Credit default swaps and a study on determining the credit default swap premium of Turkey

Credit risk is the probability assigned to the risk that a debtor might fail in paying his debt or bank credit as previously promised. A default occurs when/if a debtor cannot fulfill his basic obligations. Credit risk is classified as the most important risk type that all institutions have to face from time to time. A credit derivative is a financial instrument that can be used to transfer credit risk from one investor, who is exposed to the credit risk, to another investor, who is willing to take that risk. For credit derivatives the payoff depends on the occurrence of the credit event which should be defined very clearly. The default event for a credit default swap (CDS) as defined by ISDA are bankruptcy, failure to pay, obligation default or acceleration, repudiation or moratorium (for sovereign entities) and restructuring. There is a growing body of literature on the pricing of credit default swaps. Duffie (1999) suggests that credit default swaps can be viewed as a swap of a default free floating-rate note (FRN) for a risky floating-rate note. Hull and White (2000) suggest that with a flat risk-free curve and constant interest rates, arbitrage is perfect if the pay-off from a CDS on default is the sum of the principal amount plus accrued interest on a risky par yield bond, times one minus the recovery rate. Skinner and Townend (2002) suggest that under the put-call parity theorem, CDSs can be viewed as put options and that the five variables crucial to option pricing (risk free rate, underlying asset, volatility, maturity and exercise price) can also be used for modeling CDS premium. On the empirical front, as the aim of this study was to end up with a well functioning model that can be used to forecast Turkish CDS spreads, and to test its usability, daily data on Turkish CDS spreads for seven different maturities (1, 2, 3, 4, 5, 7 and 10 years), 3 month LIBOR rate and the yield of the Turkish 2030 Eurobond was collected from Bloomberg for the period of Oct. 2000 - Jan. 2008. Before moving on with the regression model suggested by Skinner and Townend (2002) further analysis were carried out in order to choose the appropriate risk free rate and volatility. Meanwhile, due to the available data and the type of process to be used in evaluating it, revisions were made to the original model, and two variables (maturity and exercise price) were dropped. As a first step towards analysis, all variables were tested by Augmented Dickey Fuller (ADF) unit root test to see if they were stationary or not. The variables were found to have a unit root. In the next step the initial differences were taken and the ADF was conducted once more and the null hypothesis that the variables had a unit root was rejected. The variables were said to be integrated in the first order, I(1). As a second step towards analysis, seven equations for seven different maturities were estimated using the OLS method. The overall regression performs quite well and the corrected R2 values are quite high. Error terms of the model were found to be stationary showing that there is a long term relationship between CDS spreads and the three independent variables (risk free rate, the yield of the underlying asset and volatility). As a third step towards analysis, error terms were tested to see whether some form of autocorrelation existed. Among them it was found that there indeed was autocorrelation. This information was added to the modeling procedure by using the seemingly unrelated regression (SUR) method. As a fourth step, the Wald test was conducted to check whether or not the parameters of the three variables in the model for the seven CDS equations were statistically the same. The null hypothesis that the parameters were indeed equal was rejected and it was concluded that instead of one single equation, seven different equations were to be used. As a final step of the analysis, the forecasting strength of the model was tested using the out of sample method for the year 2007. It was discovered that the model was working quite well for the first half of 2007 until the sub prime mortgage crisis peaked in July. Till then the model had begun to underestimate the actual realizations, although the 5 and 10 year CDS models estimated better than the others through out the time period concerned. In our opinion, this was due to the global shift in financial market sentiment towards the view that the sub prime mortgage crisis was transforming into a global credit crisis, which coincided with second forecasting period. In summary the estimated CDS spread model works well as an initial model. Keywords: Credit derivatives, credit default swap, swap premium, put-call parity, unit root. Kredi temerrüt swapı (Credit Default Swap – CDS) en yalın tanımıyla kredi riskini etkin bir biçimde yönetme amacıyla satın alınan bir çeşit finansal sigorta sözleşmesidir. Kredi temerrüt swap spreadi (primi) de bu sigorta sözleşmesinin prim tutarı olarak düşünülebilir. Bu çalışmanın amacı “Kredi Temerrüt Swap” sözleşmelerini derinlemesine inceleyerek Türkiye’nin kredi temerrüt swap primini tahmin edecek bir model geliştirmeye çalışmaktır. Kredi temerrüt swapları genel hatları itibariyle satım opsiyonlarına büyük benzerlik gösteren finansal enstrümanlardır. Bu yapısal benzerlikten hareketle bir satım opsiyonunun fiyatının belirlenmesinde etkili olan beş temel değişkenin aynı zamanda kredi temerrüt swap priminin belirlenmesinde de etkili olabileceği fikrinden yola çıkılmıştır. Opsiyon fiyatlama modelinde yer alan put-call paritesi teoreminden yola çıkılarak öncelikle satım opsiyonları ile kredi temerrüt swapları arasındaki ortak nokta tanımlanmıştır. Ardından Türkiye’nin yurtdışında işlem gören 1,2,3,4,5,7 ve 10 yıl vadeli CDS sözleşmelerinin prim tutarlarından oluşan ve 19/10/2000 - 17/01/2008 tarihlerini kapsayan yaklaşık 6 yıllık bir veri seti ile çalışılmış ve opsiyon fiyatlamasında etkili olan beş temel değişkenden risksiz faiz oranı, referans varlığın getirisi ve referans varlığın getirisinin volatilitesi ile CDS primleri arasında uzun dönemli bir ilişkinin mevcut olduğu sonucuna ulaşılmıştır. Ek olarak, örneklem içinden son bir yıl ve son dört aya ait veriler oluşturulan modelin dışında bırakılarak, ilgili zaman dilimleri için kestirimler yapılmıştır. Kestirimlerin sonuçları  gerçekleşmelerle kıyaslanarak modelin kestirim gücü sınanmıştır. Anahtar Kelimeler: Kredi türev ürünler, kredi temerrüt swapı, swap primi, put-call paritesi, birim kök.&nbsp