leg

For example:

• Suppose an insurance buyer buys a company's 5-year policy at a default swap spread of 300 basis points. The face value of the policy is $10 million. Therefore, the insurance buyer pays approximately $10 million x 0.03 x 0.25 = $75,000 per quarter. Assume that after a period of time, the reference entity encounters a credit event, and the recovery price of the reference entity's CTD assets is $45 per $100 face value. The payment status is as follows:

• The insurance seller indemnifies the insurance buyer for the loss of face value of the asset received by the insurance buyer. This equals $10 million times (100% - 45%) = $5.5 million.

The insurance buyer pays the premium accrued from the date of the previous premium payment to the time of the credit event. For example, if the credit event occurs one month later, the insurance buyer pays approximately $10 million × 0.03 × 1/12 = $18,750. Note that this is the standard for corporate reference entity linked default swaps. For sovereign-linked default swaps, premiums that have accrued may not be payable.

mark-to-market valuation

Unlike bonds, the gain or loss on a CDS position cannot simply be calculated as the current market quote plus the difference between the coupon received and the purchase price. To value CDS, we need to use the term structure of default swap spreads, call rate assumptions and models.

To see this, consider an investor who initially buys 5 years of insurance on a company at a default swap spread of 60 basis points, and then wishes to value the position a year later. On that day, the 4-year credit default swap spread quoted in the market was 170 basis points. The current position is:

Mark to Market (MTM) = current market value of the remaining 4 years of coverage - expected present value of 60 basis points over the 4-year premium period

The investor holds a CDS contract that has increased in value because he only paid 60 basis points, while the market is now willing to pay 170 basis points. Since the new default swap has a market value of zero, this means:

Current market value of remaining 4 years of coverage = 170 basis points present value of expected premium period

Using this, we can write that the market price to the buyer of insurance is:

MTM = Expected Present Value of 170 bps over 4 years - Expected Present Value of 60 bps over four years

MTM = 170bp×RPV01 - 60bp×RPV01 = 110bp×RPV01

If we define risk PV01 (RPV01) as the expected present value of 1 basis point paid in the premium phase before default or maturity, then we can rewrite MTM as

Therefore we need to calculate RPV01. RPV01 is called "risky" because it is the expected present value of an uncertain premium flow. The uncertainty is due to the termination of premium payments in the event of a credit event.

• To realize this mark-to-market gain or loss, investors have two options:

• Close the position with the original counterparty (or reallocate it to another counterparty) at the cash close value. The cash closeout value should be equal to the MTM of the position.

As shown, entering the hedged position, the investor sells insurance against the same reference entity for 170 basis points over the next four years.

This creates positive premium income of 170 - 60 = 110bp per annum until a credit event or maturity, whichever occurs earlier. In the event of a credit event, the investor has no major risk, because the defaulted bond delivered by one party can be delivered to the purchased insurance, and although the investor has no principal risk, there is still premium risk. The risk is that the reference entity does not survive to the contractual expiry date and receive annual revenue of 110 bps for four years. These cash flows are risky and that risk has to be accounted for by RPV01, which is basically discounted cash flows above LIBOR.

Both options have the same economic value today. However, they are fundamentally different.

If (i) the profit or loss is realized immediately, the position is terminated. If (ii) the gain or loss is realized only over the remaining term of the swap and the investor bears the risk of a credit event occurring, the realized gain or loss is less than what they would have realized had they closed out the position in cash amounts. On the other hand, if no credit event occurs and the NIM yield is positive, they will earn more than the value of the cash closeout.

Figure 3: Cash Flow Model

The present value of the position initially traded at the contract spread S(t0, tN) at time t0, the maturity date tN, and the present value of the position traded at the valuation time tV with the spread S(tV, tN) is as follows:

Among them, the positive sign is used for long insurance positions, and the negative sign is used for short insurance positions. RPV01(tV,tN), also known as risk PV01, is the present value at time tV of a 1bp premium flow that terminates at tN maturity or default. This is the same as the formula derived above, showing that the investor chooses (i) and (ii) with equal value.

Calculating the risk PV01 requires a model because we need to account for the risk per premium payment by calculating the probability of the reference entity surviving to each premium payment date. The survival probability used in evaluating PV01 at risk must be an arbitrage-free survival probability. These are the survival probabilities implied by the market default swap spread. Therefore, an evaluation model is required for calculation.

• First, it must meet the following conditions:

• Correctly characterize the default risk of the reference entity;

• Correctly simulates the percentage of redemption value and face value paid;

• time to be able to simulate a default;

• Flexibility to adjust the term structure of quoted default swap spreads;

as simple as possible

formal modeling

Credit modeling falls into two main approaches, one called structural models and the other called reduced forms. In the structured approach, the idea is to describe a default as a consequence of certain events in the company, such as the insufficient value of its assets to pay its debts. Structural models are often used to illustrate at what spreads a corporate bond should trade based on the company's internal structure. As such, they require information on corporate balance sheets that can be used to establish a link between stock and bond market pricing.

However, the models are limited in at least three important respects: they are difficult to calibrate since internal firm data are published only up to four times a year; second, the models often lack the flexibility to fully fit a given spread term structure; and, The model is also not easily generalizable to pricing credit derivatives.

In a simplified form, the credit event process is directly modeled by modeling the probability of the credit event itself. Using a security pricing model based on this approach, the probability of default can be extracted from the market price. Simplified models also typically have the flexibility to re-price various credit instruments for different maturities. They can also be extended to price more exotic credit derivatives. It is for these reasons that they are used to price credit derivatives.

The most widely used simplified form approach is to describe a credit event as the first event of a Poisson counting process that occurs at a certain moment with a defined reducible probability, as follows:

We can think of default modeling in the single-period setting as a simple binary tree in which we survive with probability 1-fit(t)dt or the default, and receive a recovery value R, recovery Probability of value for fitted(t)dt.

We assume that the hazard rate process is deterministic. By extension, this assumption also implies that the risk rate is independent of the interest rate and recovery rate. At the end of this article, we discuss the validity of this assumption in the context of pricing. What we are saying now is that these assumptions are acceptable to almost all market participants because their pricing impact is well within the typical bid-ask spread for credit default swaps (cds).

Figure 4: Example of a binary tree model

We can extend this model to multiple time periods, as shown in Figure 4, where K is the payoff upon default. By considering the limit dt→0, we can calculate the probability of continuous survival up to time tV. It can be shown that the survival probability is:

The premium stage is a series of payment behaviors when the default swap spread expires or when a credit event occurs, whichever occurs first. It also includes premiums accrued from the date of the previous premium payment to the time of the credit event. Suppose there are n=1...N contract payment dates, where tN is the maturity date of the default swap. Using S(t0,tN) to represent the tN-year contract default swap spread, ignoring the accrued premium, we can write the present value of the existing contract premium segment as:

in:

• ∆(tn-1,tn,in:

• Q(tV,B) is the premium date between tn-1 and tn

• Z(tV,tn) is the arbitrage-free survival probability of the reference entity from the valuation time tV to the premium payment time tn

tn) is the Libor discount factor from valuation date to premium payment date n

This formulation ignores the effect of premiums, i.e., upon the occurrence of a credit event, the contract usually requires the insurance buyer to pay a portion of the premium from the previous premium payment date to the occurrence of the credit event.

• To account for the effect of premium accrual, we have to consider the probability of default for each period between two premium dates to calculate the expected premium accrual and calculate the probability-weighted accrual. To do this, we must

• Consider each premium accumulation period starting at tn-1 with payment date tn;

• Determine the survival probability at each time point s from the valuation date tV to the premium period;

• Calculate the accumulated amount from the date of the last premium payment to each time;

• Discount this payment back to the valuation date using the Libor discount factor;

• Integrate all time during the premium period;

Sum from n=1 to final premium n=N.

The resulting expression for accumulated premiums is:

Let's simplify it to get:

In the event of a credit event, the buyer will want to pay a lower spread to offset possible additional accrued payments. For a contract with a CDS spread of 200 basis points and an expected recovery rate of 40%, the change in the spread due to the quarterly payment of the cumulative default swap premium equals approximately 0.83 basis points.

Conclusion

risk warning:

risk warning:

• Be vigilant against illegal financial activities under the banner of blockchain and new technologies. The standard consensus resolutely resists various illegal activities such as illegal fundraising, network pyramid schemes, ICO and various variants, and dissemination of bad information using blockchain.