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Pairs Trading. Modeling the spread as Gaussian state-space model with exogenous inputs
This article is based on the paper ‘A new approach to modeling and estimation for pairs trading’ (Do et al. 2006). It is similar to another paper I described before, but authors propose modeling the spread on returns level instead of prices level and also extend the spread model to include exogenous inputs. Let’s start with describing the proposed model. The…
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Pricing derivatives with binomial tree model (Part 2)
In the previous article we discussed several simple examples to get a general intuition behind binomial tree pricing model. Now I want to describe that model in a little bit more abstract mathematical terms. Recall that we got a formula that can be used to price any derivative in 1-period binomial model. We also discussed…
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Pricing derivatives with binomial tree model (Part 1)
In this article I will describe a discrete model (binomial tree model) for pricing derivative contracts. Most of the books and online resources that I’ve found are either too technical (math-heavy) or too simplistic (just provide formulas without explaining why it actually works). It is especially true when it comes to continuous time models. One…
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Expectation Maximization for Logistic Mixture Autoregressive (LMAR) model
In this article I will describe my unsuccessful attempt to replicate simulation studies from the paper ‘Basket trading under co-integration with the logistic mixture autoregressive mode’ (Cheng et al. 2011). It describes statistical arbitrage strategy where the spread is assumed to follow logistic mixture autoregressive (LMAR) model. My initial idea was to implement and backtest such…
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Introduction to Expectation Maximization algorithm
Expectation Maximization (EM) algorithm is widely used for estimating parameters of different statistical models. It is an iterative algorithm that allows us to break one difficult optimization problem into several simpler problems optimization problems. In this article I will explain how it works on several simple examples. Probably the most popular example of this algorithm…
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Cointegration-based multivariate statistical arbitrage
In this article I will implement and backtest a strategy based on a paper ‘Trading in the Presence of Cointegration’ (Galenko et al. 2009). Statistical arbitrage strategies are based on the same principles as pairs trading strategies, but they involve trading in a portfolio of several cointegrated assets instead of just a pair. In the paper…