HEDGE FUNDS AS KNOCK-OUT OPTIONS MARCOS ESCOBAR STEFAN KR ¨ AMER FLORIAN SCHEIBL LUIS SECO RUDI ZAGST Abstract. This paper introduces a new theoretical framework to price hedge funds’ equity. It is inspired on the famous framework of Black and Scholes for the valuation of companies’ equity as call options. Our structural model describing hedge funds uses barrier options (i.e. down-and-out call options as well as up-and-out put options) to allow for the special structure of hedge funds’ debt position. The quality of these models is evaluated by its capability to reproduce a high range of historical hedge fund returns. Different variations of the model are compared using this criteria. To fit the model parameter to real hedge fund data the method of moments is used. The application of the models to a set of over 1000 hedge funds showed that the model fits the first four moments of the real returns quite well. Especially the documented stylized features of high kurtosis and skewness are very wellcaptured by this model. Key Words: hedge fund replication, barrier options, leverage, fitting 1. Introduction Although the beginnings of hedge funds are now more than 50 years ago they had their breakthrough in the last decade. Especially big crashes like that of famous LTCM led to more public attention on hedge funds. 1 Again, in the subprime crisis in the summer of 2007 hedge funds got return to the public eye: Some for gaining tremendous returns because they anticipated the crisis, others for beeing closed because of bankruptcy. 2 It is very difficult to explain the past returns of hedge funds because of two reasons, first a lack of information about the company’s portfolio, secondly the tme sparsity of data. This is the nature of hedge funds. The strategy is the core asset of a hedge fund. Often anomalies in the capital markets or opportunities for statistical arbitrage are exploited. Therefore it is obvious that predicting the behaviour of hedge funds is an even more challenging task in the future. Most models try to explain hedge fund returns using very sophisticated and complex approaches. For example, several techniues have been developed to identify the structure of the Date : Version: Jan 28, 2009. 1 cp. Edwards (1999) 2 cp. Acharya (2007) cp. Teo (2007) 1