Dissertation, Otto-Friedrich-Universität Bamberg, 2025

This thesis develops an advanced volatility smile construction technique to improve the estimation of option-implied risk measures in the presence of sparse and noisy market data. By combining arbitrage-free RND tail modeling for smile extrapolation with a convexity-preserving spline for smile interpolation, the method enhances the accuracy of key risk metrics such as the VIX and the Rare Disaster Concern Index (RIX). An augmented version of the approach is also introduced to accommodate potentially bimodal RNDs, capturing more complex market features. A comprehensive review of option-implied risk measures is provided, alongside a critical evaluation of existing smile modeling approaches and their limitations. A thorough numerical analysis and empirical application demonstrate the proposed method’s superior robustness and precision compared to standard techniques. This research advances risk management by providing more reliable forward-looking risk measure estimates derived from option prices.