Summary: This paper focuses on techniques for constructing Bonus-Malus systems in third party liability automobile insurance. Specifically, the article presents a practical method for constructing optimal Bonus-Malus scales with reasonable penalties that can be commercially implemented. For this purpose, the symmetry between the overcharges and the undercharges reflected in the usual quadratic loss function is broken through the introduction of parametric asymmetric loss functions of exponential type. The resulting system possesses the desirable financial stability property.