- 學位論文
回顧選擇權之評價模式探討～以歐元與日圓為例
Pricing Lookback Option ~ Cases of Euro and Japanese Yen
摘要
本研究主要以歐元與日圓之匯率為標的資產，利用解析式分析法、蒙地卡羅模擬法以及二項式法三種評價模式，對各類型回顧選擇權進行評價模擬，探討其在評價上之優缺點及各項參數變動對價格產生之影響。經過實證模擬分析，本研究得到以下幾點結論： 一、三種評價模式所計算出之結果皆相當接近，表示三種模式所得之評價結果皆具有參考價值，其中蒙地卡羅模擬法所求得之買權價值較其他為低，即蒙地卡羅法之買權評價結果通常會比較便宜，因此對投資人而言，相對較為有利。 二、解析式分析法由於只能求出唯一封閉解，因此只適用於歐式選擇權之評價，不過計算上較為單純，計算效率較佳，故在評價歐式選擇權時為較佳的選擇。 三、由於蒙地卡羅模擬法要使用時間切割，且須自標準常態分配中隨機抽樣，經過上萬次重複模擬加總平均後再折現求得買權價值，故計算效率較差，因此較不適用於評價美式選擇權。 四、二項式法須經過一定次數的推演，計算的選擇權價值才會收斂至一穩定值，因此計算上相當耗時，但由於其在運算過程中，容易加入美式選擇權的調整運算，因此在評價美式選擇權時，是較佳的評價方法。 五、根據敏感度分析，歐式回顧選擇權買權與即期匯率、匯率波動性、國內無風險利率呈現正相關趨勢，與國外無風險利率及契約期間呈現負相關趨勢。
並列摘要
The purpose of this study is to pricing lookback option by using the Analytic Model, Monte Carlo Simulation Model, and the Binomial Model. The underlying assets of this investigation were Euro and Japanese Yen. This work explores the advantages and disadvantages of three models, and explores the change of parameters on value of start option by adjusting the value ofparameters. According to the initiative experiment, we can reach the following conclusion: 1. The call option prices obtained by these three pricing models should be useful for reference. However, the call price obtained by the Monte Carlo Simulation Model was cheaper than those obtained by other two methods. This means that the Monte Carlo Simulation Model is the most appropriate one for investors. 2. The Analytic Model could only be used for pricing the European Options because it obtains only one closed-solution. Actually, it is the best among three methods for valuing the European Options, because the calculation procedure is pimple and effective. 3. since the Monte Carlo Simulation Model has to be used by discrete time intervals and to repeat the initative tests for more than 10,000times the efficiency of this model is worse than the other two methods. Consequently, the Monte Carlo Simu;ation Model is not appropriate for pricing the American Options. 4. Although the Binomial Model was reqrired to be subdivided into many times calculations then the prices can converge to a stable condition, yet it is easy to adjust the parameters. Therefore, the binomial model is the best choice among the three methods for pricing the American Options. 5. According to the empirical results of sensitivity analysis, the European-type lookback call option price had a positive correlation with spot exchange rate, volatility of the foreign exchange rates, the domestic risk-free rate and the time to maturity, but had negative correlation with international risk-free rate.
參考文獻
延伸閱讀
- 張麗卿（2003）。遠期生效選擇權之評價—以歐元和日元為例—〔碩士論文，中原大學〕。華藝線上圖書館。https://doi.org/10.6840/cycu200300498
- 陳文政（2001）。歐式多重履約標的選擇權評價模式之探討-以數值分析定價方法為例〔碩士論文，中原大學〕。華藝線上圖書館。https://doi.org/10.6840/cycu200100207
- 吳明政、王南喻（2007）。外匯選擇權買權市場之效率性檢測：以日圓和瑞士法郎為例。企業管理學報，(75)，77-100。https://www.airitilibrary.com/Article/Detail?DocID=10259627-200712-x-75-77-100-a
- 林文修、蘇敏龍（2016）。基因表達規劃法於外匯保證金交易投資策略之研究– 以歐元兌美元為例。管理資訊計算，5(2)，30-46。https://doi.org/10.6285/MIC.5(2).03
- 洪雅涵（2016）。The co-movement among Japan, USA and China’s economies with the change of the yen〔碩士論文，嶺東科技大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0103-2806201611042300