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

Gian Luca Tassinari and Corrado Corradi ()

Quantitative Finance, 2013, vol. 13, issue 12, 1991-2010

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.

Date: 2013
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DOI: 10.1080/14697688.2012.749574

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