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

European Style Multi-Factor Option Pricing Approach-Numerical Analysis Pricing Method

陳文政(wen-cheng chen)

指導教授 ： 胡為善

中原大學/商學院/企業管理研究所/碩士(2001年)

https://doi.org/10.6840/cycu200100207

摘要

本研究透過二項式樹狀評價模式及蒙地卡羅模擬評價模式兩種評價方法來針對雙履約標的選擇權及兩種風險資產最大值與最小值選擇權進行評價，並比較此兩種模式所得到的選擇權價值，再調整各項參數值，以了解各參數的變動對選擇權價值所產生的影響。

由於股價的變動程度與選擇權的價值具有高度相關性，因此在履約資產的選取過程中，資產的股價波動度是一項重要的考量因素。本研究透過歷史價格波動度的計算選定IC製造業(聯電、旺宏)與DRAM製造業(力晶、鈺創)兩組共四檔股票作為履約標的。

本研究結論如下：
1.透過三個維度二項式樹狀及蒙地卡羅模擬所求得之雙履約價格選擇權、最大值與最小值選擇權之歐式買權價值極為接近，顯示出兩種評價結果相當準確。
2.由於蒙地卡羅模擬會產生標準誤差，所以三個維度二項式樹狀模擬比蒙地卡羅模擬更能穩定且精確地估計買權的真實價值。
3.因為DRAM產業的股票價格與股票之波動度均高於IC產業，所以以DRAM產業為履約標的的買權價值均高於以IC產業為履約標的之買權價值。
4.本研究藉敏感度分析發現買權契約的價格與履約標的股價及股價波動度成正向關係。但到期期間與買權價格則未必具有正向關係。

關鍵字

蒙地卡羅模擬 ； 兩種風險資產最大值與最小值選擇權 ； 三個維度二項式樹狀模擬 ； 雙履約價格選擇權

並列摘要

This study uses the binomial model and Monte Carlo simulation model to evaluate the dual-strike options, and options on the minimum or maximum value of two risky assets. This work attempts to compare the values obtained by these three models. Furthermore, this investigation explores the impact of the change in the various parameters on the option value by adjusting each parameter.

Since the extent of the stock price change is highly correlated with the options value, the volatility of stock price is a critical factor. Through calculating the historical volatility of stock price, the study chooses four stocks of two industry combinations as the underlying assets whose volatility of stock price are the most highest - IC manufacture industry (UMC、MXIC) and DRAM manufacture industry (PSC、Etron).

This study obtained four empirical results as follows:
1. The European call value of both options obtained by the binomial option pricing model and Monte Carlo simulation model are very close. It implies that the results of two pricing method are calculated accurately.
2. Since the Monte Carlo simulation will cause the error of estimation, three-dimensional binomial tree is more stable and accurate than Monte Carlo simulation method when one estimates the true value of call option.
3. Because the stock price and volatility of stock price of the DRAM industry are both higher than that of the IC industry, the call option value is higher when the underlying asset is DRAM industry.
4. Through sensitivity analysis, the value of call option has a positive relationship with the stock price and the volatility of stock price； Furthermore, the value of call option does not certainly have a positive relationship with the time to maturity.

並列關鍵字

Dual-Strike Options ； Monte Carlo simulation model ； Options on the minimum or maximum of two risky a ； Three-dimensional binomial tree.

參考文獻

Barraquand, J., and D. Martineau (1995): “Numerical Valuation of High Dimensional Multivariate American Securities”, Journal of Financial and Quantitative Analysis, 30(3), pp.383-405.

Boyle, P. P. (1977): “Options:A Monte Carlo Approach”, Journal of Financial Economics, 4, pp.323-338.

Boyle, P. P. (1988): “A Lattice Framework for Option Pricing with Two State Variables”, Journal of Financial and Quantitative Analysis, 23, pp.1-12.

Boyle, P.P., J. Evnine, and S. Gibbs (1989): “Numerical Evaluation of multivariate Contingent Claims”, Review of Financial Studies, 2, pp.241-250.

Boyle, P. P. and Y.K. Tse (1990): “An Algorithm for Computing Values of Options on the Maximum or Minimum of Several Assets”, journal of Financial and Quantitative Analysis, 25, 215-227.