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In light of the fact that no existing tree algorithms can guarantee the recombination property for general Ornstein-Uhlenbeck processes with time-dependent parameters, a new trinomial recombination-tree algorithm is designed in this research. The proposed algorithm enhances the existing mechanisms in interest-rate modelings with the comparisons to [1,2] methodologies, and the proposed framework provides a more efficient way in discrete-time mean-reverting simulations.
Alternative alpha represents risk-adjust absolute return of an alternative investing instrument regressed on alternative risk factors. Over the years, the definition is extended to the absolute return generated from alternative asset speculation-long-only or long-short strategy on alternative assets to generate additional return on top of existence alpha. In this article, we examine and propose a model with state-dependent stochastic differential equations based on Gaussian mixture model and multi-class Gaussian-kernel support vector machine to analyze hedge fund ETF alpha. We provide a new type of long-short speculation which trades on hedge fund strategies. This long-short alternative portfolio is build based on a Sharpe-ratio-like alpha ratio optimization program, and the historical performance from the portfolio shows statistically significant improvement adding to existing alphas. For passive investors, the portfolio also yields a simple portable alpha strategy which outperforms the S&P 500 benchmark return by 7.8% since 2012.