Credit Derivatives. By A. V. Vedpuriswar

Transcription

1 Credit Derivatives By A. V. Vedpuriswar September 17, 2017

2 Historical perspective on credit derivatives Traditionally, credit risk has differentiated commercial banks from investment banks. Commercial banks are in the credit risk business. Investment banks are in the market risk business. Investment banks are not comfortable with holding credit risk which has a much longer tenure. Commercial banks on the other hand use their huge balance sheets and ability to take credit risk to gain more business. 1

3 Historical perspective on credit markets One way to deal with credit risk was to sell it. But selling a loan required the permission of the borrower. This might hamper the relationship. How could banks transfer the credit risk without actually selling the loan? 2

4 Innovations from Banker s Trust (1) The first innovation was the total return swap. Suppose a bank wanted to accommodate a client without increasing credit risk. The bank entered into a swap with Bankers Trust. BT got the interest on the loan and capital gain. But BT had to pay compensation in case of capital loss. BT paid a funding cost to the bank. The loan was held on the bank s balance sheet without assuming credit risk. 3

5 Innovations from Banker s Trust (2) Japanese banks had sold options to Bankers Trust (BT). These options were now deep in the money. BT faced a lot of credit risk vis a vis the banks which were not doing well. BT sold investors a five year bond, linked to a portfolio of five Japanese banks, each rated A. The bond paid a relatively high rate of interest. But if any of the banks defaulted on its obligation, the investors suffered losses and did not get their investment back. Instead they got bonds issued by the defaulting bank. The bonds delivered had a face value equal to the initial investment. 4

6 Total return swap (1) A ten year corporate bond has a coupon rate of 7.5%. Coupon is paid semi annually. The bond is currently trading at 100. The LIBOR rate is currently 4.5%. Explain the cash flows if we invest in a total return swap at LIBOR + 50 basis points, assuming the bond value went up to 102 and fell to 98. Bond price moving up to 102 Coupon = 7.5/2 = 3.75 Capital gain = 2 Total returns = 5.75 Payment made by investor ( )/2 = 2.5 Net gain for investor = =

7 Total return swap (2) Bond price moving down to 98 Return to investor Coupon = 7.5/2 = 3.75 Capital loss = 2 Total returns = 1.75 Payment made by investor ( )/2 = 2.5 Net loss for investor = =

8 The emergence of Credit Default Swaps CDS emerged out of the need for credit protection. In a CDS, the protection buyer pays the protection seller a fee. The protection seller compensates the protection buyer for losses in case of default. 7

9 What is a CDS? Is it an insurance? Is it a swap? Is it a forward? It is actually an option, bought by the protection buyer and sold by the protection seller. The strike price is the par value of the reference asset. The option can only be exercised in case of a credit event. 8

10 CDS vs Insurance Only licensed players can sell insurance. Insurance is a highly regulated business. CDS is an unregulated business. CDS is a bet between two people on whether the borrower will pay up. It has little to do directly with the loan. Imagine buying insurance on a house we do not own! 9

11 Who is the reference entity? The reference entity lies at the heart of a CDS. But identifying the entity is not always easy. In 2000, UBS bought protection on Armstrong World Industries (AWI) from Deutsche Bank. AWI was restructured and sold to Armstrong Holding. UBS claimed the reference entity was bankrupt. Deutsche Bank refused to pay up. Eventually, the dispute was settled out of court. 11

12 Credit events Credit events can be of various types: - Failure to pay - Bankruptcy - Moratorium - Repudiation - Restructuring 12

13 How much will be paid? There are two mechanisms: - Cash settlement - Delivery The key in cash settlement is in establishing the market price of the bond after default. But a market may not exist for these bonds. Sometimes, physical settlement will be difficult. Other times, physical settlement will be preferred. 13

14 Cheapest to deliver bond Usually, a number of different bonds can be delivered in the event of a default. When a default happens, the protection buyer can review the alternative deliverable bonds and deliver the cheapest bond. 14

15 Dynamic Credit Default Swap Here, the notional amount used in calculating the payout in the event of default is not static. The amount will fluctuate with the mark-to-market value of a reference swap or portfolio of swaps. However, the periodic premium paid by the protection buyer is fixed. 15

16 Credit Intermediation Swap A credit intermediation swap occurs when a third counterparty facilitates a trade between two counterparties that would not otherwise trade swaps directly with one another. The two parties may not want to trade with one another because one party's credit lines are full with regard to the other. Or one of the parties may be restricted to trading swaps exclusively with AAA-rated counterparties. The intermediating party is usually a very highly rated entity known as an AAA-rated special purpose vehicle (SPV). The intermediary earns a spread for assuming credit risk. The intermediary will pay out a lower fixed rate on one swap than it will receive on the other swap. 16

17 Basket Credit Default Swap A basket credit default swap allows the protection buyer to sell the default risk on a basket of reference obligations or assets (rather than on a single obligation). Upon the default of one of the obligations, the basket credit default swap is terminated. The premium paid by the protection buyer is based on the weakest credit among the reference obligations in the basket. However, the premium is also lower than buying protection on the three credits separately because there is usually some correlation among the credits. 17

18 First to Default Swap The first-to-default swap terminates upon the event of first default. The basket of reference credits should be chosen carefully. If the basket consists of many strong credits and one very weak credit, the first credit to default will likely be the weak credit. The reference obligations should be of a similar credit quality to make the use of a basket swap advantageous. The correlation between the components of the basket and the protection seller should also be low. Otherwise, the seller may well default at the same time as a correlated credit in the basket of reference obligations. 18

19 CDS Indexes (1) CDS indexes allow investors to buy and sell protection against default on basket credit default swaps. Introduced in 2004, there are principal 'families' of CDS indexes: CDX (USA) Traxx (Europe) itraxx indexes cover credit derivatives markets in Europe, Asia and Australia. CDX indexes cover credit derivatives markets in North America and emerging markets 19

20 CDS Indexes (2) Reference names in each CDS index are determined by a poll of participating dealers according to strict guidelines. The most liquid (traded) CDS contracts are chosen for the index. After polling, outlier quotes may be omitted before calculating the average CDS measure for a given index. This ensures that one dealer's quote does not exert influence on the average index calculation. 20

21 CDS Indexes (3) Once an index is formed, it will remain static over its lifetime, except in the case of default (in this case the defaulted entity is removed from the index). Every six months a new rebalanced index is issued. However, the original index also remains in existence until maturity. Standard maturities for itraxx and CDX indexes are 3, 5, 7 and 10 years (5 and 10 years for itraxx sector sub-indexes). There are many market makers in the itraxx indexes (16 in the CDX indexes) to ensure market liquidity and transparency. 21

22 Valuation of CDS Valuation of CDS is based on the principle that risk free arbitrage is not possible. The present value of expected payments for the protection seller is equated with the pay off in case of a default. Default probabilities have to be estimated. The recovery rate also has to be estimated. The exception is a binary CDS, where the pay off in case of a default is independent of recovery rate. 22

23 Related instruments A forward CDS is the obligation to buy or sell a particular CDS on a particular reference entity at a particular future time, T. If the reference entity defaults, before T, forward contract cases to exist. A CDS option is an option to buy or sell a particular CDS on a particular reference entity at a particular time, T. A basket CDS involves a number of reference entities. An add up basket CDS provides a pay off when any of the reference entities default. A first to default CDS provides a pay off only when the first default occurs. A second to default CDS provides a pay off only when the second default occurs. An n th default CDS provides a pay off only when the nth default occurs. 23

24 Total Rate of Return Swap (1) The protection buyer is the total return payer. The protection seller is the total return receiver. The 'total return on reference obligation is exchanged in return for a stream of LIBOR based cash flows. If the reference obligation rises in value, the protection seller benefits from this higher return. But if the reference obligation falls in value the protection seller must compensate the buyer for the loss. If a default or other credit event occurs with the reference obligation, the swap usually terminates. 24

25 Total Rate of Return Swap (2)) A credit default swap simply transfers credit risk, typically by reference to some designated reference obligation. A total return swap transfers effectively all the risks of owning the designated obligation. Typically, the protection buyer retains the servicing and voting rights to the underlying obligation. However, certain rights may be passed through to the protection seller under the terms of the TRORS. 25

26 Total Rate of Return Swap (3) If there is an agreed default event on the reference obligation prior to the maturity of the TRORS, the TRORS is usually terminated. The payer of the TRORS either: delivers the reference obligation to the receiver of the TRORS against a cash payment equal to the notional amount. receives cash payment from the receiver of the TRORS which is equal to the difference between the notional amount of the reference obligation and the market value of the reference amount. The receiver of a TRORS (the protection seller) is not the legal owner of the reference obligation. But it effectively owns a synthetic asset as it has both the income and the credit risk. 26

27 Total Rate of Return Swap (4) A TRORS is similar to a repurchase agreement under which the seller of the underlying security pays an agreed rate of interest to the buyer who then lends money for an agreed period. The seller is equivalent to the total return receiver on the swap. The buyer is equivalent to the total return payer on the swap. Upon the maturity of the agreement, the seller is obligated to buy back the underlying obligation at a predetermined price. However, there is no exchange of the underlying obligation at the maturity of a TRORS unless there is a defined credit event. 27

28 Problem A bank has lent $ 100 million to a client at a rate of 11%. The bank enters into a total return swap with a counterparty which will pay LIBOR + 40 bp. After 1 year, the value of the loan has fallen by 4 % and the LIBOR is 10%. What will be the impact on the bank s cash flows as a result of the swap? Solution: Outflow =.11(100) = $ 11 million Inflow =.04(100) +.104(100) = $ 14.4 million Net inflow = $ 3.4 million 28

29 Problem A bank has lent $ 200 million at a rate of 12% to a client. The bank enters into a TRS with a counterparty which will pay LIBOR + 50 bp. After a year, the loan value falls by 5% and the LIBOR is 11%. What are the implications of the TRS for the bank. Solution Outflows = (.12) ( 200) = $ 24 million Inflows = ( ) ( 200) = $ 33 million Net inflows = $ 9 million 29

30 Credit linked notes Credit Linked Notes convert credit derivatives into bond form. A CLN is a security issued with an embedded credit default swap. The protection buyer issues the CLN to the protection seller. The coupon represents the interest and the credit risk premium and will usually be more than that for a comparable bond. The investor will receive the par value of the note at maturity if no credit event has occurred before that time. In case of a credit event, the amount due is deducted and only the balance is given to the protection seller. The maturity of the credit-linked note is usually the same as the maturity of the reference obligation. 30

31 Credit spread options The holder of the option is the protection buyer. If the spread of a particular bond exceeds a spread over LIBOR ( the strike spread), the protection buyer can exercise the option. Credit spread options are not based only on credit default. Spreads can be related to various factors besides credit events. 31

32 Collateralised Debt Obligations (1) A CDO is a way of creating securities with widely different risk characteristics from a portfolio of debt instruments. These tranches are called equity, mezzanine (subordinated) and senior trenches respectively. The creator of the CDO normally retains the equity tranche and sells the remaining tranches in the market. Senior note holders take a hit only when losses on the equity/mezzanine trenches cross pre specified limits. Collateralized bond obligations (CBOs) and Collateralized loan obligations (CLOs) are backed by bonds, loans, respectively. 32

33 Collateralised Debt Obligations (2) The first step is to place a package of corporate bonds in a special-purpose vehicle (SPV). Assume that we have a total of $1,000 million, representing exposures of $10 million to 100 entities, or names. Multiple tranches are then issued by the SPV, with a waterfall structure, or priority of payments to the various tranches. Tranches are categorized as senior, mezzanine, and subordinate or equity. In the simplest structure, the SPV is ideally a passive entity. 33

34 Collateralised Debt Obligations (3) The SPV redistributes cash flows according to well-defined rules. There is no need for other management action. Say 80% of the capital structure is apportioned to tranche A, which has the highest credit rating of Aaa, using Moody s rating, or AAA. It pays LIBOR + 45bp, for example. Other tranches have lower priority and rating. These intermediate, mezzanine, tranches are typically rate A, Baa, Ba, or B which is not rated. 34

35 Collateralised Debt Obligations (4) Due to leverage, the return can be very high if there is no default. But the equity is exposed to the first door loss in the portfolio. The pricing of the equity tranche differs from others. The investor, or protection seller, first invests the notional amount. In exchange, he receives a spread, called running spread, and an up-front fee. This fee is quoted in percent and is typically around 40% for an investment-grate CDO. 35

36 Collateralised Debt Obligations (5) In this case, the investor would get 40% x $30 = $12 million up front. Cumulative losses of $20 million would reduce the notional of the equity tranche to $30 - $20 = $10 million. The investor in the equity tranche would then receive the running spread, say 500 bp, applied to the new notional of $10 million. For losses amounting to $45 million, the first tranche is wiped out, and investors in tranche C receive only $70-$15=$55 million back. Thus, the rating enhancement for the senior classes is achieved through prioritizing the cash flows. 36

37 Synthetic CDO (1) Credit is transferred but not the loan itself. The bank keeps the loans on its books. The bank enters into a CDS on the loans with the SPV. SPV receives fees and offers credit protection. SPV raises money as in a normal CDO. But the money is parked in government bonds. The bonds are pledged to cover any payments that the SPV may have to make under the CDS if any entity defaults. SPV acquires primarily synthetic assets by selling protection rather than purchasing assets for cash. Interest received from these bonds, and the premium paid by the protection buyer, is then passed through the SPV to investors. 37

38 Synthetic CDO (2) If a default occurs in the portfolio of reference entities, the SPV compensates the protection buyer through a payoff, as per a traditional credit default swap. The SPV uses the funds invested in high-quality bonds to make the payoff. On maturity of the CDO, the remainder of the proceeds from the original sale of securities is returned to investors. The investors are therefore the end-sellers of credit protection and are exposed to the entire credit risk of the reference entity(ies). 38

39 Synthetic CDO (3) Synthetic CDOs may be: fully funded or partially funded. A fully funded synthetic CDO is one, in which the entire credit risk is transferred to investors. With a partially funded structure, the SPV issues a lower amount of CDO notes because it provides protection on a portion of the portfolio of reference entities. The unfunded part (referred to as super senior) can remain outstanding with the protection buyer taking on the risk of default. Alternatively, the protection buyer may conclude a credit default swap with an AAA-rated counterparty, for example an insurance company, to cover the credit risk of this portion. 39

40 Cash Flow and Market Value CDOs In the case of cash flow CDOs, payments to investors solely come from collateral cash flows. In contrast, with market value CDOs, payments are made from collateral cash flows as well as sale of collateral. If the market value of the collateral falls below some level, payments to the equity tranche are suspended. This creates more flexibility for the portfolio manager. 40

41 Static and Managed CDOs CDOs may differ in the management of the asset pool. In static CDOs, the asset pool is basically fixed. In case of managed CDOs, a portfolio manager is allowed to trade actively the underlying assets. 41

42 CDO-squared structure A CDO can invest in CDO tranches instead of individual credits. This is a CDO-squared structure. The main benefit of this structure is the greater degree of diversity. 42

43 Other instruments The market now also trades credit default swaps on assetbacked securities (ABS) tranches, called asset-backed credit default swaps (ABCDS). Buying an ABCDS is equivalent to acquiring protection, or shorting the security. A corporate CDS makes a payment if the underlying company suffers a credit event. In contrast, with an ABS, the issuing SPV cannot go bankrupt but defaults can occur for individual loans in the pool. Also, the notional amount is not fixed but amortizes over time as principal is paid back on the loans. Another recent innovation is the constant proportional debt obligation (CPDO). 43

44 Problem The total notional amount of a set of corporate bonds is $ 1,000,000. The duration is 4. The bonds are selling at par. The current bond yield is 8% while the T Bill yield is 6%. Credit spread put options are available with a strike spread of 3%. They will mature in 90 days. On the day of expiry of the options, the bond price has dropped to $ 93. The bond yield is 10%. The T bill yield remains unchanged. How will an investor in the corporate bonds benefit by buying the option? Spread on the date of maturity = 10-6 = 4% Since this is more than 3%, the option will be exercised. Payoff = $ (1,000,000 ) (4) ( ) = $ 40,000 Loss on the face value of the bond = $1,000,000(.07) = $ 70,000. The net loss is 70,000 40,000 = $ 30,

45 Problem The notional principal of a credit spread put option is $ 1,000,000. The yield is 9% while the duration is T bill yield is 7%. The option has a strike spread of 3%. On the date of maturity, the bonds are yielding 13.79% and trading at $ 860,000. What is the payoff? Loss on the bond principal = 1,000, ,000 = $ 140,000. Gain on the put = ( ) (.01) (3.57) (1,000,000) = $ 135,303 Net loss = 140, ,303 = $

46 Problem The notional principal in a credit spread forward contract is $ 1,000,000. The spread agreed to at the beginning of the contract is 3%. The duration of the bonds is 4. If the spread decreases to 2%, what will be the implications for the contract buyer? The loss for the buyer = (1,000,000)(4)( ) = $ 40,000. This is the gain for the seller. 46

47 Problem The notional principal in a credit spread forward contract is $ 3,000,000. The spread agreed to at the beginning of the contract is 4.3%. The duration of the bonds is 3.6. If the spread increases to 6.86% on the date of maturity, what will be the implications for the buyer? The spread widens. Gain for the buyer = (3,000,000)( )(3.6) = $ 276,480 47

48 Problem The probability of a reference entity defaulting during a year, conditional on no earlier default is 2%. The risk free LIBOR rate is 5%. The recovery rate, in case of a default is 40%. Assume the notional principal is 1 and the payment for protection, s is made every year at the end of the year. If defaults happen midway during the year and the maturity of the swap is 5 years, calculate s. Year Default probability Survival probability Discount factor (e -rt ) PV of expected payment s s s s s s 50

49 Expected compensation payoff Now we calculate the present value of the amounts that cannot be recovered. The defaults happen in the middle of the year. So the recovery also happens in the middle of the year. Time (Years) Probability of default Expected pay off Discount factor PV of expected pay off (.6) (.02) = (.6) (.0196) = (.6) (.0192) = (.6) (.0188) = (.6) (.0184) =

50 Now we calculate the accrual amount in the event of a default. Time (Years) Probability of default Expected accrual payment Discount factor PV of expected accrual payment s s s s s s s s s s.0426 s So to break even, s s =.0511 s =.0124 So the quote must be 124 basis points per year. 52

51 Problem A enters into a 4 year credit default swap with B to hedge a $500 million bond. The probability of default is 3%, recovery 30% in the event of default and the risk free rate is 6% compounded continuously. The premium is paid annually. Defaults happen only mid way during a year. What is the CDS spread? Let the CDS spread be s. Premium payable every year = (500(s) Present value of premium payment (no default) Year Probability of default Survival probability e -(.06)t Present value Present value = (500s) (3.2068) = s 53

52 Present value of accrued premium payment (default) Year Probability of default e -(.06)t Present value (500s)(.1022) 2 Present value = = 25.55s Present value of compensation receivable (in case of default) Year Probability of default e -(.06)t Present value Present value = (.1022) (500) (.70) = To break even, we can write s s = or s = /1629 = % 220 basis points 54

53 Problem It has been 60 days since the last coupon payment was made. The notional principal of the swap is $ 20,000,000 and the reference amount is 100%. The final price is estimated at 30% and the annual coupon rate was 8%. Calculate the cash settlement amount. Compensation = LGD =.7 * 20,000,000 = 14,000,000. Adjustment for coupon payment =.08*(60/360) (20,000,000) = 266,667 So cash settlement amount = 14,000, ,667 = 13,733,333 55

54 Problem It has been 40 days since the last coupon payment was made. The notional principal of the swap is $ 10,000,000 and the reference amount is 100%. The final price is estimated at 35% and the annual coupon rate was 7%. Calculate the cash settlement amount. Compensation = LGD =.65 * 10,000,000 = 6,500,000. Adjustment for coupon payment =.07*(40/360) (10,000,000) = 77,800 So cash settlement amount = 6,500,000 77,800 = 6,422,