3 a total return swaps is an agreement to exchange

Info icon This preview shows pages 22–24. Sign up to view the full content.

View Full Document Right Arrow Icon
3. A total return swaps is an agreement to exchange the total return on a bond (or any portfolio of assets) for LIBOR plus a spread. The total return includes coupons, interest, and the gain or loss on the asset over the life of the swap . The spread over LIBOR received by the payer is compensation for bearing the risk that the receiver will default. The payer will lose money if the receiver defaults at a time when the reference bond’s price has decline. The spread therefore depends on the credit quality of the receiver and of the bond - 22 -
Image of page 22

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Study Notes: Risk Management and Financial Institutions By Zhipeng Yan issuer, and on the default correlation between the two. 4. Basket CDS - Add-up CDS provides a payoff when any of the reference entities default. - An n th -to-default CDS provides a payoff only when the nth default occurs. 5. CDOs - Cash CDO (based on bonds) - Synthetic CDO: the creator sells a portfolio of CDSs to third parties. It then passes the default risk on to the synthetic CDO’s tranche holders. The first tranche may be responsible for the payoffs on the CDS until they have reached 5% of the total notional principal;…; The income from the CDS is distributed to the tranches in a way that reflects the risk they are bearing. 6. Valuation of a basket CDS and CDO - The spread for an n th -to-default CDS and the tranche of a CDO is critically dependent on default correlation . As the default correlation increases the probability of one or more defaults declines and the probability of ten or more defaults increases. - The one-factor Gaussian copula model of time to default has become the standard market model for valuing an n th -to-default CDS or a tranche of a CDO. - Consider a portfolio of N firms, each having a probability Q(T) of defaulting by time T. Æ the probability of default, conditional on the level of the factor F, is 1 [ ( )] ( | ) [ ] 1 N Q T F Q T F N ρ ρ = - The trick here is to calculate expected cash flows conditional on F and then integrate over F. The advantage of this is that, conditional on F, defaults are independent. The probability of exactly k defaults by time T, conditional on F, is ! ( | ) (1 ( | )) !( )! k n k n Q T F Q T F k n k - Derivates dealers calculate the implied copula correlation rho from the spreads quoted in the market for tranches of CDOs and tend to quote these rather than the spreads themselves . This is similar to the practice in options markets of quoting B-S implied volatilities rather than dollar prices. - Correlation smiles : the compound correlation is the correlation that prices a particular tranche correctly. The base correlation is the correlation that prices all tranches up to a certain level of seniority correctly. In practice, we find that compound correlations exhibit a ‘smile’ with the correlations for the most junior (equity) and senior tranches higher than those for intermediate tranches. The base correlations exhibit a ‘skew’ where the correlation increases with the level of seniority considered.
Image of page 23
Image of page 24
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern