The reload provision in an employee stock option entitles its holder to receive X/S units of

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The reload provision in an employee stock option entitles its holder to receive X/S units of newly “reloaded” at-the-money options from the employer upon exercise of the stock option. Here, X is the original strike price and S is the prevailing stock price at the exercise moment. The “reloaded” option has the same date of expiration as the original option. The exercise payoff is given by S∗ − X + X/S c(S,τ ; S,r,q). By the linear homogeneity property of the call price function, we can express the exercise payoff as S−X+Sĉ(τ ;r,q), where

and d (t; r, q) = e-9N() - eN(), -qt r9+ and  = O r-q --9-7. t. 0

Let S(τ ;r,q) denote the optimal exercise boundary that separates the stopping and continuation regions. The stopping region and the optimal exercise boundary S∗(τ) observe the following properties (Dai and Kwok, 2008).

1. The stopping region is contained inside the region defined by

{(S, ) : S > X, 02. At a time close to expiry, the optimal stock price is given by

S* (0+;r, q) = X, q0,r> 0.3. When the stock pays dividend at constant yield q > 0, the optimal stock price at infinite time to expiry is given by 

S* (o; r, q) = +r M + -1 -X,

where μ+ is the positive root of the equation:

02 7/7  + (r = 9 - 7/) - - 2 2 ur=0.

4. If the stock pays no dividend, then 

(a) for r  2, S* (t; r, 0) is defined for all t > 0 and S* (; r, 0) = ; (b) for r>, S* (t; r, 0) is defined

unique solution to the algebraic equation 

2/

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