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A company enters into a total return swap where it receives the return on a corporate...

A company enters into a total return swap where it receives the return on a corporate bond paying a coupon of 5% and pays LIBOR. Explain the difference between this and a regular swap where 5% is exchanged for LIBOR.

Assume that the default probability for a company in a year, conditional on no earlier defaults is x and the recovery rate is r The risk-free interest rate is 5% per annum. Default always occur half way through a year. The spread for a five-year plain vanilla CDS where payments are made annually is 120 basis points and the spread for a five-year binary CDS where payments are made annually is 160 basis points. Estimate x and r

Solutions

Expert Solution

a). In this case of a total return swap a company receives (pays) the increase (decrease) in the value of the bond. in the regular swap this does not happen.

b).  Estimating the recovery rate is fairly easy. The spread for the vanilla CDS should be 1- r times the spread for the binary swap. This means that 1-r equals 0.75. It follows that r = 0.25.

To find x, we search for the conditional annual default rate that leads to the present value of payments being equal to the present value of payoffs. Solver for the value of x, that causes the spread to be 120 basis points. The answer is 0.0155 or 1.55% per year.

With this default probability the present value of regular payments is 4.1245, the present value of the accrual payments is 0.0332, and the present value of payoffs is 0.0499.

jeff jeffy answered 2 years ago
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