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Pricing equity and debt tranches of collateralized funds of hedge fund obligations: An approach based on stochastic time change and Esscher-transformed martingale measure

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  • Gian Luca Tassinari
  • Corrado Corradi

Abstract

Collateralized Funds of Hedge Fund Obligations (CFOs) are relatively recent structured finance products linked to the performance of underlying funds of hedge funds. The capital structure of a CFO is similar to traditional Collateralized Debt Obligations (CDOs), meaning that investors are offered different rated notes and equity interests. CFOs are structured as arbitrage market value CDOs. The fund of funds manager actively manages the fund to maximize total returns while limiting price volatility within the guidelines of the structure. The aim of this paper is to provide a useful framework to evaluate Collateralized Funds of Hedge Fund Obligations, that is pricing the equity and the debt tranches of a CFO. The basic idea is to evaluate each CFO liability as an option written on the underlying pool of hedge funds. The value of every tranche depends on the evolution of the collateral portfolio during the life of the contract. Care is taken to distinguish between the fund of hedge funds and its underlying hedge funds, each of which is itself a portfolio of various securities, debt instruments and financial contracts. The proposed model incorporates skewness, excess kurtosis and is able to capture more complex dependence structures among hedge fund log-returns than the mere correlation matrix. With this model it is possible to describe the impact of an equivalent change of probability measure not only on the marginal processes but also on the underlying dependence structure among hedge funds.

Suggested Citation

  • Gian Luca Tassinari & Corrado Corradi, 2013. "Pricing equity and debt tranches of collateralized funds of hedge fund obligations: An approach based on stochastic time change and Esscher-transformed martingale measure," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1991-2010, December.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:12:p:1991-2010
    DOI: 10.1080/14697688.2012.749574
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    3. Jim Clayton & David Geltner & Stanley W. Hamilton, 2001. "Smoothing in Commercial Property Valuations: Evidence from Individual Appraisals," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 29(3), pages 337-360, March.
    4. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    5. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    6. Chris Brooks & Harry. M Kat, 2001. "The Statistical Properties of Hedge Fund Index Returns," ICMA Centre Discussion Papers in Finance icma-dp2001-09, Henley Business School, University of Reading.
    7. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    8. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    9. Morton, David P. & Popova, Elmira & Popova, Ivilina, 2006. "Efficient fund of hedge funds construction under downside risk measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 503-518, February.
    10. Geltner, David Michael, 1991. "Smoothing in Appraisal-Based Returns," The Journal of Real Estate Finance and Economics, Springer, vol. 4(3), pages 327-345, September.
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    Cited by:

    1. Gian Luca Tassinari & Michele Leonardo Bianchi, 2014. "Calibrating The Smile With Multivariate Time-Changed Brownian Motion And The Esscher Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-34.
    2. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.

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