Credit Derivatives


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Introduction to Credit derivatives

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Credit Derivatives

  1. 1. Credit Derivatives September 11, 2009 By A. V. Vedpuriswar
  2. 2. Historical perspective on credit derivatives <ul><li>Traditionally, credit risk has differentiated commercial banks from investment banks. </li></ul><ul><li>Commercial banks are in the credit risk business. </li></ul><ul><li>Investment banks are in the market risk business. </li></ul><ul><li>Investment banks are not comfortable with holding anything for a long time. </li></ul><ul><li>Commercial banks on the other hand use their huge balance sheets and ability to take credit risk to gain more business. </li></ul><ul><li>Commercial banks are also not subject to mark-to-market accounting, unlike investment banks. </li></ul>
  3. 3. Historical perspective on credit markets <ul><li>Investment banks wanted to enter credit markets. </li></ul><ul><li>The only way to deal with credit risk was to sell it. </li></ul><ul><li>But selling a loan required the permission of the borrower. </li></ul><ul><li>This might hamper the relationship. </li></ul><ul><li>How could banks transfer the credit risk without actually selling the loan? </li></ul>
  4. 4. Innovations from Banker’s Trust (1) <ul><li>The first innovation was the total return swap. </li></ul><ul><li>A bank wanted to accommodate a client without increasing credit risk. </li></ul><ul><li>The bank entered into a swap with Bankers Trust. </li></ul><ul><li>BT got the interest on the loan and capital gain. </li></ul><ul><li>BT had to pay in case of capital loss. </li></ul><ul><li>BT paid a funding cost to the bank. </li></ul><ul><li>Loan was held on the bank’s balance sheet without assuming credit risk. </li></ul>
  5. 5. Innovations from Banker’s Trust (2) <ul><li>Japanese banks had sold options to BT. </li></ul><ul><li>These options were now deep in the money. </li></ul><ul><li>BT faced a lot of credit risk vis a vis the banks. </li></ul><ul><li>Japanese banks were not doing well. </li></ul><ul><li>BT sold investors a five year bond. </li></ul><ul><li>It was linked to a portfolio of five Japanese banks, each rated A. </li></ul>
  6. 6. Innovations from Banker’s Trust (2) cont.. <ul><li>The bonds paid a relatively high rate of interest. </li></ul><ul><li>But if any of the banks defaulted on obligation, the investors suffered losses and did not get their investments back. </li></ul><ul><li>Instead they got bonds issued by the defaulting bank. </li></ul><ul><li>The bonds delivered had a face value equal to the initial investment. </li></ul>
  7. 7. The emergence of Credit Default Swaps <ul><li>CDS emerged out of the need for credit protection. </li></ul><ul><li>Protection buyer pays counterparty a fee. </li></ul><ul><li>The investor agrees to indemnify the bank against losses in case of default. </li></ul><ul><li>Compensation is payable in case of default. </li></ul><ul><li>CDS is effectively an insurance against bankruptcy. </li></ul>
  8. 8. What is a CDS? <ul><li>Is it an insurance? </li></ul><ul><li>Is it a swap? </li></ul><ul><li>Is it a forward? </li></ul><ul><li>It is actually an option. </li></ul><ul><li>Bought by the protection buyer. </li></ul><ul><li>Sold by the protection seller. </li></ul><ul><li>The strike price is the par value of the reference asset. </li></ul><ul><li>The option can only be exercised in case of a credit event. </li></ul>
  9. 9. CDS vs Insurance <ul><li>Only licensed players can sell insurance. </li></ul><ul><li>CDS is an unregulated business. </li></ul><ul><li>The CDS is a bet between two people on whether the borrower will pay up. </li></ul><ul><li>It has little to do directly with the loan. </li></ul><ul><li>Imagine buying insurance on a house we do not own! </li></ul>
  10. 10. The Basics of CDS <ul><li>Pay off is linked to credit events. </li></ul><ul><li>Insurance is provided against default by a particular company, known as the reference entity. </li></ul><ul><li>Buyer makes periodic payments to seller until the end of the life of the CDS or until a credit event. </li></ul><ul><li>In the event of a default, settlement takes place by physical delivery of bonds or cash payment. </li></ul><ul><li>CDS spread is the total amount paid per year as a percent of the notional principal. </li></ul><ul><li>The CDS spread should be roughly equal to the difference between corporate bond and risk free bond. </li></ul><ul><li>If this is not so, arbitrage is possible. </li></ul>
  11. 11. Who is the reference entity? <ul><li>The reference entity lies at the heart of a CDS. </li></ul><ul><li>But identifying the entity is not always easy. </li></ul><ul><li>In 2000, UBS bought protection on Armstrong World Industries from Deutsche Bank. </li></ul><ul><li>AWI was restructured and sold to Armstrong Holding </li></ul><ul><li>UBS claimed the reference entity was bankrupt. </li></ul><ul><li>Deutsche Bank refused to pay up. </li></ul><ul><li>Eventually, the dispute was settled out of court. </li></ul>
  12. 12. Credit events <ul><li>Credit events can be of various types: </li></ul><ul><li>- Failure to pay </li></ul><ul><li>- Bankruptcy </li></ul><ul><li>- Moratorium </li></ul><ul><li>- Repudiation </li></ul><ul><li>- Restructuring </li></ul>
  13. 13. How much will be paid? <ul><li>There are two mechanisms: </li></ul><ul><li>- Cash settlement </li></ul><ul><li>- Delivery </li></ul><ul><li>The key in cash settlement is in establishing the market price of the bond after default. </li></ul><ul><li>But a market may not exist for these bonds. </li></ul><ul><li>Sometimes physical settlement will be difficult. </li></ul><ul><li>Sometimes physical settlement will be preferred. </li></ul>
  14. 14. Cheapest to deliver bond <ul><li>Usually, a number of different bonds can be delivered in the event of a default. </li></ul><ul><li>When a default happens, the protection buyer can review alternative deliverable bonds. </li></ul><ul><li>The cheapest bond can be delivered. </li></ul>
  15. 15. Dynamic Credit Default Swap <ul><li>The notional amount used in calculating the payout in the event of default is not static. </li></ul><ul><li>The l amount will fluctuate with the mark-to-market value of a reference swap or portfolio of swaps. </li></ul><ul><li>However, the periodic premium paid by the protection buyer is fixed. </li></ul>
  16. 16. Credit Intermediation Swap <ul><li>A credit intermediation swap occurs when a third counterparty facilitates a trade between other counterparties that would not otherwise trade swaps directly with one another. </li></ul><ul><li>They may not want to trade with one another because one party's credit lines are full with regard to the other. </li></ul><ul><li>Or one of the parties may be restricted to trading swaps exclusively with AAA-rated counterparties. </li></ul><ul><li>The intermediating party is usually a very highly rated entity known as an AAA-rated special purpose vehicle (SPV). </li></ul><ul><li>The intermediary earns a spread income for assuming credit risk. </li></ul><ul><li>It will pay out a lower fixed rate on one swap than it will receive on the other swap. </li></ul>
  17. 17. Basket Credit Default Swap <ul><li>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). </li></ul><ul><li>Upon the default of one of the obligations, the basket credit default swap is terminated. </li></ul><ul><li>The premium paid by the protection buyer tends to be based on the weakest credit among the reference obligations in the basket. </li></ul><ul><li>However, the premium is also lower than buying protection on the three credits separately because there is usually some correlation among the credits. </li></ul>
  18. 18. Constructing a Basket Credit Default Swap <ul><li>The basket credit default swap (often referred to as first-to-default swaps) terminates upon the event of first default. </li></ul><ul><li>So the protection buyer must re-hedge the credit risk of the non-defaulting obligations at this time. </li></ul><ul><li>The basket of reference credits should be chosen carefully. </li></ul><ul><li>If basket consists of many strong credits and one very weak credit, the first credit to default will likely be the weak credit. </li></ul>
  19. 19. <ul><li>Protection buyers need to pay particular attention to the composition of the basket of reference obligations when considering the credit risk protection offered by such a structure. </li></ul><ul><li>The reference obligations should be of a similar credit quality to make the use of a basket swap advantageous. </li></ul><ul><li>The correlation between the components of the basket and the protection seller should also be low. </li></ul><ul><li>Otherwise, the seller may well default at the same time as a correlated credit in the basket of reference obligations </li></ul>
  20. 20. Credit Indices <ul><li>CDX – (USA) </li></ul><ul><li>Traxx – (Europe) </li></ul>
  21. 21. CDS Indexes <ul><li>A credit default swap (CDS) index is a measure of the performance of a pre-selected group of CDS quotes (or premiums). </li></ul><ul><li>CDS indexes allow investors to buy and sell protection against default on basket credit default swaps. </li></ul><ul><li>Introduced in 2004, there are principal 'families' of CDS indexes: </li></ul><ul><li>iTraxx indexes cover credit derivatives markets in Europe, Asia and Australia. </li></ul><ul><li>CDX indexes cover credit derivatives markets in North America and emerging markets </li></ul>
  22. 22. CDS Indexes <ul><li>Reference names in each CDS index are determined by a poll of participating dealers according to strict guidelines. </li></ul><ul><li>The most liquid (traded) CDS contracts are those chosen for the index. </li></ul><ul><li>After polling, certain high and low CDS quotes may be omitted before calculating the average CDS measure for a given index. </li></ul><ul><li>This ensures that one dealer's quote does not exert influence on the average index calculation. </li></ul><ul><li>. </li></ul>
  23. 23. <ul><li>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). </li></ul><ul><li>Every six months a new rebalanced index is issued. </li></ul><ul><li>However, the original index also remains in existence until maturity. </li></ul><ul><li>Standard maturities for iTraxx and CDX indexes are three, five, seven, and ten years (five and ten years for itTraxx sector sub-indexes). </li></ul><ul><li>There are many market makers in the iTraxx indexes (16 in the CDX indexes) to ensure market liquidity and transparency. </li></ul>
  24. 24. Valuation of CDS <ul><li>Present value of expected payments for protection seller is equated with the pay off in case of a default. </li></ul><ul><li>Default probabilities have to be estimated. </li></ul><ul><li>Recovery rate also has to be estimated. </li></ul><ul><li>The exception is a binary CDS, where the pay off in case of a default is independent of recovery rate. </li></ul>
  25. 25. Related instruments <ul><li>A forward CDS is the obligation to buy or sell a particular CDS on a particular reference entity at a particular future time, T. </li></ul><ul><li>If the reference entity defaults, before time, T, the forward contract cases to exist. </li></ul><ul><li>A CDS option is an option to buy or sell a particular CDS on a particular reference entity at a particular time, T. </li></ul><ul><li>A basket CDS involves a number of reference entities. </li></ul><ul><li>An add up basket CDS provides a pay off when any of the reference entities default. </li></ul>
  26. 26. <ul><li>A first to default CDS provides a pay off only when the first default occurs. </li></ul><ul><li>A second to default CDS provides a pay off only when the second default occurs. </li></ul><ul><li>An n th default CDS provides a pay off only when the nth default occurs. </li></ul>Related instruments
  27. 27. Total return swap <ul><li>This is a swap of the total return of the asset against a contracted pre fixed return. </li></ul><ul><li>The protection buyer is not only concerned with credit losses but also mark to market losses. </li></ul><ul><li>Usually, mark to market losses continue for sometime before defaults start. </li></ul><ul><li>By total returns we mean actual earnings from the reference asset and the actual appreciation or depreciation in price. </li></ul><ul><li>The protection seller guarantees a pre fixed spread. </li></ul><ul><li>The protection buyer passes on actual collections and variations in prices to the protection seller. </li></ul>
  28. 28. <ul><li>The protection buyer is the total return payer. </li></ul><ul><li>The protection seller is the total return receiver. </li></ul><ul><li>The 'total return‘ on reference obligation is exchanged in return for a stream of LIBOR based cash flows. </li></ul><ul><li>If the reference obligation rises in value, the protection seller benefits from this higher return. </li></ul><ul><li>But if the reference obligation falls in value the protection seller must compensate the buyer for the loss. </li></ul><ul><li>If a default or other credit event occurs with the reference obligation, the TRORS usually terminates. </li></ul>
  29. 29. <ul><li>A credit default swap simply transfers credit risk, typically by reference to some designated reference obligation </li></ul><ul><li>A total return swap transfers effectively all the risks of owning the designated obligation. </li></ul><ul><li>Typically, the protection buyer retains the servicing and voting rights to the underlying obligation. </li></ul><ul><li>However, certain rights may be passed through to the protection seller under the terms of the TRORS. </li></ul>
  30. 30. <ul><li>If there is an agreed default event on the reference obligation prior to the maturity of the TRORS, the TRORS is usually terminated. </li></ul><ul><li>The payer of the TRORS either: </li></ul><ul><ul><li>delivers the reference obligation to the receiver of the TRORS against a cash payment equal to the notional amount </li></ul></ul><ul><ul><li>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 </li></ul></ul><ul><li>The receiver of a TRORS (the protection seller) is not the legal owner of the reference obligation. </li></ul><ul><li>But it effectively owns a synthetic asset as it has both the income and the credit risk. </li></ul>
  31. 31. <ul><li>A TRORS is similar to a repurchase agreement under which the seller of the underlying security (the position similar to the total return receiver on a TRORS) pays an agreed rate of interest to the buyer (the position similar to the total return payer on a TRORS) who then lends money for an agreed period. </li></ul><ul><li>Upon the maturity of the agreement, the seller is obligated to buy back the underlying obligation at a predetermined price. </li></ul><ul><li>However, there is no exchange of the underlying obligation at the maturity of a TRORS unless there is a defined credit event under the TRORS agreement. </li></ul>
  32. 32. Credit linked notes <ul><li>CLNs convert credit derivatives into bond form. </li></ul><ul><li>A credit-linked note (CLN) is a security issued with an embedded credit default swap. </li></ul><ul><li>The CLN enables the issuer (protection buyer) to pass on the credit risk to the CLN investor (protection seller). </li></ul><ul><li>The protection buyer issues the CLN. </li></ul><ul><li>The protection seller buys the CLN. </li></ul><ul><li>In case of credit events, the amount due is deducted and only the balance is given to the protection seller. </li></ul><ul><li>The coupon represents the interest on the funding and the credit risk premium on the protection sold </li></ul>
  33. 33. <ul><li>Usually, the investor (protection seller) will receive an increased, regular coupon payment. </li></ul><ul><li>The investor will also receive the par value of the note at maturity if no credit event has occurred on the reference obligation before that time. </li></ul><ul><li>The maturity of the credit-linked note is usually the same as the maturity of the reference obligation. </li></ul>
  34. 34. Credit spread option <ul><li>It is a call or put option on an asset exercisable, based on a certain spread. </li></ul><ul><li>The holder of the option is the protection buyer. </li></ul><ul><li>If the spread of a particular bond exceeds or falls below a spread over LIBOR ( the strike spread), the protection buyer can exercise the option. </li></ul><ul><li>An option to put an asset is an option to call a pre determined spread. </li></ul><ul><li>An option to call an asset is an option to put a pre determined spread. </li></ul><ul><li>Credit spread options are not based only on credit default. </li></ul><ul><li>Spreads can be related to various factors besides credit events. </li></ul>
  35. 35. Credit (Spread) Option <ul><li>One counterparty is selling the credit risk of a reference obligation to the other party. </li></ul><ul><li>But, by structuring the trade as an option, the counterparties can leverage their credit perceptions. </li></ul><ul><li>The payoff under the credit option depends not on a credit event, but on a change in market value of reference obligation. </li></ul><ul><li>The reference obligation underlying a credit option is usually a floating rate security. </li></ul><ul><li>Any changes in the price of the security will be primarily due to changes in the credit spread of that security. </li></ul>
  36. 36. Collateralised Debt Obligations <ul><li>A CDO is a way of creating securities with widely different risk characteristics from a portfolio of debt instruments. </li></ul><ul><li>These tranches are called equity, mezzanine (subordinated) and senior trenches respectively. </li></ul><ul><li>The creator of the CDO normally retains the equity tranche and sells the remaining tranches in the market. </li></ul><ul><li>Senior note holders take a hit only when losses on the equity/mezzanine trenches cross pre specified limits. </li></ul>
  37. 37. Synthetic CDO <ul><li>Credit is transferred but not the loan itself. </li></ul><ul><li>Bank keeps the loans on its books. </li></ul><ul><li>Enters into a CDS on the loans with the SPV. </li></ul><ul><li>SPV receives fees. </li></ul><ul><li>In turn, SPV offers credit protection. </li></ul><ul><li>SPV raises money as in a normal CDO. </li></ul><ul><li>But the money is parked in government bonds. </li></ul><ul><li>The bonds are pledged to cover any payments that the SPV may have to make under the CDS if any entity defaults. </li></ul><ul><li>Synthetic securitisation avoids the need to get the client’s consent. </li></ul>
  38. 38. <ul><li>With the cash CDO structure, assets are transferred to a special purpose vehicle (SPV) that then issues the CDO. </li></ul><ul><li>A synthetic CDO is one in which the SPV acquires primarily synthetic assets by selling protection rather than purchasing assets for cash. </li></ul><ul><li>The reference asset for a synthetic CDO is typically a portfolio of credit default swaps on various reference entities instead of cash securities or loans. </li></ul><ul><li>The proceeds from selling the synthetic CDO securities are then invested in high-quality bonds. </li></ul><ul><li>Interest received from these bonds, and the premium paid by the protection buyer, is then channeled through the SPV to synthetic CDO investors. </li></ul>
  39. 39. <ul><li>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. </li></ul><ul><li>The SPV uses the funds invested in high-quality bonds to make the payoff. </li></ul><ul><li>When the synthetic CDO matures, the remainder of the proceeds from the original sale of securities is returned to investors. </li></ul><ul><li>The investors are therefore the end-sellers of credit protection and are exposed to the entire credit risk of the reference entity(ies). </li></ul>
  40. 40. <ul><li>Synthetic CDOs may be: fully funded or partially funded . </li></ul><ul><li>A fully funded synthetic CDO is one, in which the entire credit risk is transferred to investors. </li></ul><ul><li>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. </li></ul><ul><li>The unfunded part (referred to as super senior) can remain outstanding with the protection buyer taking on the risk of default. </li></ul><ul><li>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 . </li></ul>
  41. 41. Problem <ul><li>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? </li></ul>
  42. 42. <ul><li>Spread on the date of maturity= 10-6 = 4% </li></ul><ul><li>Since this is more than 3%, the option will be exercised. </li></ul><ul><li>Payoff = $ (1, 000, 000 ) (4)( .04-.03) = $ 40,000 </li></ul><ul><li>Loss on the face value of the bond </li></ul><ul><li> = $1,000,000(.07) = $ 70,000. </li></ul><ul><li>The net loss is 70,000 – 40,000 = $ 30,000. </li></ul>
  43. 43. Problem <ul><li>The notional principal of a credit spread put option is $ 1,000,000. The yield is 9% while the duration is 3.57. 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? </li></ul>
  44. 44. <ul><li>Loss on the bond principal </li></ul><ul><li>= 1,000,000 – 860,000 = $ 140,000. </li></ul><ul><li>Gain on the put </li></ul><ul><li> = (13.79- 7 - 3)(.01)(3.57)(1,000,000) = $ 135,303 </li></ul><ul><li>Net loss </li></ul><ul><li>= 140,000 - 135,303 = $ 4697 </li></ul>
  45. 45. Problem <ul><li>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 increases to 4%, what will be the implications for the buyer? </li></ul>
  46. 46. <ul><li>The loss for the buyer = (1,000,000)(4)(.04 -.03) = $ 40,000. </li></ul><ul><li>This is the gain for the seller. </li></ul>
  47. 47. <ul><li>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 ? </li></ul>
  48. 48. <ul><li>The spread widens. So the buyer incurs a loss. </li></ul><ul><li>Loss for the buyer </li></ul><ul><li>= (3,000,000)(0.0686-0.0430)(3.6) = $ 276,480 </li></ul><ul><li>This is a gain for the seller. </li></ul>
  49. 49. Problem <ul><li>Suppose the probability of a reference entity defaulting during a year, conditional on no earlier default is 2%. Assume 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. Assume defaults happen midway during the year. If the maturity of the swap is 5 years, how will you price the credit default swap. </li></ul>
  50. 50. Solution <ul><li>4.0705 s is the amount of payment made to receive credit protection. </li></ul>Year Default probability Survival probability Discount factor (e -rt ) PV of expected payment 1 .02 .98 .9512 .9322 s 2 .0196 .9604 .9048 .8690 s 3 .0192 .9412 .8607 .8101 s 4 .0188 .9224 .8187 .7552 s 5 .0184 .9040 .7788 .7040 s 4.0705 s
  51. 51. Solution Cont.. <ul><li>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. </li></ul>Time (Years) Probability of default Expected pay off Discount factor PV of expected pay off 0.5 .0200 (.6) (.02) = .0120 .9753 .0117 1.5 .0196 (.6) (.0196) = .0118 .9277 .0109 2.5 .0192 (.6) (.0192) = .0115 .8825 .0102 3.5 .0188 (.6) (.0188) = .0113 .8395 .0095 4.5 .0184 (.6) (.0184) = .0111 .7985 .0088 .0511
  52. 52. Solution Cont.. <ul><li>Now we calculate the accrual amount in the event of a default. </li></ul>Time (Years) Probability of default Expected accrual payment Discount factor PV of expected accrual payment 1 .0200 .0100 s .9753 .0097 s 2 .0196 .0098 s .9277 .0091 s 3 .0192 .0096 s .8825 .0085 s 4 .0188 .0094 s .8395 .0079 s 5 .0184 .0092 s .7985 .0074 s .0426 s
  53. 53. Solution Cont.. <ul><li>So to break even, </li></ul><ul><li>4.0705s + .0426 s = .0511 </li></ul><ul><li>s = .0124 </li></ul><ul><li>So the quote must be 124 basis points per year (124 basis points = 1.24% = 0.124) </li></ul>
  54. 54. Problem <ul><li>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? </li></ul>
  55. 55. Solution <ul><li>Let the CDS spread be s. </li></ul><ul><li>Premium payable every year = (500( s ) </li></ul><ul><li>Present value of premium payment (no default) </li></ul><ul><li>Present value = (500s) (3.2068) = 1603.4s </li></ul>Year Probability of default Survival probability e -(.06)t Present value 1 .03 .97 .9418 .9135 2 .0291 .9409 .8869 .8345 3 .0282 .9127 .8353 .7624 4 .0274 .8853 .7866 .6964 3.2068
  56. 56. Solution (Cont..) <ul><li>Present value of accrued premium payment (default) </li></ul><ul><li>Present value = = 25.55s </li></ul>Year Probability of default e -(.06)t Present value 0.5 .03 .9705 .0291 1.5 .0291 .9139 .0266 2.5 .0282 .8607 .0243 3.5 .0274 .8106 .02221 .1022
  57. 57. Solution (Cont..) <ul><li>Present value of compensation receivable (in case of default) </li></ul><ul><li>Present value = (.1022) (500) (.70) = 35.77 </li></ul><ul><li>To break even, we can write 1603.4s + 25.55s = 35.77 </li></ul><ul><li>or s = = .02196 </li></ul><ul><li>≈ 2.20% ≈ 220 basis points </li></ul>Year Probability of default e -(.06)t Present value 0.5 .03 .9705 .0291 1.5 .0291 .9139 .0266 2.5 .0282 .8607 .0243 3.5 .0274 .8106 .02221 .1022