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Term paper ON Derivatives and Risk Management TOPIC:- Introduction to Credit Default Swap - types CDS valuation, the motivations to use CDS and pricing SUBMITTED TO: - SUBMITTED BY:- Miss Avinash Kaur SONU KUMAR ROLL NO:-A22 SECTION:-RT1903 REG NO:-10905481 CONTENTS TOPIC:- Origin of CDS Definition of credit default swas How Credit Derivatives Work Significance of Credit Default Swaps: Uses and Benefits of Credit Default Swaps Types of credit default swap Settlement methods for CDS: Uses of Credit Default Swaps: CDS Pricing: TYPES OF CREDIT DEFAULT SAWAPS VALUATION Origin of CDS: By the mid-'90s, JPMorgan's books were loaded with billions of dollars in loans to corporations and foreign governments, and by federal law it had to keep huge amounts of capital in reserve in case any of them went bad. But what if JPMorgan could create a device that would protect it if those loans defaulted, and free up that capital? And the solution they come up with is nothing but the origin of ―Credit Default Swap‖. Credit Default Swap (CDS) is some sort of insurance policy where the third party assumes the risk of debt going sour and in exchange will receive regular payments from the bank who issues debt, similar to insurance premiums. Although the idea was floating for a while JP Morgan was the first bank to make a bet on CDS. They opened up a Swap desk in mid-‗90s and formally brought the idea of CDS into reality. The Credit Default Swaps (CDS) have grown rapidly in the credit risk market since their introduction in the early 1990s. It is believed that current usage is but a small fraction of what it will ultimately represent in the credit risk markets. In particular, the CDS market will become as central to the management of credit risk as the interest rate swap market is to the management of market risk. Definition of credit default swas A credit default swap (CDS) is a credit derivative contract between two counterparties. The buyer makes periodic payments to the seller, and in return receives a payoff if an underlying financial instrument defaults. There are three parties involved in a typical CDS contract – 1. Protection Buyer (Risk Hedger) 2. Protection Seller 3. Reference Entity Protection buyer is the one who pays a premium (CDS spread, generally a quarterly premium) to the protection seller for taking credit risk to a reference entity and if the credit event happens then protection seller will have to payoff. Typical credit events include – material default, bankruptcy, and debt restructuring. The size of the payment is usually linked to the decline in the reference asset‘s market value following the credit event. The concept of CDS is explained pictorially below: How Credit Derivatives Work The vast majority of credit derivatives take the form of the credit default swap (CDS), which is a contractual agreement to transfer the default risk of one or more reference entities from one party to the other (Figure 1). One party, the protection buyer, pays a periodic fee to the other party, the protection seller, during the term of the CDS. If the reference entity defaults or declares bankruptcy or another credit event occurs, the protection seller is obligated to compensate the protection buyer for the loss by means of a specified settlement procedure. The protection buyer is entitled to protection on a specified face value, referred to in this paper as the notional amount, of reference entity debt. The reference entity is not a party to the contract, and the buyer or seller need not obtain the reference entity‘s consent to enter into a CDS. Credit default swap xx basis point per annum Protection buyer Protection seller Default payment Reference entity A credit default swap (CDS) is a credit derivative contract between two counterparties. The buyer makes periodic payments to the seller, and in return receives a payoff if an underlying financial instrument defaults. Significance of Credit Default Swaps: CDS creates Liquidity: The CDS adds depth to the secondary market of underlying credit instruments which may not be liquid for many reasons. Risk Management: Credit derivatives makes risk management more efficient and flexible by allocation of credit risk to most efficient manager of that risk. Risk Separation: Credit derivatives allows for separation of credit risk from other risks of the asset. Reliable funding source: Credit derivatives help exploit a funding advantage or avoiding a funding disadvantage. Since there is no up-front principal outlay required for most Protection Sellers when assuming a Credit Swap position, these provide an opportunity to take on credit exposure in off balance-sheet positions that do not need to be funded. On the other hand, institutions with low funding costs may capitalize on this advantage by funding assets on the balance sheet and purchasing default protection on those assets. The premium for buying default protection on such assets may be less than the net spread such a bank would earn over its funding costs. Uses and Benefits of Credit Default Swaps Effective tool for hedging against changes in Credit Spreads - Default swaps are dynamic, market-sensitive products whose mark-to-market performance is closely related to changes in credit spreads. As a result, they are an effective tool for hedging (or for assuming exposure to) changes in credit spread as well as default risk. Ability to create custom maturity products - An investor wants a three-year maturity and duration exposure to an issuer that has only 2-year and 10-year securities outstanding. Selling a three-year Default Swap on the 10-year security can create the required exposure. In effect, the investor will have taken on the credit risk for the duration of the swap, i.e. 3 years. Management of concentration of credit risk within credit portfolios - An investor who owns a portfolio of credits can alter the concentration risk of their portfolio by buying or selling credit risk on different names and varying maturities by using credit default swaps. Management of credit limits - For banks that have loans or transactions with counterparties that require further funding but are constrained because of internal or regulatory credit limits, credit default swaps can allow the bank to reduce the credit exposure to that counterparty without damaging the business relationship. Types of credit default swap Binary swap Where a standard CDS requires a post-default valuation, a binary swap avoids this by simply specifying a fixed dollar amount. The binary CDS is analogous to a cash-or-nothing binary stock option (i.e., where payoff is either a fixed amount or nothing, instead of a variable amount). Basket CDS Instead of a single-name reference, the basket CDS has a multi-name reference. The reference is a basket of assets, say, 100 high-quality bonds. The payout trigger can be the first default (1st-to-default), the second default (2nd-to-default) or the nth default (nth-to-default). In the case of a 2nd-to-default, for example, upon the first default nothing happens: the protection buyer continues to pay the CDS spread and the protection seller has no payout, yet. Then if the second asset in the reference basket defaults, the basket CDS transacts normally: the protection seller pays net of recovery and the basket CDS terminates. The basket CDS is well-suited to protection buyers who have a better expectation about default frequencies than about particular name defaults. The value of a basket CDS depends highly on correlation among the underlying reference asset. can be counterintuitive. For a 1st-to-default, 2nd-to-default, and the typical nth-to-default basket CDS (where the n is a small number compared to the number of total reference assets), lower correlations imply higher default risk (and a higher price on the basket CDS). But that is just the tail of the distribution. If instead we "move over to the right" on the distribution, at a certain point, the nth-to-default becomes less risky with lower correlation. Cancelable default swap (callable CDS or putable CDS) The cancelable default swap is analogous to a compound stock option. As Meissner says, "a cancelable default swap is a combination of a default swap and a default swap option." In the case of a callable CDS, the protection buyer has the right to terminate; in the case of a putable CDS, the protection seller has the right to terminate. Contingent CDS Here the trigger requires both the typical default plus some contingent event; e.g., default on another credit. Default correlation between the two credits, of course, is the critical variable. To illustrate with an extreme, under perfect correlation (correlation = 1.0), the contingent CDS would be identical to the regular CDS. On the other hand, under perfect negative (default) correlation, the contingent CDS would have no value because there can be no concurrent default. The valuation boundaries, therefore, are zero and the value of the CDS without the contingent event. Leveraged CDS The leveraged CDS adds-on a percentage of the notional to the standard payoff (the standard payoff, to remind, is the par value of the reference net of recovery). Asset from a speculative motive, Meissner explains that a single leveraged CDS might be used to hedge a portfolio of assets. That is, rather that individually protecting (insuring) portfolio assets, use the leverage to cover additional assets. But he makes an important point about a weakness of this: "the [leveraged] default swap buyer is exposed to basis risk." Basis risk is a critical idea. This would be yet another example, among many, of where the protected asset and its hedge are not the same thing. Most hedges are imperfect (i.e., the exposure is not identical to the asset underlying the derivative) and so carry basis risk. Settlement methods for CDS: The settlement for CDSs can be done in either of two ways: Physical Settlement or Cash Settlement. Physical Settlement: The seller of the protection will buy back the distressed reference entity at par. Clearly given that the credit event will have reduced the secondary market value of the underlying reference entity, this will result in protection seller (CDS seller) incurring a loss. This was the most common means for the settlement in CDSs and will generally take place no later than 30 days after the credit event. Till 2006 ISDA2 allowed settlement only in the form of physical settlement. But due to increased amount of naked CDSs in the credit market ISDA has now allowed the choice between cash and physical settlement. Cash Settlement: The seller of the protection will pay the buyer the difference between the notional of the default swap and a final value for the same notional of the reference obligation. Cash settlement is less prevalent because obtaining precise quotes can be difficult when the reference credit is distressed. After the Auction process being started for the settlement of CDSs as per ISDA, this problem has been resolved. The example for the Physical and Cash settlement shown below will explain the process. Uses of Credit Default Swaps: As mentioned already CDSs can be used for speculation, hedging or arbitrage. Out of which we will be considering hedging and speculation in detail. CDSs for Hedging: When JP Morgan invented the credit instrument named CDS they meant it to be for hedging there credit risk. Although market has changed a lot since then but still the use of CDSs for hedging purpose remains to be a primary reason. Credit default swaps are often used to manage the credit risk (i.e. the risk of default) which arises from holding debt. Typically, the holder of, for example, a corporate bond may hedge their exposure by entering into a CDS contract as the buyer of protection. If the bond goes into default, the proceeds from the CDS contract will cancel out the losses on the underlying bond. For example, if you own a bond of Apple worth $10 million maturing after 5 years and you are worried about its future then you can create a CDS contract with an insurance company like AIG which will charge a premium of say 200bps annually for insuring your bond. In this way you are hedging the risk of losing $10 million in case Apple goes bankrupt. Here you will be paying $200000 to AIG for insuring your bond. If Apple goes bankrupt you will receive the par value of bond from AIG and even if does not, you will lose premium value at the most which is worth transferring the risk to AIG. Counterparty Risks: When entering into a CDS, both the buyer and seller of credit protection take on counterparty risk. Examples of counter party risks: The buyer takes the risk that the seller will default. If reference entity and seller default simultaneously ("double default"), the buyer loses its protection against default by the reference entity. If seller defaults but reference entity does not, the buyer might need to replace the defaulted CDS at a higher cost. The seller takes the risk that the buyer will default on the contract, depriving the seller of the expected revenue stream. More important, a seller normally limits its risk by buying offsetting protection from another party - that is, it hedges its exposure. If the original buyer drops out, the seller squares its position by either unwinding the hedge transaction or by selling a new CDS to a third party. Depending on market conditions, that may be at a lower price than the original CDS and may therefore involve a loss to the seller. As is true with other forms of over-the-counter derivative, CDS might involve liquidity risk. If one or both parties to a CDS contract must post collateral (which is common), there can be margin calls requiring the posting of additional collateral. The required collateral is agreed on by the parties when the CDS is first issued. This margin amount may vary over the life of the CDS contract, if the market price of the CDS contracts changes, or the credit rating of one of the party‘s changes. CDSs for Speculation: Credit default swaps allow investors to speculate on changes in CDS spreads of single names or of market indexes such as the North American CDX index3 or the European iTraxx index4. An investor might speculate on an entity's credit quality, since generally CDS spreads will increase as credit-worthiness declines and decline as credit-worthiness increases. The investor might therefore buy CDS protection on a company in order to speculate that the company is about to default. Alternatively, the investor might sell protection if they think that the company's creditworthiness might improve. As there is no need to own an underlying entity to enter into a CDS contract it can be viewed as a betting or gambling tool. For example if you feel that Microsoft is not performing well and may go bankrupt in near future then you might enter into a CDS contract with AIG for a notional value of $10 million for 5 years even if you don‘t own a single share of Microsoft. This kind of CDS is known as Naked CDS. CDS Pricing: The main aim of CDS pricing is to calculate the amount of premium to be paid by protection buyer to the protection seller. A typical CDS contract usually specifies two potential cash flow streams – a fixed leg and a contingent leg. On the fixed leg side, the buyer of protection makes a series of fixed, periodic payments of CDS premium until the maturity, or until the reference credit defaults. On the contingent leg side, the protection seller makes one payment only if the reference credit defaults. The amount of a contingent payment is usually the notional amount multiplied by (1 – R), where R is the recovery rate, as a percentage of the notional. Hence, the value of the CDS contract to the protection buyer at any given point of time is the difference between the present value of the contingent leg, which the protection buyer expects to receive, and that of the fixed leg, which he expects to pay, or, Value of CDS (to the protection buyer) = PV [contingent leg] – PV [fixed (premium) leg] In order to calculate these values, one needs information about the default probability of the reference credit, the recovery rate in a case of default, and risk- free discount factors. A less obvious contributing factor is the counterparty risk. For simplicity, we assume that there is no counterparty risk. [We assume that the parties involved in the contracts do their due diligence and are involved in the contract only when there is high credit rating (AAA) virtually eliminating counterparty risk.] On each payment date, the periodic payment is calculated as the annual CDS premium, S, multiplied by di, the accrual days (expressed in a fraction of one year) between payment dates (i.e. di S). However, this payment is only going to be made when the reference credit has not defaulted by the payment date. So, we have to take into account the survival probability q(t), or the probability that the reference credit has not defaulted on the payment date. Then, using the discount factor for the particular payment date, D(ti), the present value for this payment is D(ti)q(ti)Sdi . Summing up PVs for all these payments, we get N Σ D(ti) q(ti) Sdi ------------------------- (1) However, there is another piece in the fixed leg - the accrued premium paid up to the date of default when default happens between the periodic payment dates. The accrued payment can be approximated by assuming that default, if it occurs, occurs at the middle of the interval between consecutive payment dates. Then, when the reference entity defaults between payment date ti-1 and payment date ti, the accrued payment amount is Sdi/2. This accrued payment has to be adjusted by the probability that the default actually occurs in this time interval. In other words, the reference credit survived through payment date ti-1, but NOT to next payment date, ti. This probability is given by {q(ti-1)- q(ti)}. Accordingly, for a particular interval, the expected accrued premium payment is {q(ti-1)- q(ti)}Sdi /2. Therefore, present value of all expected accrued payments is given by N Σ D(ti) {q(ti-1) - q(ti)} Sdi/2 ----------------------------- (2) i=1 Now we have both components of the fixed leg. Adding (1) and (2), we get the present value of the fixed leg: N N PV [fixed leg] = Σ D(ti) q(ti) Sdi + Σ D(ti) {q(ti-1) - q(ti)} Sdi/2 -------------(3) i=1 i=1 where, D(ti) = Discounting Factor q(ti) = Survival Probability S = CDS Premium (Spread) di = Accrual days expressed in a fraction of a year {q(ti-1) - q(ti)} = Survival Probability till credit default event Next, we compute the present value of the contingent leg. Assume the reference entity defaults between payment date ti-1 and payment date ti. The protection buyer will receive the contingent payment of (1-R), where R is the recovery rate. This payment is made only if the reference credit defaults, and, therefore, it has to be adjusted by {q(ti-1)- q(ti)}, the probability that the default actually occurs in this time period. Discounting each expected payment and summing up over the term of a contract, we get N PV [contingent leg] = (1-R) Σ D(ti) {q(ti-1) - q(ti)} --(4) i=1 where, D(ti) = Discounting Factor R = Recovery Rate {q(ti-1) - q(ti)} = Survival Probability till credit default event Plugging equation (3) and (4) into the equation in the beginning, we arrive at a formula for calculating value of a CDS transaction. When two parties enter a CDS trade, the CDS spread is set so that the value of the swap transaction is zero (i.e. the value of the fixed leg equals that of the contingent leg). Hence, the following equality holds: N N N Σ D(ti) q(ti) Sdi + Σ D(ti) {q(ti-1) - q(ti)} Sdi/2 = (1-R) Σ D(ti) {q(ti-1) - q(ti)} i=1 i=1 i=1 Given all the parameters, S, the annual premium payment is set as: N (1-R) Σ D(ti) {q(ti-1) - q(ti)} i=1 S= ------------------5 N N Σ D(ti) q(ti) di + Σ D(ti) {q(ti-1) - q(ti)} di/2 i=1 i=1 TYPES OF CREDIT DEFAULT SAWAPS VALUATION Mid-market CDS – mid-markt CDS spreads on individual reference entities (example the average of the bid and offer CDS spreads quoted by brokers ) can be calculated from default probability estimates. We will illustrate how this is done with a simple example. Suppose that the probability of a reference entity defaulting during a year conditional on no earlier default is 2% Table -1 show survival probability and unconditional default probability of default during the first year is .02 and the probability the Table -1 unconditional default probability and survival probabilities. Time (year) Default probability Survival probability 1 0.0200 0.9800 2 0.0196 0.9604 3 0.1920 0.9412 4 0.0188 0.9224 5 0.0184 0.9039 Table -2 Calculation of the present value of expected payment. Payment=s per annum Reference entity will survive until the end of the first year is 0.98. the probability of a default during the second year is 0.02 x 0.98=0.0196 and the probability of survival until the end of the year is 0.02x0.9604=0.0192. And so on We will assume that default always happen halfway through a year and that payment on the CDS are made once a year, at the end of each year. We also assume that the risk-free (LIBOR) interest rate is 5% per annum with continuous compounding and the recovery rate is 40%. There parts to the calculating. These are in tabe 1,2,3 and 4. Table -2 show the calculating of the expected present value of the payment made on the CDS assuming that payment are made at the rate of s per year and the notional principle is $1.For example ,there is a 0.9412 probability that the third payment of s( per year) is made .the expected payment is therefore 0.9412s and its present value is 0.8101s.( apply formula) the total value of the expected payment is 4.0704s. Table -3.show the calculating of the expected present value of the payoff assuming a notional principal of $1. As mentioned earlier, we are assuming that defaults always happen halfway through a year. For example , there is a 0.0192 probability of payoff halfway through the third year. Given that the recovery rate is 40% the expected payoff at this time is 0.0192 x0.6=0.0115.the present value of expected payoff is $0.0511. Table -3 calculating of the present value of expected payoff national principal =$1 Table -4.calculating of the present value of accrual payment. As a final step we evaluated in table -4 the accrual payment made in the event of a default .for example there is a 0.0192 probability that there will be a final accrual payment halfway through the third year. The accrual payment is 0.5s. the expected accrual payment at this time is therefore 0.0192x 0.5s =0.0096s.its present value is o.0085s. the total present value of the expected accrual payments is 0.0426s. From table -2 and table -3 the present value of the expected payment is 4.0704s+0.0426s=4.1130s From table -2 the present value of expected payoff is 0.0511.Equating the two,we obtain the CDS spread for new CDS as 4.1130s=0.0511 Or s=0.0124. the mid- market spread should be 0.0124 times the principal or 124 basis points per year.this example is designed to illustrate the calculated methodology. In practice we are likely to find that calculation are more extensive than once a year and (b) we might want to assume that defaults can happen more frequently than once a year Marking to market a CDS At the time it is negotiated, a CDS, like most other swaps ,is worth close to zero. Later it may have a positive or negative value ,suppose,for example the credit default swap in our example had been negotiated some time ago for a spread of 150 basis point, the present value of the payment by the buyer would be 4.1130x0.0150=0.0617 and the present value of the payment by the buyer would be 0.0511 as above . the value of swaps to the seller would therefore be 0.0617- 0.0511 or 0.0106 time the principal. Similarly te mark- to- market value of the swap to the buyer of protection would be -0.0106 time the principal. Estimated default probabilities The default probabilities used to value a CDS should be risk- neutral default probability,not real world default probabilities ( risk neutral default probability can be estimated from bond price or asset swaps as Table -5 calculation of the present value of expected payoff from a binary credit default swaps. Principal=$1. From CDS quotes. The latter approach is similar to the practice in option markets of implying volatilities from the price of actively traded options. Suppose we change the example in table 2,3,4 so that we do not know the default probabilities.instead we know that the mid –market CDS spread for a newly issued 5 year CDS is 100 basis points per year. We can reverse engineer our calculations to conclude that implied default probability per year( conditional on no earlier default) is 1.61 per year. Binary credit default swaps A binary credit default swap is structured similarly to regular credit default swap except that the payoff is a fixed dollar amount. Suppose that in the example we have considered in table -1 to 4 the payoff is $1, instead of (1 - R) dollar, and the swap spread is s( per year) table -1,2 and 4 the same, but table -3 is replaced by table -5 .the CDS for a new binary CDS is given by 4.1130s = 0.0852 So that the CDS spread, s, is 0.0207 or 207 basis point. motivation to use credit default swaps motivation to use credit default swaps is that the instruments enable investors to tap into a market that's bigger than that of tradable securities. A desired credit exposure that is not available in the cash market can be synthetically created via a default swap. Given the historically low levels of interest rates and the flatness of the yield curve, a disproportionate share of new-issue volume has been both fixed and dated. As a result, the supply of corporate floaters and short-dated fixed-rate bonds has been concentrated in a handful of credits—generally in the financial services. The number of credits available in the default swap market, by contrast, is far larger, since the exposures financial institutions need to transfer are broader. Banks, for example, may want to hedge a revolving line of credit with an industrial credit by buying protection on the underlying credit, rather than sell the loan and risk affecting a banking relationship. In addition, I anticipate that a large percent of the commercial paper backstop market will be securitized via default swaps— providing another source for synthetic assets. END

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