利用投資組合保險的觀念求解選擇權的價格

On Using the Portfolio Insurance Concepts to Value Options

許溪南(Hsi-Nan Hsu) ； 何怡滿(Emily Ho)

《Asia Pacific Management Review》 4卷4期 (1999/12) Pp. 357-367

https://doi.org/10.6126/APMR.1999.4.4.02

摘要

對於選擇權價格的計算，至今仍以Black and Scholes（1973）所提出的模式為主，甚少從其他不同的方向來思考，有鑑於此，本研究擬從投資組合保險的觀點來探討選擇權價格。本研究首先以蒙地卡羅模擬法（the Monte Carlo simulation method）得出股價，然後求算有保險的利益，進而得出賣權的價格，再依買權賣權平價模式（put-call parity）得出買權價格。最後將本研究的結果與Black-Scholes模式的結果作一比較，探討兩者是否有所不同。研究結果發現，不論是以不連續的動態過程，或是連續動態過程下所模擬出來的股價，再從投資組合保險的觀點求得選擇權價格，所得之結果均與Black-Scholes模式的結果差距不大。此結果的含意是，吾人似乎可從投資組合保險的觀點來評估選擇權的價格。

關鍵字

投資組合保險 ； 選擇權 ； 蒙地卡羅模擬法

並列摘要

The Black-Scholes option pricing model has perhaps the biggest impact on the option pricing. This paper uses a different way to calculate option prices. We uses the portfolio insurance concepts to value options. At first, the Monte Carlo method is used to get stock prices, and then insured profits are calculated. By the insured profits, we can get the put option prices. After using the put-call parity, we can get the call prices. Finally we compared our results with the results of Black-Scholes model. We find that whether using the discrete dynamic process or the continuous dynamic process to simulate stock prices, the option prices by using the portfolio insurance concepts do not differ from the results of Black-Scholes model. The findings indicate that the portfolio insurance concepts can be used to value options.

並列關鍵字

portfolio insurance ； option ； the Monte Carlo simulation method

參考文獻

許溪南 Hsu, Hsi-Nan、 黃凱靖 Huang, Kai-Ching(1998)。股價分配對選擇權定價之影響 The Impact of Stock Price Distributions on the Option Pricing。亞太管理評論 Asia Pacific Management Review。3(1)

Black, F., Scholes, M. S.(1973).The Pricing of Options and Corporate Liabilities.Journal of Political Economy.81(3)

Boyle, Phelim P.(1977).Options: A Monte Carlo Approach.Journal of Financial Economics.4

Clarke, Roger G., Arnott, Robert D.(1987).The cost of portfolio insurance: Tradeoffs and choices.Financial Analysis Journal.43(6)

Ingersoll, J.(1976).A Theoretical and Empirical Investigation of The Dual Purpose Funds: An Application of Contingent Claims Analysis.Journal of Financial Economics.3(1/ 2)