Summary: Estimating financial risk is a critical issue for banks and insurance companies. Recently, quantile estimation based on extreme value theory (EVT) has found a successful domain of application in such a context, outperforming other methods. Given a parametric model provided by EVT, a natural approach is maximum likelihood estimation. Although the resulting estimator is asymptotically efficient, often the number of observations available to estimate the parameters of the EVT models is too small to make the large sample property trustworthy. In this paper, we study a new estimator of the parameters, the maximum \(L_q\)-likelihood estimator (ML\(q\)E), introduced by D. Ferrari and Y. Yang [“Estimation of tail probability via the maximum \(L_q\)-likelihood method”, Technical Report 659, School of Statistics, University of Minnesota (2007)]. We show that the ML\(q\)E outperforms the standard MLE, when estimating tail probabilities and quantiles of the generalized extreme value (GEV) and the generalized Pareto (GP) distributions. First, we assess the relative efficiency between the ML\(q\)E and the MLE for various sample sizes, using Monte Carlo simulations. Second, we analyze the performance of the ML\(q\)E for extreme quantile estimation using real-world financial data. The ML\(q\)E is characterized by a distortion parameter \(q\) and extends the traditional log-likelihood maximization procedure. When \(q\to 1\), the new estimator approaches the traditional maximum likelihood estimator (MLE), recovering its desirable asymptotic properties; when \(q\neq 1\) and the sample size is moderate or small, the ML\(q\)E successfully trades bias for variance, resulting in an overall gain in terms of accuracy (mean squared error).