Credit Default Swap - Assignment Example

30 Dec Credit Default Swaps Question According to the International Swaps and derivatives Association (ISDA)a credit default swap (CDS) is: A contract designed to transfer the credit exposure or debt obligation between parties. The buyer of a credit swap receives credit protection, whereas the seller of the swap guarantees the credit worthiness of the underlying security. In a CDS the risk of default is transferred from the holder of the security to the seller of the swap. Most credit derivatives take the form of credit default swap. (isda.org) It is done in the event that a borrower defaults on his debts. There are really three parties. However, the borrower (C) knows nothing about the credit default swap. He simply borrows a loan from Bank (A) who then goes to Bank (B) to seek protection from the risk of C defaulting on the loan. B sells protection against default to A (the protection buyer) in return for half yearly payments. B receives monthly coupon payments from C. If C defaults then A will get the principal portion of the debt from B. If however, the bond never defaults C (the borrower) will pay A the principal and A would continue making half yearly payments to B until the maturity date of the debt. Question 2 Companies use CDS to hedge against default on loans by borrowers. Company (A) would essentially seek protection from a third party B, by going short the credit. B would therefore be going long. A is the buyer of the protection and B is the seller. A would pay B a periodic fee until the contract expires or a credit event such as a default occurs. Desrosiers (2007) states: A credit default swap is a contract, indexed to a single reference asset, which provides insurance against a default event on that asset. There are three parties involved in a credit default swap. The first is the protection buyer; this is the investor and owner of the reference asset, for example a General Motors bond. The bond issuer, General Motors in this example, is the second party that plays a role, indirectly, in the CDS. Based on the bond investment, General Motors pays the investor periodic coupon payments and promises to pay the principal portion of the bond at a set maturity date. After purchasing the bond, the investor becomes nervous that General Motors will suffer a credit event and default on its promised, future payments. So, the bond owner purchases protection against the possibility of this credit event in the form of a credit default swap. The CDS is a contract between the protection buyer and a protection seller. The latter is typically an insurance company or a securities company, e.g. Morgan Stanley. In this agreement, the protection buyer makes periodic premium payments (periods are usually half year increments) to the protection seller, in this case Morgan Stanley, and Morgan Stanley agrees to pay the entire face value of the bond to the protection buyer if General Motors defaults on the bond. The CDS will terminate either at the bond’s maturity or the date a default event occurs, whichever comes first. If default never occurs, General Motors continues to pay the periodic coupon payments and at maturity pays the principal portion of the bond to the investor, and the investor pays the CDS premium payments to Morgan Stanley until the bond matures. Morgan Stanley will never have to make any payments and profits for assuming the credit risk of the bond. If a default event occurs before the set maturity, Morgan Stanley instantly compensates the protection buyer for its loss and has no further obligations in the CDS contract. In this event, the investor would have minimized its losses by entering into the credit default swap. Question 3 A fair price (value) of Credit Default Swap would involve calculating the present value of periodic premium payments equal to the asset backed value of the entity at the time of maturity of the loan or the probable time of default. This would then be added to a payment for the possibility of default which is based on the recovery rate. Both items will be discounted to present value. Question 4 The structure and timing of the cash flows that would be made between First American Bank (FAB) and Charles Bank International (CBI), if they agreed on credit default swap to support the two year £50 million loan that CBI is hoping to make to CapEx Unlimited (CEU) would be as follows: - the standard fee payment period is semi-annually. The payment will involve the risk free interest rate with a premium added to allow for the credit risk involved. This credit risk will be based on the credit rating which was last BB and which suggests that CEU is speculative. It will also involve an additional charge for the possibility of default which his based on the recovery rate expected on this event. The risk free rate at the time of the deal was 4.5%. This rate is comparable to the 5 year Treasury STRIP yield of 4.51% but way above the 2 year Treasury STRIP yield of 3.2%. That is a difference of 1.3%. The credit spread for 2 year and 5 year by maturity and at the closest available rating related to the telecommunications industry were 260 basis points and 256 basis points respectively. This translates to 2.6 and 2.56% respectively. The credit spread and the risk free rate applicable would be 3.2% plus 2.6% equals 5.8%. An extra default premium should be added to account for the above average risk. Question 5 The option pricing approach to firm default risk to calculate the CEU’s expected default frequency (EDF) during the next five years will be the Black-Scholes Option Pricing Model. There are three sets of equations that are involved. Moody’s states: “There are essentially three steps in the determination of the default probability of a firm: Estimate asset value and volatility; calculate the distance to default (N(-d2 used instead); and calculate the default probability of expected default frequency (EDF). Calculation of Expected Default Frequency (EDF) Using the Option Pricing Approach VE VA VA/ VE X ln(VA/X) e T √T r σE σA σ2A d1 d2 DD N(d1) N(-d2) EDF 6.80. 10.95 1.6103 4.15 0.97023 2.718 5 2.2361 0.045 0.53 0.3291 0.566 3.547330569 2.811360253 --0.297933212 0.9998 0.0025 25bps The expected default frequency of 25 basis points translates to 2.5 %. This means there is a 2.5% probability that CEU will default. This probability is considered low. Question 6 Based on the five year EDF calculated in Question 5 and FAB’s expected losses, the periodic fee that CBI pays every six months to FAB for the credit default swap is calculated below. Calculation of Total Protection Value of CDS PV Factor P Q(t,Tj-1) Q(t,Tj) 1-R(t,Tj) V 4.5 0.9569 4.3 1 0.975 0.4 0.043 0.9158 4.12 0.975 0.95 0.4 0.0412 0.8764 3.94 0.95 0.925 0.4 0.0394 0.8386 3.77 0.925 0.9 0.4 0.0377 0.8024 3.61 0.9 0.875 0.4 0.0361 19.74 4.75 4.625 2 4.935 V equals 4.94 and is the Total protection value of the CDS (Kesarwani, nd.) Calculation of Periodic Fee payable every six months The rate s, at which the payments are made by the protection buying party (CBI) is: = 4.94 91.30 s = 0.054054 or 5.41% Periodic fee is: 6.66% of $50mn/2 = 1.351351 ie $1.35mn Question 7 The probability for default (2.5%) based on the calculations in Question 5 would suggest that FAB should hold on to the credit risk of CEU. Kittal should assess CEU regularly to determine if there is anything that would change his expectations. CEU may no longer have a BB credit rating and so that has to be considered. The best way for Chris Kittal to transfer the risk from First American Bank’s Balance Sheet is to sell portions to other institutions through a credit linked note. This is the next most popular means of protection against default. Based on the information presented in the Case a credit default swap to other institutions is unlikely due to the security that the protection sellers would require. Therefore, it is very unlikely that a CDS would be taken up. FAB would not be able to benefit much if that was done because the rate as it is currently (based on calculations in Question 6) would not be beneficial to the bank. It is already below the market interest rate of 5.8%. Furthermore, CEU does not have AAA credit rating to make the bond attractive to investors. Investors are coming out of a situation where they were told by certain institutions that they were investing in bonds with AAA rating when this was not so. MYSMP (2010) states: The credit crisis of 2008 has brought a lot of public scrutiny to the credit derivatives market. Lehman Brothers had sold billions of dollars worth of credit-linked notes to investors in Hong Kong, packaging them as mini bonds. These mini bonds were sold as a low risk investment with a third party insurer in the event the bonds were worthless…Once Lehman went under, it left a number of investors with bonds that were not worth the paper they were printed on. It will be a hard sell for FAB with the level of premium received from CBI. FAB could however, cut its losses by offering the same interest rate to investors. References Crosbie, P & Bohn, J (2003). Modeling Default Risk: Modeling Methodology. Available: http://www.ma.hw.ac.uk/~mcneil/F79CR/Crosbie_Bohn.pdf. Last accessed 27 Dec 2010 Crouhy, M., Galai, D & Mark, R (1998). Credit Risk Revisited: An Option Pricing Approach. Available: http://www.sigma-pcm.co.il/Media/Uploads/%D7%98%D7%A4%D7%A1%D7%99%D7%9D%20%D7%9C%D7%A4%D7%A8%D7%A1%D7%95%D7%9E%D7%99%D7%9Dpdf/CREDIT%20RISK%20REVISITED%20-%20%20AN%20OPTION%20PRICING%20APPROACH.pdf. Last accessed 12th Dec 2010. Derivatives Consulting Group (2010). Glossary. Available: http://www.isda.org/. Last accessed 12th Dec 2010 Desrosiers, M. E (2007). Prices of Credit Default Swaps and the Term Structure of Credit Risk. Available: http://www.wpi.edu/Pubs/ETD/Available/etd-050107-220449/unrestricted/CDS-Default_Probability.pdf. Last accessed 18th Dec 2010 Dubofsky, D. A & Miller, T. W (2003). Derivatives: Valuation and Risk Management. Oxford: Oxford University Press Hull, J., Predescu, M. & White, A. (nd.). Bond Prices, Default Probabilities and Risk Premiums. Available: http://www.rotman.utoronto.ca/~hull/downloadablepublications/CreditSpreads.pdf. Last accessed 28th Dec 2010 Kesarwani, Y. (2…) Credit Risk Modeling and Credit Default Swaps. Available: http://www.matrixiitg.in/wp-content/plugins/downloads-manager/upload/Credit%20Risk%20Modeling.pdf. Last accessed: 18th Dec 2010 Merton, Robert C. (1973). On the Pricing of Corporate Debt: The Risk Free Structure of Interest Rates. Available: http://stat.fsu.edu/~jfrade/PAPERS/Credit%20risk%20modeling%20papers/SWP-0684-14514372.pdf. Last accessed: 18th Dec 2010 My Stock Market Power (2010). Credit Linked Notes & Effects on Global Markets. Available: http://www.mysmp.com/bonds/credit-linked-note.html. Last accessed: 28th Dec 2010. Appendix Formula Used 1. VE – the market value of equity ($6.8bn) was taken from the Case. 2. VA – the market value of assets was derived from the formula: VA = X + VE where X is the book value of liabilities 3. σE – represents the volatility of equity which is taken from the implied volatility rates in the case 4. σA – represents the volatility of assets and is calculated from the following expression: σE = (VA/VE)/ ∆ σA 5. d1 = ln (VA/X) + (r + σ2V/2)T (Crosbie & Bohn, 2003) σ√T r is the risk free interest rate. In this case the five (5) year Treasury STRIP yield in the case. 6. d2 = d1 - σA√T 7. V = ∑j1nP(t, Tj) [Q(t, Tj-1) – Q(t, Tj)] [1-R(Tj)] (Kesarwani) where P( , ) is the risk- free discount factor, R ( , ) is the recovery rate and Q(t, T) up to time t. V is the total protection value. 8. s = V/[∑j1nP(t, Tj) Q(t, Tj)], the rates at which payments are made to the buying party. (Kesarwani) NB: N(-d2) which is another estimate of the probability of default was used instead of DD – the distance from default. See Crouhy, et al (pg4). Read More