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Unformatted text preview: Derivative Securities Fall 2007 Section 11 addendum Notes by Robert V. Kohn, extended and improved by Steve Allen. Courant Institute of Mathematical Sciences. Supplement to the discussion of single-name credit topics. Steve Allens Section 11 notes discuss the modeling of defaultable bonds, credit default swaps, as well as other issues involving the possibility that a single firm might default. Rather than repeat that material, I simply provide a brief overview and some additional examples. (Thus, these are not stand-alone notes but rather a supplement to the Section 11 presently posted on Blackboard.) ************************ Overview . Here is a compact overview of the main discussion points: (1) The big picture . Risk of default is a huge issue for banks and other insitutitions with large bond portfolios. So we need models (for regulators and risk managers) and methods for reducing risk (by hedging part of it, or by diversification). The main methods for reducing risk are now credit default swaps (a single-name product) and collateralized debt obligations (a multi-name product). These are rapidly growing markets. The fact that large bankruptcies like Enron and Worldcom had relatively little impact on any single institution was largely due to the use of instruments like these. In discussing default probabilities, be careful to distinguish between the conditional probability of default in time period i d i , and the unconditional probability of default in time period i . The latter is S i- 1 d i where S i is the probability of surviving until the end of year i . Notice that S i +1 = S i (1- d i ) and S = 1....
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- Fall '11