以球狀蒙地卡羅模擬法，評價匯率連動選擇權

On Pricing Quanto Options with Spherical Monte Carlo Simulation

匯率連動選擇權(Quanto Options)為一同時考量外國資產與匯率之新奇選擇權，其提供投資人於投資外國資產的同時，得以避免匯率風險之保護機制。隨著全球化的快速蔓延以及國外投資機會，該類選擇權可以使投資人有效率地對匯率風險進行避險。Generalized Autoregressive Conditional Heteroskedasticity (GARCH)模型具有捕捉資產報酬時間序列之波動率群聚與厚尾的實證現象，然而此模型於該選擇權定價上無法得到封閉解。因此，如何準確及有效地評價匯率連動選擇權成為一重要議題。本文介紹球狀蒙地卡羅方法，並應用於匯率連動選擇權於GARCH模型下的定價。透過數值分析，我們驗證了所提的球狀蒙地卡羅法可以有效降低變異數並縮短計算時間。

"Quanto options are financial options that involve a foreign stock of interest and its exchange rate. Alone with the rapid spread of globalization and foreign investment opportunities, quanto options enable investors to effectively hedge exchange rate risk. The generalized autoregressive conditional heteroskedasticity (GARCH) model allows to capture stylized features such as fat tail and volatility clustering of financial time series data. However, there exists no closed-form formula for the price of quanto options under GARCH model. Therefore, pricing quanto options accurately and efficiently is of considerable importance. To tackle this problem, this paper introduces a spherical Monte Carlo simulation scheme and applies it to price quanto options. Our numerical experiments confirm the superiority of the proposed spherical estimator in terms of variance reduction and computing time."