後定選擇權之評價與模擬分析

The Pricing and Simulation Analysis of Chooser Option

邱育寬(Yu-Kuan, Chiu)

指導教授 ： 胡為善

中原大學/商學院/企業管理研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200063

摘要

台灣加入WTO後，需立即逐步開放本國的金融市場及新金融商品。其中選擇權市場在國外的交易早已非常的熱絡且為外商所熱愛操作的新金融商品。我國期交所與證交所均為了因應此種趨勢，均積極籌畫各種選擇權契約交易市場。目前僅於2001年推出台指選擇權，為我國選擇權交易市場的第一個商品。預期不久的將來也將陸續推出各種選擇權商品。
本研究主要在於探討新奇選擇權之中的後定選擇權，並藉由修正後二項式模型、修正後三項式模型與分析性模式三種方法，來探討後定選擇權的評價過程。並探討在上述的三種方法下，調整各個參數的數值對選擇權價值的影響，並比較各方法間的差異性。研究對象為西元2000年3月的台灣總統大選與11月美國總統大選兩個重大事件。本研究實證結果主要有：
1. 修正後二項式與修正後三項式的最小收斂步驟（MCS）分析中，考慮精確度5%的情況下，本研究選擇n=300作為模擬分析的基礎。
2. 修正後三項式的收斂步驟會低於修正後二項式之收斂步驟，且修正後三項式的精確度也高於修正後二項式之精確度。
3. 有關三種方法評價與模擬方面，本研究發現修正後二項式與修正後三項式模式計算出的後定選擇權之價值相差在0.1% 之內，甚至沒有未產生誤差，顯示以修正後二項式與修正後三項式模型來評價後定選擇權具有相當高的參考價值。但就整體而言，修正後二項式的評價較結果會高估後定選擇權的價值。
4. 在調整標的物的個別參數，分析其對於後定選擇權的影響時，本研究發現當履約價與現價的比值（S/K）若偏離1越遠時，後定選擇權的價值就會越大。
5. 透過兩種不同產業別的比較分析，本研究可發現標的物的波動程度（σ）與決定買賣權的時間（t1）對於後定選擇權的影響程度均不大，但最大的影響來源是在於現價與履約價的大小（以台塑與台積電為例）。這點與其他選擇權之撥動性影響最大有所不同，因此，在訂定後定選擇權價值時，必須要慎重考慮到現價與履約價格。

關鍵字

修正二項式模式 ； 修正三項式模式 ； 後定選擇權 ； 新奇選擇權

並列摘要

Taiwan has been in WTO since 2001. Financial markets as well as all financial instruments should be open to all members. Among various financial markets, option market transactions have been very active and all kinds of options become very popular by international traders. TAMEX and TSEC have aggressively planned to open the option contract-traded market。Up to now, they provided TAIEX Option at the end of 2001, and became the first product of the option transaction system. There will be a lot of option products provided in the future.
The purpose of this study concentrates on chooser option of exotic option. Using three methods, including the closed-form model, the revised binomial tree model, and the revised Trinomial tree model, this work analyzes the valuation process of chooser option. In addition to the tree methods mentioned above, this investigation adjusts the amount of parameters to check how the option value will be affected and compare the differences among these methods. The sampling is between two important events including the election of Taiwan and USA in 2000. The empirical results are as follows:

(1) In the analysis of the Minimum Convergence Step (MCS) of the revised binomial tree model and the revised Trinomial tree model, and with the condition of precision by 5%, this study chooses n=300 as the basis of the next simulation.
(2) The MCS of the revised Trinomial tree model was lower than the revised binomial tree model. In addition, the revised Trinomial tree model had better precision than the revised binomial tree model.
(3) Regarding the simulation of three models, this study finds that the chooser option values obtained by the revised binomial tree model and the revised Trinomial tree model had only 0.1% differences. The result shows that the revised binomial tree model and the revised Trinomial tree model are accurate methods. This work also finds that the option value of the revised binomial tree method has been overvalued compared with that of the revised Trinomial tree model.

(4) By adjusting the parameters of the underlying assets and analyzing the impact on chooser option, this study finds that the further the ratio between stock price and strike price (S/K) deviates from 1, the greater value of chooser option.
(5) According to the comparison analysis of two industries, this work finds the volatility, and the decision time of buying or selling only had a little influence on option value, which is contrary to other findings. However, the highest on option value is stock price Vs strike price, such as TSMC and FPC. As a result, when pricing the value of chooser option, one should carefully consider the difference price between stock price and strike price.

並列關鍵字

the revised trinomial tree model ； Chooser option ； the revised binomial tree model ； Exotic option

參考文獻

Boyle, P. P., 1988, “A Lattice Framework for Option Pricing with Two State Variables,” Journal of Financial and Quantitative Analysis, Vol. 23, No.1, pp.1-12.

Boyle, P. P., and S. H. Lau, Summer 1994, “Bumping Up Against the Barrier with Binomial Method,” Journal of Derivatives,, pp.6-14.

Cox, John. C., Stephen A. Ross, and Mark Rubinstein., 1979, “Option Pricing：A Simplified Approach,” Journal of Financial Economics, Vol.7, pp.229-263.

Galitz L. C., 1994, Financial Engineering, Irwin, pp.310.

Garman, M. B., and M. J. Klass, 1980, “On the Estimation of Security Price Volatilities from Historical Data,” Journal of Business, Vol. 53, No.1, pp.67-78.