Credit Default Swaps - Essay Example

CREDIT DEFAULT SWAPS     By         Location Credit Default Swaps Introduction Credit Default Security (CDS) is a new emerging tool in the capital market that is being used to leverage investors against losses associated with the default in credit. It has grown to become an important instrument in the market today with many successful firms using it to protect their investments and assuring their income. With the fluctuation in interest rates in the current economies, CDS is the way to go to encourage more investments. The tool, like any other financial tool in the capital market such as the stock, has a price fixed on it, but the added advantage is that the price of a CDS is predetermined at the beginning of the contract so that the compensation in case of credit default and the CDS charge is predetermined early in advance. The use of CDS has affected trade and the economy in various sovereign states. Valuation principle of single name CDS security Credit default security is the trade in security to protect the seller from risk resulting from default so that the risk is transferred to the buyer. The trade in CDS has increased over time, so that the trade of CDS with a particular reference entry is traded more than the bonds issued by the same reference entry. CDS are instruments that insure companies or sovereign country against default on its debtors (Hull and White2001, p.1). The company is the reference entity while its default on credit is the credit event. The buyer makes periodic payments to the seller until the maturity date of the contract or occurrence of a credit event, whichever comes first, at a fixed annual rate. In the occurrence of a credit event, the seller is presented with the bond by the buyer of the protection in exchange for its face value (Duffie 1998, p.2). The CDS spread are the annual payments made annually by the buyer of the protection. Estimates of Recovery rate and probability of default is required for valuation of a CDS. Plain vanilla pricing is relatively insensitive to recovery rate. Potential buyers back by potential seller and the premium paid by protection buyer are the two parts involved in valuing CDS. To value premium at time t with a maturity of T* and Qfee, the expectation under standard pricing measure E’ is: (Ericsson Wang & reneby 2009, p.9). The maturity of of credit default occurs before the maturity of the bond instrument. In the event of bankrupsy, the bond holder is able to recover a fraction of the per value of the bond. Thus the expected value to be received by the bond holder in case of default is the difference between the market price of the bond and its face value; Two models of default risk exist in the literature; the reduced form model and structural model (hull & White200 p.3). Given that a firm has a debt of face value D without any coupon that matures at time T, the firm’s equity is regarded as a European call option costing D and matures at T. This is the source of structural model which is more of a traditional approach. This approach is not efficient as it does not incorporate the risk neutral probabilities of bond prices and the spread of CDS. This created an avenue for the formation of the reduced form model which incorporates risk neutral hazard rate h(t). This is the probability of default at time t assuming no earlier defaults were experienced and the changes in it as observed at time t. The reduced model can be aligned with risk neutral probability. The limited range of correlation that is achievable through this approach is an advantage to it. However, this rule is defied when the relative financial health of one firm is dependent on another firm so that there exist a high correlation between default rate of the two firms. The equilibrium point of payments made by the CDS buyer and seller form the price of the single name CDS. This is the point where benefit to bith parties are maximized. Given s pecent annual payment and N CDS spread, the expected payment will be arrived at as follows: The expected value is the premium leg also known as the fixed leg. S(ti) is the probability of survival at time ti. is the fraction of payment and the value of the payment for unit zero coupon default free bond whose maturity is tk at the time ti. incorporation of default default in this bond will give us the floating leg. default payment is considered a possible occurrence in the life of the contract and the expectation of default or the floating leg is calculated as below: R being the recovery rate, with t maturity and f(u) the probability density of time to default. The CDS seller incures expenses and has to extract the expense incurred between the last agreed upon payment and the actual time. This expense is associated directly with default thus it is a fraction of the payment fee propotion to the fraction of a payment period that has already elapsed. Thus it has expectation which can be arrived at as follows: . With the fixed leg, default leg and accrued payment at hand, the spread of the CDS can be deduced as below: Default probability density, q(t), expressed as q(t)∆t is the probability of default between time t and t+∆t as observed at time zero (Hull &White2003, p.6). The difference between q(t) and h(t) is that the former is measured at time zero while the latter is measured at time t with no earlier default. However the two are related in a way. They jointly inform of the default probability environment. The risk neutral probability density of companies is assumed to be estimated either from bond prices of CDS spreads so that there is a variable Xj(t) describing the credit worthiness of a company j at time t given that N is the number of companies (1≤j≥N). Given a CDS that commits holder to buy protection on a given reference entity between time T and T* , K being the spread per year and L the notional principal. When T=0, it is a regular CDS; when 0 Yan H, 2007, liquidity and credit defaults wap spreads. Columbia Ericsson J, Reneby J; 2006. Can structural models predict default risk? Evidence from the bond and credit derivatives market. Journal of Finance Coudert V, Gex M; 2010. Credit Default Swap and bond markets: which leads the other? Financial stability review, No 14 Read More