很多研究發現財務資料如匯率、利率及股票報酬存在馬可夫狀態轉換(Markov switching) 的現象，然而卻很少有文獻研究在Markov-switching 模型下，衍生性商品的評價問題。有鑑於此，本研究擬探討Markov-switching 模型下之選擇權評價數值方法。本文擬修正Duan, Popova and Ritchken (2002) 所提的Markov-switching 選擇權樹狀訂價法(DPR lattice) 之機率公式，以提高DPR樹狀訂價法的準確度。此外，本文亦探討當標的資產動態過程為Markov-switching 模型時，如何應用Least-squares Monte Carlo (LSM)模擬法進行選擇權評價。由於本文所提出的extended LSM模擬法運用較多的攸關(relevant) 資訊，故我們預期新的模擬方法會比既有的LSM模擬法更具效率。最後，由於大量文獻發現匯率資料存在Markov-switching現象，本文將運用 revised DPR樹狀訂價法及extended LSM模擬法探討在將狀態轉換風險(regime-shift risk) 納入考量後，外幣選擇權價格表現是否與標的資產之動態過程一致。 Many studies have provided evidences concerning to Markov switching in ?nancial time-series data, including exchange rates, interest rates and stock returns, whereas few ar- ticles address the valuation of derivatives under the Markov-switching framework. Accord- ingly, this research intends to investigate the numerical methods under Markov-switching option pricing models. We revise the inaccuracy probability formulae of the Markov- switching lattice algorithm (DPR lattice) proposed by Duan, Popova and Ritchken (2002), and investigate how to implement the Least-squares Monte Carlo (LSM) simulation when the dynamics of the underlying asset follows Markov-switching processes. By using the revised DPR prices as the benchmark, we will compare the performance of the extended LSM approach with that of the LSM counterpart. Since our extended LSM algorithm is capable of embedding more relevant information, we expect the new algorithm to perform better than the LSM counterpart does. We also plan to shed new light on exploring the relationship between the exchange rates and the currency option prices by taking the regime-shift risk into account based on our revised DPR lattice and the extended LSM algorithm
