歐式障礙敲出選擇權在隨機波動下的靜態避險與定價

Abstract

本研究重新探討在 Heston 隨機波動模型下，針對歐式障礙選擇權的靜態避險投資組合（SHP）架構，並奠基於 Fink（2003）的開創性方法。Fink 的方法將障礙選擇權報酬拆解為多個波動率狀態下的歐式選擇權線性組合，但實務上往往難以取得所需的完整選擇權組合。 為了解決這項限制，我們採用 Chen、Hung、Ko 與 Wang（2024）所提出的兩種近似未來條件變異數的實用策略：一種是基於蒙地卡羅模擬，另一種則為解析近似方法。這些方法提供了估計變異數輸入的可行途徑，降低了對完整市場上歐式選擇權的依賴。雖然這些近似並非完全精確，但在隨機波動率環境下，它們提供了一種可處理的替代方案，使我們能透過系統性的數值分析來評估其成效。

This study revisits the static hedging portfolio (SHP) framework for barrier options under the Heston stochastic volatility model, building on the foundational work of Fink (2003). While Fink’s method decomposes exotic payoffs into linear combinations of European options across multiple volatility states, it requires an extensive set of options that may not be available in practice. To address this limitation, we adopt two practical strategies proposed by Chen, Hung, Ko, and Wang (2024) for approximating the conditional expectation of future variance: one based on Monte Carlo simulation and the other using an analytical approximation. These approaches offer a way to reduce reliance on a full set of market-traded options by estimating variance inputs from more accessible information. While not exact, these approximations provide a tractable alternative for SHP construction under stochastic volatility, allowing us to assess their effectiveness through systematic numerical analysis.