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LectureNotes06Print - IEOR E4731: Credit Risk and Credit...

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Unformatted text preview: IEOR E4731: Credit Risk and Credit Derivatives Lecture 06: Pricing CDS Notes originally written by Prof. Rama Cont Instructor: Xuedong He Spring, 2012 1 / 32 Pricing CDS I In this lecture, we are going to use reduced form models to price CDS I We need to decide the mark-to-market value of a CDS contract given a spread. Consequently, the CDS spread is the one that makes the value of the CDS contract zero at its inception. 2 / 32 Undwinding a CDS Contract I The mark-to-market represents the unwind cost of the contract, i.e., how much we would have to pay or receive to remove the contract from the trading book. I For example, consider a protection buyer, who we will call party A , who buys $10 million of a protection in five-year default swap contract at a default swap spread of 75bp. The protection seller is party B I One year later, spreads have moved and the spread of 4Y protection in the CDS market is 320bp I Although we know that the value of the contract is now positive to party A , we want to be able to determined exactly how much it is worth. I The value of the contract is the value at which the contract can be unwound. It is known as unwind value, tear-up value, or mark-to-market value . 3 / 32 Mark-to-market value of a CDS Contract There are three ways that this gain can be realized: 1. Party A to the CDS requests party B to agree a cash payment at which the contract can be closed out 2. Party A to the CDS agrees with a third party, C , an unwind value and then request to party B that the default swap be reassigned to party C . The mark-to-market amount is paid from party C to party A 3. Party A enters into an offsetting transaction in which they sell 4Y protection at 320bp. The protection leg is therefore perfectly hedged. What remains is a series of positive risky premium payments: 320-75 = 245bp premium payments until default or maturity. 4 / 32 Mark-to-market value of a CDS Contract (Contd) I The unwind value of 1 and 2 should be identical since from A s perspective, they accomplish the same thing. I The unwind value of 1 and 2 is V ( t ) = PV of 4Y of Protection- PV of 4Y of risky premium payments at 75bps I Since the current 4Y market spread is 320bp, PV of 4Y of Protection- PV of 4Y of risky premium payments at 75bps = 0 I Thus, we have V ( t ) = PV of 4Y of risky premium payments at 320-75=245bps I The unwind value of 1 and 2 is also same as the value of 3. 5 / 32 Notations I Market information: {F t } t I Short interest rate: r ( s ) ,s . I Date of default event triggering payment by protection seller: random time: . I Intensity of the default time: ( s ) ,s I Full information: {G t } t I Risk-neutral probability Q (with e R t r ( u ) du ,t to be the numeraire)....
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LectureNotes06Print - IEOR E4731: Credit Risk and Credit...

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