Optimal Allocation Between Subprime Structured Mortgage Products and Treasuries

This conference paper discusses a risk allocation problem for subprime investing banks involving investment in subprime structured mortgage products (SMPs) and Treasuries. In order to solve this problem, we develop a L'evy process-based model of jump diffusion-type for investment choice in subprime SMPs and Treasuries. This model incorporates subprime SMP losses for which credit default insurance in the form of credit default swaps (CDSs) can be purchased. In essence, we solve a mean swap-at-risk (SaR) optimization problem for investment which determines optimal allocation between SMPs and Treasuries subject to credit risk protection via CDSs. In this regard, SaR is indicative of how much protection investors must purchase from swap protection sellers in order to cover possible losses from SMP default. Here, SaR is defined in terms of value-at-risk (VaR). Finally, we provide an analysis of the aforementioned optimization problem and its connections with the subprime mortgage crisis (SMC).

• MP. Mulaudzi
• MA. Petersen
• J. Mukuddem-Petersen
• IM. Schoeman
• B. de Waal
• JM. Manale

• Investors; Jump Diffusion Process
• Structured Mortgage Products
• Treasuries
• Credit Risk
• Credit Default Swaps
• Tranching Risk
• Counterparty Risk
• Value-at-Risk
• Swaps-at-Risk
• Subprime Mortgage Crisis.

[1] D. Cuoco and H. Liu, An analysis of VaR-based capital requirements.
Journal of Financial Intermediation, 15, 362-394 (2006).
[2] FJ. Fabozzi, X. Cheng and R-R. Chen, Exploring the components of
credit risk in credit default swaps, Finance Research Letters, 4, 10-18
(2007).
[3] Gorton, G. B. (2008). The subprime panic. Yale ICF Working Paper, 08,
25, Available: http://ssrn.com/abstract=1276047.
[4] J. Hull , M. Predescu and A. White, The relationship between credir
default swap spreads, bond yields and credit rating announcements,
Journal of Banking and Finance, 28, 2789-2811 (2004).
[5] MA. Petersen, MP. Mulaudzi , IM. Schoeman and J. Mukuddem-Petersen,
A note on the subprime mortgage crisis: Dynamic modeling of bank
leverage profit under loan securitization. Applied Economic Letters,
17(15), 1469-1474 (2010).
[6] MA. Petersen , MC. Senosi and J. Mukuddem-Petersen, Subprime
Mortgage Models, New York: Nova Science Publishers, ISBN: 978-1-
61728-694-0 (2011).
[7] MA. Petersen , MC. Senosi , J. Mukuddem-Petersen , MP. Mulaudzi
and IM. Schoeman, Did bank capital regulation exacerbate the subprime
mortgage crisis ? Discrete Dynamics in Nature and Society, 2009, Article
ID 742968, 37 pages (2009).
[8] R. Cont and P. Tankov, Financial Modelling with Jump Processes.
Chapman & Hall/CRC (2004).
[9] RC. Merton, Continuous-Time Finance (2nd Edition). Cambridge,
Massachusetts: Blackwell Publishers (1992).
[10] Y. Demyanyk and O. Van Hemert, Understanding the subprime mortgage
crisis. Available at SSRN: http://ssrn.com/abstract=1020396 (19 August
2008).