14 hours agoIntroduction to Expectation Maximization algorithmExpectation 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…Em Algorithm8 min read

May 14Cointegration-based multivariate statistical arbitrageIn this article I will implement and backtest a strategy based on a paper ‘Trading in the Presence of Cointegration’ (Galenko et al. 2009). …Pair Trading9 min read

May 3Granger causality test in pairs tradingMany traditional pairs trading strategies use cointegration tests for pair selection. If a pair of stocks is found to be cointegrated then this pair is accepted for trading. In this article I will check if using Granger causality test in pair selection process can improve the performance of such strategies…Pair Trading7 min read

Apr 27Quasi-multivariate pairs tradingThis article is based on a paper ‘M of a kind: A Multivariate Approach at Pairs Trading’ (Perlin, 2007). In this paper author proposes using an artificial portfolio of assets to generate trading signals for a particular stock. It is not a pairs trading strategy in a traditional sense because…Finance9 min read

Apr 23Pairs trading with Markov regime switchingIn this article I am going to test a pairs trading strategy based on the paper ‘A regime-switching relative value arbitrage rule’ (Bock and Mestel, 2009). It describes how to use Markov regime switching models to identify trading signals in pairs trading strategies. The main reasoning behind this idea is…Pair Trading7 min read

Apr 1Pairs trading with copulasTwo previous articles were dedicated to describing the general idea behind copula and different copula families. Now we can apply these ideas to implementing a pairs trading strategy. In this article I am going to implement and backtest a strategy based on paper ‘Trading strategies with copulas’ by Stander at…Copula7 min read

Mar 20Introduction to copulas (Part 2)In this article I’m going to describe several more advanced copula functions (compared to the ones described in the previous part). I will consider copulas from Archimedean family — Clayton, Gumbel, Frank and Joe copulas. …Copula8 min read

Mar 9Introduction to copulas (Part 1)Copula is a method of modeling dependencies between several variables, which is widely used in finance. In this article I will try to describe its basic principles and demonstrate how it works on simple examples. I assume that the reader is familiar with basic probability theory and understands the concepts…Copula9 min read

Feb 22Modeling marginal returnsSometimes in finance it is necessary to model marginal returns of a given asset. Marginal in this case means that there are no serial correlations between returns in different time periods (returns are independent and identically distributed). A couple of examples: We might believe that returns of a certain asset…Algorithmic Trading6 min read

Feb 14Pairs trading. Modeling the spread with mean-reverting Gaussian Markov chain modelThis article is based on the paper ‘Pairs Trading’ by Elliot et al. (2005). The paper describes how we can model the spread as a mean-reverting Gaussian Markov chain observed in Gaussian noise and how to calibrate such model from market observations. I will implement one of the proposed algorithms…Pair Trading8 min read