2008-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/693499摘要：靜態避險投資組合有二種表示方法：第一種方法，由Bowie 與 Carr (1994)，Carr、Ellis與 Gupta (1998)等提出，是使用具有相同之履約到期日，但不同履約價格之連續標準選擇權組成靜態避險投資組合，此組合價值能夠在到期日與邊界上與原先之新奇式選擇權的報酬相同。第二種方法，由Derman、Ergener與Kani (1994, 1995)建立，則是使用具有相同之履約價格，但不同履約到期日之連續標準選擇權組成靜態避險投資組合，此組合價值能夠在到期日與邊界上與原先之新奇式選擇權的報酬相同。我們的美式選擇權之靜態避險投資組合，則是同時運用不同的履約價格與不同的履約到期日。本計畫試著解決下列問題： 1. 假設股價遵循幾何布朗運動、Merton式的跳躍擴散以及CEV，分別使用靜態複製法評價一般型美式選擇權並與文獻作數值評價效率上比較。 2. 分別分析一般型美式選擇權Black-Scholes、Merton式的跳躍擴散模型以及CEV模型下鄰近履約到期日時之履約邊界。 3. 針對一般型美式選擇權，比較靜態複製法與動態避險法對於不同的隨機過程，諸如Black-Scholes、Merton式的跳躍擴散模型以及CEV模型下的避險表現。 4. 將靜態複製法擴充至評價美式障礙選擇權，在Black-Scholes，Double Exponential Jump Diffusion模型以及CEV模型下進行評價。 5. 分別分析美式障礙選擇權在Black-Scholes，Double Exponential Jump Diffusion模型以及CEV模型下鄰近履約到期日時之履約邊界，並與一般型美式選擇權做一比較。 <br> Abstract: In the literature, the static hedge portfolios are formulated in two different ways. The first approach, proposed by Bowie and Carr (1994), Carr, Ellis, and Gupta (1998), etc., is to construct static positions in a continuum of standard options of all strikes, with the maturity date matching that of the exotic option. The second approach, developed by Derman, Ergener, and Kani (1994, 1995), uses a standard option (matching the boundary at maturity of the exotic option) and a continuum of standard options (matching boundary before maturity of the exotic option) of all maturities from time 0 to time , with the same strikes. Our static hedge portfolios of American options take advantages of both approaches by using multiple strikes and multiple maturities. We try to solve the following problems: 1. We use static hedging method to price plain vanilla American options and investigate if static hedging method is more numerically efficient than the other methods in the literature under Black-Scholes model, jump diffusion model of Merton and constant elasticity of variance model. 2. We analyze the early exercise boundary of plain vanilla American options near expiration under Black-Scholes model, jump diffusion model of Merton and constant elasticity of variance model. 3. We compare the hedge performance of static hedging method and dynamic hedging method for plain vanilla American options under Black-Scholes model, jump diffusion model of Merton and constant elasticity of variance model. 4. We extend the static hedge portfolio method to price American barrier options under Black-Scholes model , Double Exponential Jump Diffusion model and CEV model. 5. We analyze the early exercise boundary of American barrier options near expiration under Black-Scholes model, Double Exponential Jump Diffusion model and constant elasticity of variance model. These results will be compared with those of plain vanilla American options.靜態避險一般型美式選擇權美式障礙選擇權履約邊界避險表現static hedgingplain vanilla American optionsAmerican barrier optionsearly exercise boundaryhedge performance