Finding the Nearest Valid Covariance Matrix: A FX Market Case

European University at St. Petersburg Department of Economics Working Paper Ec-07/13

Posted: 26 Jun 2014

See all articles by Alexey Minabutdinov

Alexey Minabutdinov

National Research University Higher School of Economics

Ilia Manaev

Saint Petersburg State Polytechnical University - Institute of Computing and Control

Maxim Bouev

New Economic School (NES); European University at St.Petersburg

Multiple version iconThere are 2 versions of this paper

Date Written: June 6, 2014

Abstract

We consider the problem of finding a valid covariance matrix in the FX market given an initial non-PSD estimate of such a matrix. The standard no-arbitrage assumption implies additional linear constraints on such matrices, which automatically makes them singular. As a result, one cannot just take the given estimate plug it into the standard optimization problem and solve it by applying even the most advanced numerical techniques developed recently. The reason is that such a problem is not well-posed while the PSD-solution is not strictly feasible. In order to deal with this issue we described a low-dimensional face of the PSD cone that contains the feasible set. After projecting the initial problem onto this face, we come out with a reduced problem, which turns out to be well posed and of a smaller scale. We show that after solving the reduced problem the solution to the initial problem can be uniquely recovered in one step. We run numerous numerical experiments to compare performance of different algorithms in solving the reduced problem and to demonstrate the advantages of dealing with the reduced problem as opposed to the original one. The smaller scale of the reduced problem implies that virtually any numerical method can be applied effectively to find its solution.

Keywords: Covariance, Correlation matrix, FX

JEL Classification: C02, C63, C65

Suggested Citation

Minabutdinov, Alexey and Manaev, Ilia and Bouev, Maxim, Finding the Nearest Valid Covariance Matrix: A FX Market Case (June 6, 2014). European University at St. Petersburg Department of Economics Working Paper Ec-07/13. Available at SSRN: https://ssrn.com/abstract=2458817 or http://dx.doi.org/10.2139/ssrn.2458817

Alexey Minabutdinov

National Research University Higher School of Economics

Myasnitskaya street, 20
Moscow, Moscow 119017
Russia

Ilia Manaev

Saint Petersburg State Polytechnical University - Institute of Computing and Control ( email )

29 Polytechnicheskaya ul
St.Petersburg, 195251,
Russia

Maxim Bouev (Contact Author)

New Economic School (NES) ( email )

100A Novaya Street
Moscow, Skolkovo 143026
Russia

European University at St.Petersburg ( email )

3 Gagarinskaya Street
St. Petersburg, 191187
Russia

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