We compute nonparametric and forward-looking option-implied quantile and expectile curves, and we study their properties on a 5-year dataset of weekly options written on the S&P 500 Index. After studying the dynamics of the single curves and their joint behaviour, we investigate the potentiality of these quantities for risk management and forecasting purposes. As an alternative form of variability mesaures, we compute option-implied interquantile and interexpectile differences, that are compared with a weekly VIX-like index. In terms of forecasting power we investigate how different quantities related to the implicit quantile and expectile curves predict future logreturns and future realized variances.

我们计算非参数性和前瞻性期权隐含的分位数和预期曲线，并在标普500指数所写的每周期权的5年数据集上研究它们的特性。在研究了单曲线及其联合行为的动力学之后，我们研究了这些数量在风险管理和预测方面的潜力。作为可变性度量的另一种形式，我们计算期权隐含的分位数和预期间差异，并与每周类似VIX的指数进行比较。在预测能力方面，我们研究了与隐式分位数和预期曲线相关的不同数量如何预测未来的对数回报和未来实现的方差。