553.445/645: Interest Rate and Credit Derivatives Final Exam

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Final Exam (Take Home portion)

April, 2023

553.445/645:  Interest Rate and Credit Derivatives

Submit your spreadsheet work (along with this summary answer sheet) for the problems below through the portal, under Final Exam Module in Canvas.

Indicate your “bottom line” answers in the space provided below for each question (which will require a spreadsheet model to determine the solution).

This page should also be returned by Sunday, April 30th .

You may only use DerivaGem to check your answer, but not to use as your submission – we want your spreadsheet model.

This assessment is open-book and open notes, but you must work individually, with no collaboration.

Problem:          (a) (10) Consider the iTraxx Europe 5-year index (newly constituted).  With

quarterly payments and a quoted CDS spread on the index of 24 bps .  Find the corresponding     constant conditional default probability (conditional on no default in earlier periods) expressed as a default intensity.  Assume a 40% recovery rate, a correlation of 0.15, and that the term       structure of risk-free rates is flat at 3.5%.  (Hint:  Refer to the technique used in the spreadsheet for Example 25.2 – we are looking for the same default probability here, but with quarterly        periods – to facilitate the process described in Section 25.2.  Consider reconstructing Hull’s         result for Example 25.2 as a check.)

(b) (20) Price the equity tranche of the iTraxx Europe 5-year index – again with the assumptions stated above (and use your result from (a) for the constant hazard rate in     equation (25.6), as in Example 25.2) – but also assume a copula correlation of 0.15.  Use an    M=60 Gaussian quadrature to find the unconditional values necessary to determine the          solution.

(c) (15) If the quoted price on the equity tranche was 11.25%, what is the implied compound correlation and what is the implied base correlation.