Credit Default Swap –Pricing Theory, Real Data Analysis and Classroom Applications Using Bloomberg Terminal Yuan Wen * Assistant Professor of Finance State University of New York at New Paltz 1 Hawk Drive, New Paltz, NY 12561 Email: weny@newpaltz.edu Tel: 845-257 … The CDS survival curve is the fundamental element in the pricing of credit derivatives. The primary advantage of using CDS to estimate hazard rates is that CDS spreads are observable. Although we can create a model to estimate the hazard rate (the probability of default in the next period conditional on surviving until the current period), the estimated value would inherently be a guess. In this case, the corporate bond is said to be trading at a 300-basis-point spread over the T-bond. For example, the credit spread between a 10-year Treasury bond trading at a yield of 5% and a 10-year corporate bond trading at 8% is 3%. The first example is handled normally by cdsbootstrap: This file bootstraps hazard rates from a series of 1/3/5/7/10-year par spreads. I've also discussed some of the nitty-gritty around dates in my last post. We describe the focus of the paper, which can encompass the term structure (TS), foreign exchange rates (FX), and CDS quantos (Quanto). Futhermore, we can observe than the hazard rate does not have the same dynamic for both issuers. In other words, investors think that the issuer has room to improve with age (become less risky) or less potential to worsen considering that it is very risky today. The hazard rate is assumed constant between subsequent CDS maturities. Our ndings suggest that the residuals are transient, while the tted curves re By iterating this process, we obtain the hazard rates: $$\lambda_{0,1},\lambda_{1,3},\lambda_{3,5},\lambda_{5,7}$$. I have been using QuantLib 1.6.2 to bootstrap the hazard rates from a CDS curve. Suggested Citation, Bobst Library, E-resource Acquisitions20 Cooper Square 3rd FloorNew York, NY 10003-711United States, Subscribe to this fee journal for more curated articles on this topic, We use cookies to help provide and enhance our service and tailor content.By continuing, you agree to the use of cookies. In this case, the default leg value can be expressed as: $$\text{DL PV}(t_{V},t_{N})=(1-R)\sum_{m=1}^{M\times t_{N}}Z(t_{V},t_{m})\left(Q(t_{V},t_{m-1})-Q(t_{V},t_{m})\right)$$. We make the simplifying assumption that the hazard rate process is deterministic. Available at SSRN: If you need immediate assistance, call 877-SSRNHelp (877 777 6435) in the United States, or +1 212 448 2500 outside of the United States, 8:30AM to 6:00PM U.S. Eastern, Monday - Friday. This page was processed by aws-apollo5 in. 2 Bootstrapping of Zero Curves 11 2.1 Money market rates 12 2.2 Forward rates 13 2.3 Swap rates 14 2.4 Interpolation issues 15 3 A Plethora of Credit Spreads 17 3.1 Introduction '"" 17 3.2 CDS spread 21 3.2.1 Product description 21 3.2.2 Bootstrapping hazard rates from CDS spreads 23 3.2.3 Standard CDS contracts 25 3.2.4 Floating recovery rates 27 As a comparison, it is more than two times than the Greece 5Y CDS as of 3 August 2015 (2203.70bp). JP Morgan Credit Derivatives and Quantitative Research (January 2005), D. O'kane and S. Turnbull. ... We use the CDS spreads and run a bootstrapping algorithm to calculate the survival probability. Unreasonable inputs can result in meaningless outputs, such as negative probability values. Hazard rate is a piece-wise constant function of time (i.e. We present a simple procedure to construct credit curves by bootstrapping a hazard rate curve from observed CDS spreads. Par spreads and Libor rates are defined in the input file input.xls. We will look at 2 specific US Issuers as of 27 May 2014: Pfizer (Pfizer Inc - PFE) and Radioshak (RadioShack Corp - RSH). Within the hazard rate approach we can solve this timing problem by conditioning on each small time interval $$[s,s+ds]$$ between time $$t_V$$ and time $$t_N$$ at which the credit event can occur. In pricing the default leg, it is important to take into account the timing of the credit event because this can have a significant effect on the present value of the protection leg especially for longer maturity default swaps. Bootstrapping from Inverted Market Curves. Equivalently solution for the CDS is: S=R−1tlog(1−P(0,t)). Suppose that the spreads over the risk-free rate for 5-year and a 10-year BBB-rated zero-coupon bonds are 130 and 170 basis points, respectively, and there is no recovery in the event of default. where ˉλ is the average default intensity (hazard rate) per year, s is the spread of the corporate bond yield over the risk-free rate, and R is the expected recovery rate. BT4016 4. $$Q_{1,3}=Q_{0,1}*exp(-h_{1,3}\times2)=91.9\%$$, $$\lambda_{0,1},\lambda_{1,3},\lambda_{3,5},\lambda_{5,7}$$, RR, premiumFrequency, defaultFrequency, accruedPremium). Although in this chapter's introduction we said that a default is not always a clear, linear, and transparent process, we assume that there is a precise moment in time r when this takes place. (Not on the quiz -but important info that builds on the slide in class) What do you think are the advantages of using CDS market to estimate hazard rates? This table summarizes the main affine term structure models proposed for the pricing of sovereign credit spreads using intensity-based frameworks. Informally, a credit spread is the difference in yield between two bonds of similar maturity but different creditquality. Note that reasonable implied default probabilities depend on reasonable bond yield spreads (or bond prices) and reasonable recovery rates. Letâs assume we have quotes for 1Y, 3Y, 5Y and 7Y for a given issuer. The default probabilities can be inferred from the term structure of credit spreads as follows: P[τ ≤ 5] = Q(5) = 1 − e−0.013×5 = 0.0629 We can also easily calculate the survival probabilities from this hazard rate term structure (as we have seen earlier). Therefore we have the 1Y survival probability $$Q_{0,1}=exp(-h_{0,1}\times1)=99\%$$ and the 3Y survival probability $$Q_{1,3}=Q_{0,1}*exp(-h_{1,3}\times2)=91.9\%$$. The reduced-form model that we use here is based on the work of Jarrow and Turnbull (1995), who characterize a credit event as the first event of a Poisson counting process which occurs at some time $$t$$ with a probability defined as : \(\text{Pr}\left[\tau