A new lattice approach for risk-minimization hedging under generalized autoregressive conditional heteroskedasticity models
提出一种统一的柳树方法，用于在广义自回归条件异方差模型下高效计算欧式期权的局部和全局风险最小化对冲策略，生成每个离散时间步的期权值和对冲比率表，并在低频对冲中表现稳健。
This paper explores the calculation of risk-minimization hedging strategies, specifically local and global risk minimization strategies for contingent claims under affine and non-affine GARCH models with the known closed forms of its first four moments across times under the physical measure. A unified and efficient willow tree method is introduced for various GARCH models. Unlike methods that provide option values and hedging ratios solely at the inception time, the proposed willow tree method generates a comprehensive table of option values and hedging ratios at each discrete time step across possible asset prices. Additionally, the method showcases robust performance in hedging at lower frequencies than the underlying asset’s modeling frequency (e.g., weekly or monthly hedging using a daily GARCH model). Lastly, the willow tree method outperforms the Monte Carlo method, offering greater efficiency, accuracy, and flexibility in solving risk-minimization hedging problems. • Propose a unified tree structure for GARCH models. • Efficiently and accurately compute quadratic risk-minimization for hedging European options. • Demonstrate robust performance at lower hedging frequencies.