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Matching a Distribution by Matching Quantiles Estimation.

Nikolaos Sgouropoulos, Qiwei Yao, Claudia Yastremiz

    Journal of the American Statistical Association
    |December 23, 2015
    PubMed
    Summary
    This summary is machine-generated.

    We introduce Matching Quantiles Estimation (MQE) to select representative portfolios for credit risk backtesting. This method matches target distributions using linear combinations of random variables, offering flexibility with optional sparsity and quantile range restrictions.

    Keywords:
    Goodness-of-matchLASSOOrdinary least-squares estimationPortfolio trackingRepresentative portfolioSample quantile

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    Area of Science:

    • Quantitative Finance
    • Risk Management
    • Statistical Modeling

    Background:

    • Selecting representative portfolios is crucial for accurate backtesting of counterparty credit risks.
    • Existing methods may lack the flexibility to precisely match complex target distributions.

    Purpose of the Study:

    • To propose a novel Matching Quantiles Estimation (MQE) method for distribution matching.
    • To develop a robust estimation procedure and analyze its statistical properties.
    • To demonstrate the practical application of MQE in financial risk management.

    Main Methods:

    • Developed an iterative ordinary least-squares estimation (OLS) procedure for MQE.
    • Incorporated LASSO penalty for sparse representations and quantile range restrictions for partial distribution matching.
    • Established convergence and asymptotic properties of the MQE algorithm, with and without LASSO.
    • Proposed a goodness-of-match measure and statistical test.

    Main Results:

    • The MQE method effectively matches target distributions using linear combinations of random variables.
    • The iterative OLS-based algorithm demonstrates convergence.
    • Theoretical properties (convergence, asymptotic behavior) are established for MQE with and without LASSO.
    • Simulations and a real-world dataset application confirm the method's efficacy in portfolio selection and tracking.

    Conclusions:

    • MQE provides a flexible and statistically sound approach for distribution matching in quantitative finance.
    • The method is effective for selecting representative portfolios for counterparty credit risk backtesting and portfolio tracking.
    • The combination of MQE with LASSO enhances its applicability for sparse and targeted distribution matching.