The Valuation of Employee Reload Options with Stochastic Interest Rates

Abstract

This paper proposes an adjusted binomial approach to price employee reload options (EROs) under the assumption of stochastic interest rates. We generalize Hull and White's (1993) model by incorporating the bivariate binomial approach to adapt the valuation of EROs to a stochastic interest rate economy. The numerical analysis reveals that the differences between values of EROs considering stochastic interest rates and those considering constant interest rates increase with correlations between stock prices and interest rates, but decrease as volatility of stock return increases. These results suggest that interest rates are important determinants in the valuation of EROs.本文將Hull and White（1993）模型一般化，並加入雙變數二元樹方法，使其能在隨機利率假設下評價具重載特質之員工選擇權。數值分析結果顯示：分別考慮隨機利率與固定利率之具重載特質員工選擇權價值，其兩者差異會隨股價與利率的相關係數增加而增加，但會隨著股票報酬波動性的增加而減少。此結果顯示利率為決定此類選擇權價值之重要因素。