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Caveats in Calibrating the OU Process

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This is a series where we aim to cover in detail various aspects of the classic Ornstein-Uhlenbeck (OU) model and the Ornstein-Uhlenbeck Jump (OUJ) model, with applications focusing on mean-reverting spread modeling under the context of pairs trading or statistical arbitrage. Given the universality and popularity of those models, the techniques discussed can easily be applied to other areas where the OU or OUJ model seems fit.

In this article, we aim to dive into the classic OU model, and illustrate the most common tasks encountered in applications:

1. How to generate an OU process.
2. Caveats in fitting an OU process.

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Minimum Profit Optimization: Optimal Boundaries for Mean-reversion Trading

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It is time to get down to the nitty-gritty of the implementation of a mean-reversion strategy.

The crux of implementing a mean-reversion trading strategy is to pinpoint the trade location. Apparently, we want to initiate a trade when the spread value has deviated considerably from its long-term mean. However, “a considerable deviation” is a rather vague description and needs to be quantified when it comes to trade execution. For the sake of convenience and clarity, I will use “boundary” to refer to the trade location and “spread” to both the spread of the long-short asset pairs and the value of the multi-asset portfolio in the remainder of this article.

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Sparse Mean-reverting Portfolio Selection

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“Buy low, sell high.” One cannot find a more succinct summary of a mean-reversion trading strategy; however, single assets that show stable mean-reversion over a significant period of time such that a mean-reversion trading strategy can readily become profitable are rare to find in markets today. Even if such gems were found, celebrating the discovery of the gateway to easy money could prove premature:

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Online Portfolio Selection: Mean Reversion

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Mean Reversion is an effective quantitative strategy based on the theory that prices will revert back to its historical mean. A basic example of mean reversion follows the benchmark of Constant Rebalanced Portfolio.
By setting a predetermined allocation of weight to each asset, the portfolio shifts its weights from increasing to decreasing ones. This module will implement four types of mean reversion strategies:

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