在隨機利率下具重載特質之員工選擇權的評價

The Valuation of Employee Reload Options with Stochastic Interest Rates

鄭濰昌(Wei-Chang Cheng)

指導教授 ： 張傳章

國立中央大學/管理學院/財務金融學系/碩士(2006年)

摘要

過去的文獻提供數種對於具重載特質之員工選擇權的定價方法。這些評價方法皆假設無風險利率為常數。然而具重載特質之員工選擇權的到期日相對於市場上其它型態的選擇權為長，因此我們認為將利率的變動納入評價中是合宜的。在本篇論文中，使用不同於過去文獻中所提供評價具重載特質之員工選擇權的方法，我們修改 Hull and White (1993) 的模型並且應用在評價具重載特質之員工選擇權。接著將修改後的 Hull and White (1993) 的模型與 Hillard, Schwartz, and Tucker (1996) 的模型合併後,評價隨機利率下具重載特質的員工選擇權。結果發現到期日越長，具重載特質之員工選擇權的價格在隨機利率與假設利率為常數之間的差也較大，並且當股價波動率越大時，這兩者之間的差距也越小。我們認為這是由於影響具重載特質之員工選擇權的主要因子為股價，而利率的影響相對而言較為薄弱之故。

關鍵字

具重載特質之員工選擇權 ； 隨機利率

並列摘要

In the previous published literature, there are several methods for pricing employee reload options. All of them assume that the interest rate is constant. However, maturity of employee reload options is always longer than that of financial options in practice. Hence we think that it is more appropriate to value employee reload options with stochastic interest rates. In this study, we first modify the Hull and White (1993) model to fit the properties of reload options. We then combine the modified Hull and White (1993) model and Hilliard, Schwartz, and Tucker (1996) model to value employee reload options with stochastic interest rate. From numerical results, we find two interesting results. One is that the percentage of the difference between employee reload options with stochastic interest rates and with constant interest rates is larger when maturity of employee reload options is relatively long. The other is that the volatility of the stock price increases, the difference between employee reload options with stochastic interest rate and that with constant interest rate decreases. We find that the major factor which decides the value of reload options is the underlying stock price.

並列關鍵字

Employee reload options ； Stochastic interest rates

參考文獻

Benninga, S., T. Bjork, and Z. Wiener, 2002, “On the Use of Numeraires in Option Pricing”, The Journal of Derivatives, winter, 43-58.

Dai, M. and Y. K. Kwok, 2004, “Valuing employee reload options under the time vesting requirement”, Quantitative Finance, February, 61-69.

Dybvig, P. H. and M. Loewenstein, 2003, “Employee Reload Options: Pricing Hedging, and optimal exercise”, The Review of Financial Studies, spring, 145-171.

Hemmer, T., S. Matsunaga, and T. Shevlin, 1998, “Optimal Exercise and Cost of Granting Employee Stock Options with a Reload Provision”, Journal of Accounting Research, autumn, 231-255.

Hilliard, J. E., A. L. Schwartz, and A. L. Tucker, 1996, “Bivariate Binomial Options Pricing with Generalized Interest Rate Processes”, The Journal of Financial Research, winter, 585-602.