By Michael Duncan
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Additional info for Credit Derivatives: An introduction to the products, applications, participants and pricing.
Default probability). This can potentially result in confusion for the practitioner unless the relationship between the two is defined. e. h(t)dt is the probability of default between time t and time t + dt conditional on no default between time zero and time t). The default probability density, q(t) is defined such that q(t)dt is the unconditional probability of default between times t and t + dt as seen at time zero. Either h(t) or q(t) can be utilised in describing default probabilities. They provide equivalent information and the relationship between the two is t q(t ) h(t )e 0 h ( ) d (8) The table below shows the relationship between that of hazard rates and default probabilities.
Short Default Protection (sell CDS) Long Default Protection (buy CDS) = Long Risky Bond + Short Risk-free Bond = Short Risky Bond + Long Risk-free Bond However although correct, why use bonds when asset swaps are a more efficient alternative? Asset swaps99 Because a CDS can be synthetically replicated, CDS valuation does not have to be model dependent. Similarly it is a reasonable assumption to consider that the underlying cash market is efficient, on average. Asset swaps provide a pricing source for valuing default risk.
Options, Futures and Other Derivatives: Prentice Hall, 5 th Edition, 2000. MGSM 952, Research Project, November 2004, London Page 42 Credit Derivatives: An introduction to the products, applications, participants and pricing. This is demonstrated using the same financial data as previously in the following table. 4136 Note that in calculating the default probability with a recovery amount, it results in a default probability that is higher than if no recovery amount is assumed. Which is a slight problem, as the probability of default should in theory be independent of the expected recovery amount (as recovery occurs after a default).
Credit Derivatives: An introduction to the products, applications, participants and pricing. by Michael Duncan