In this paper, we implement a multi-variate extension of Dybvig (1988) Payoff Distribution Model that can be used to replicate not only the marginal distribution of most hedge fund returns but also their dependence with other asset classes. In addition to proposing ways to overcome the hedging and compatibility inconsistencies in Kat and Palaro (2005), we extend the results of Schweizer (1995) and adapt American options pricing techniques to evaluate the model and also derive an optimal dynamic trading (hedging) strategy. The proposed methodology can be used as a benchmark for evaluating fund performance, as well as to replicate hedge funds or generate synthetic funds.

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We propose optimal mean-variance dynamic hedging strategies in discrete time under a multivariate Gaussian regime-switching model. The methodology, which also performs pricing, is robust to time-varying and clustering risk observed in financial time series. As such, it overcomes the main theoretical drawbacks of the Black-Scholes model. To support our approach, we provide goodness-of-fit tests to validate the model and for choosing the appropriate number of regimes, and we illustrate the methodology using monthly S & P 500 vanilla options prices. Then, we present the associated out-of-sample hedging results in the context of harvesting the implied versus realized volatility premium. Using the proposed methodology, the Sharpe ratio derived from the strategy doubles over the Black-Scholes delta-hedging methodology.

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