Vesting, Forfeiture, And Early Exercise Incentives

Why Vesting Changes an Employee Option

An employee option is a right to buy shares at a specified exercise price, but the employee may not be free to exercise it as soon as it is granted. A vesting schedule makes the right conditional, commonly on continued employment. If the employee leaves, unvested options are often forfeited; the treatment of vested options depends on the plan, which may allow only a limited period to exercise them.

These conditions affect the employee’s opportunity to benefit from a rise in the share price. A market-traded option can generally be sold or transferred, but an employee option is often nontransferable. The employee may therefore be unable to sell the option to realize its value while keeping the exercise decision open. A vested employee may choose to exercise early to secure value or reduce exposure to employment-related restrictions, even though early exercise is not optimal for a standard market-traded call under the assumptions considered below.

Definition: Vesting is the process by which an employee satisfies conditions to acquire an enforceable right to an option or other compensation award. Forfeiture is the loss of an award under the plan’s terms, commonly when an employee leaves before vesting. Exercisability is the period during which an option may be exercised. Vesting does not by itself determine how long an employee has to exercise after departure; the plan specifies that period.

Calculating Vesting and Forfeiture

A cliff schedule vests a specified portion on a particular date, subject to the employee satisfying the service condition. A graded schedule vests portions in installments. A schedule can combine the two: a first portion vests at a cliff date, and the remainder vests in equal installments later. The plan’s exact dates and rounding rules control; an installment should not be counted before its vesting date.

For a schedule with a cliff at month $c$, a fraction $q$ vesting at the cliff, and the remainder vesting equally over $m$ monthly installments beginning after the cliff, the vested count at month $t$ is:

V(t)= \begin{cases} 0, & t<c,\\ Nq+N(1-q)\dfrac{t-c}{m}, & c\le t\le c+m,\\ N, & t>c+m, \end{cases}

Here $N$ is the original grant count. The middle expression applies when each installment has vested at the end of its month; if the contract uses different dates, count the installments actually vested under those terms. If unvested options are cancelled when the employee leaves, the forfeited count is $N-V(t)$. A calculated fractional option is not necessarily issuable: the plan may require rounding to a whole option.

Worked Example: Applying a Cliff and Monthly Vesting

An employee receives 840 options. Twenty percent vest at month 9, provided the employee is still employed then. The remaining 80% vest in 27 equal monthly installments from month 10 through month 36. The employee leaves at the end of month 21, and the plan cancels unvested options. How many options are vested and forfeited?

Method. Count the cliff and the monthly installments vested by the departure date, then subtract vested options from the grant. This avoids counting 21 installments merely because departure occurs in month 21: the first installment is in month 10.

Cliff portion. The cliff vests $840(0.20)=168$ options at month 9.

Installments. Months 10 through 21 comprise $21-9=12$ installments. The installment portion of the grant is $840(0.80)=672$, so each of the 27 installments represents $672/27=24.8889$ options.

The 12 vested installments total $12(672/27)=298.6667$ options. Thus vested options are $168+298.6667=466.6667$, and forfeited options are $840-466.6667=373.3333$. These are unrounded calculated counts; the plan’s rounding rule determines any whole-option amounts. As a check, $466.6667+373.3333=840$.

Worked Example: Vesting at a Later Departure Date

A grant contains 900 options. Thirty percent vest at month 12, and the remaining 70% vest in 24 equal monthly installments from month 13 through month 36. An employee leaves at the end of month 28. Unvested options are cancelled. Find the vested and forfeited counts.

Method. Apply the cliff fraction first, then count only installments from month 13 through month 28. The number of installments is $28-12=16$.

The cliff vests $900(0.30)=270$ options. The installment portion is $900(0.70)=630$, so 16 of the 24 installments vest $630(16/24)=420$ options.

The total vested count is $270+420=690$. The forfeited count is $900-690=210$. The check is $690+210=900$. This calculation assumes the employee remains eligible through the end of month 28 and that the plan counts that month’s installment as vested at that time.

Uncertain Departure and Expected Vesting

If departure timing is uncertain, calculate the vested count separately for each possible departure date, then weight each count by its probability. This gives the expected number vested at departure. It does not imply that an individual employee receives a fractional option; it is an average across the specified outcomes.

Worked Example: Expected Vested Options Across Departure Dates

A grant has 500 options. Twenty percent vest at month 12, and the remainder vest in 16 equal installments from month 13 through month 28. Departure occurs at month 12 with probability 0.20, month 20 with probability 0.50, or month 28 with probability 0.30. Unvested options are forfeited. Find the expected vested and forfeited counts.

Method. Calculate the vested count for each departure date, check that the stated probabilities sum to 1, and take the probability-weighted average.

At month 12, $500(0.20)=100$ options are vested. At month 20, there are $20-12=8$ installments; the remainder is $500(0.80)=400$, so the vested count is $100+400(8/16)=300$. At month 28, all 16 installments have vested, so the count is 500.

The probabilities sum to $0.20+0.50+0.30=1$. Expected vested options are $0.20(100)+0.50(300)+0.30(500)=20+150+150=320$. Since the grant is 500 options, expected forfeited options are $500-320=180$. Equivalently, the forfeited counts are 400, 200, and 0, giving $0.20(400)+0.50(200)+0.30(0)=180$. The two calculations agree.

Why a Standard Call Is Not Exercised Early

The standard comparison is a useful benchmark, but it applies only under stated conditions. Consider an American call on a non-dividend-paying share, with current share price $S$, exercise price $K$, remaining time $\tau>0$, and continuously compounded risk-free rate $r>0$. Assume the option is freely transferable, there are no taxes or transaction costs, and exercising early gives no benefit other than acquiring the share. Its immediate exercise payoff is $\max(S-K,0)$.

A European call with the same terms gives a lower bound on the value of holding the American call, because the American option can also be held to expiration. Put-call parity for European options gives $C-P=S-Ke^{-r\tau}$, where $P$ is the European put value. Since $P\ge0$, the call value satisfies $C\ge S-Ke^{-r\tau}$. This inequality explains why waiting can be more valuable than exercising: it preserves the upside while deferring payment of $K$.

C \ge S-Ke^{-r\tau}

If $S>K$, then $e^{-r\tau}<1$, so $S-Ke^{-r\tau}>S-K$. The holding value therefore exceeds the immediate exercise payoff. If $S\le K$, immediate exercise pays zero, while the option’s holding value is nonnegative, so exercising cannot be better. Thus early exercise is never optimal under these assumptions; it strictly sacrifices value when the holding value exceeds the immediate exercise payoff. This result need not hold when the share pays dividends or when taxes, trading restrictions, or other frictions change the comparison.

Worked Example: Benchmarking Immediate Exercise Against Holding

A transferable American call on a non-dividend-paying share has $S=\$55$, $K=\$40$, and 1.5 years remaining. Assume a continuously compounded risk-free rate of 4% per year, with no taxes or transaction costs. Compare immediate exercise with the lower bound on holding value.

Method. Compare the intrinsic value with the European-call lower bound, which is also a lower bound on the American call’s holding value.

Immediate exercise produces $\$55-\$40=\$15$. The present value of the exercise price is $40e^{-0.04(1.5)}=40e^{-0.06}$. Using $e^{-0.06}\approx0.9417645$, this is approximately $\$37.6706$.

The lower bound on holding value is therefore $\$55-\$37.6706=\$17.3294$. The holding-value lower bound exceeds the immediate payoff by $\$17.3294-\$15=\$2.3294$. Under the stated assumptions, exercising early sacrifices value. This is a lower-bound comparison, not a calculation of the call’s exact market value.

Why Employee Options May Be Exercised Early

An employee option differs from the benchmark in ways that can alter the employee’s decision. Vesting may require continued service, unvested options may be forfeited at departure, and vested options may have a short post-departure exercise window. Nontransferability can prevent the employee from selling the option to convert its value into cash while retaining the choice to exercise later. Exercising also requires paying $K$; unless the employee sells shares after exercise, the employee exchanges an option for a concentrated shareholding rather than cash.

These features do not establish that early exercise is always beneficial. They mean the standard call result cannot be applied without adjustment: it assumes an option that can be held or traded without employment conditions. The employee’s decision may depend on the plan’s termination terms, available cash, tax consequences, ability to sell shares, risk preferences, and the employee’s other financial exposure. The next example isolates one employment-related constraint using a simplified expected-proceeds calculation.

Worked Example: A Short Post-Departure Window

An employee holds a vested option with $S=\$40$, $K=\$25$, and one year to expiration. Assume zero interest, no taxes or transaction costs, and that the employee can exercise and immediately sell the shares today. If the employee waits, there is a 40% probability of departure at month 6, when the share price is $\$30$; the plan then allows exercise for 30 days. If the employee remains employed through expiration, the share price is $\$60$ with probability 0.50 and $\$20$ with probability 0.50. Compare immediate exercise and sale with expected proceeds from waiting.

Method. Calculate the net option proceeds in each mutually exclusive outcome and weight by its probability. This is a simplified expected-dollar comparison, not a general option-pricing model.

Exercising and selling today yields $\$40-\$25=\$15$. If departure occurs at month 6, the employee can exercise within the specified window at the assumed share price of $\$30$, yielding $\$30-\$25=\$5$. If the employee stays, the expiration payoff is $\max(60-25,0)=\$35$ in the high-price outcome and $\max(20-25,0)=\$0$ in the low-price outcome.

Conditional on staying, expected proceeds are $0.50(\$35)+0.50(\$0)=\$17.50$. The expected proceeds from waiting are $0.40(\$5)+0.60(\$17.50)=\$2+\$10.50=\$12.50$. Since $\$12.50<\$15$, immediate exercise and sale give higher expected proceeds in this simplified model. The calculation assumes the stated prices and probabilities, zero interest, and no additional costs; it does not show that early exercise is optimal for every employee option.

Common Mistakes and Practical Interpretation

Counting the cliff month as an installment. If installments begin after the cliff, count from the first installment month, not from the grant date.
Equating vesting with exercise availability. A vested option may still be subject to a post-departure deadline or other plan conditions.
Calling the whole grant forfeited at departure. Under many plan terms, only unvested options are cancelled; vested options have separate treatment.
Applying the standard call result without checking its assumptions. The no-early-exercise argument is for a non-dividend-paying share and a transferable option without relevant frictions.
Treating exercise value as cash received. Exercising costs $K$ per share. Cash is realized only if shares can be sold, and retaining shares leaves the employee exposed to their price.

Vesting schedules and forfeiture rules determine how much of a grant survives continued-service conditions. Transfer restrictions and post-departure deadlines affect whether an employee can preserve the option’s flexibility. Together, these terms explain why early exercise incentives for employee options can differ from the standard result for a freely traded call. These distinctions are aligned with the SOA VEE Accounting and Finance syllabus.

Check Your Understanding

For each schedule, use the stated vesting dates and terms. Treat the probabilities as applying to mutually exclusive departure outcomes.

A grant of 600 options has a 25% cliff at month 12, with the rest vesting in 18 equal monthly installments from month 13 through month 30. Departure occurs at the end of month 21, and unvested options are cancelled. How many are vested and forfeited? (Answer: 375 vested and 225 forfeited.)
A grant of 1,200 options has a 15% cliff at month 10, with the rest vesting in 20 equal installments from month 11 through month 30. The employee leaves at the end of month 25. How many options are vested and forfeited? (Answer: 945 vested and 255 forfeited.)
A 300-option grant has 40% vest at month 12, and the remainder vests in 12 equal installments from month 13 through month 24. Departure occurs at month 12 with probability 0.25, month 18 with probability 0.50, and month 24 with probability 0.25. What is the expected vested count? (Answer: 210 options.)
A non-dividend-paying share has $S=\$55$; a transferable call has $K=\$40$, 1.5 years remaining, and a continuously compounded risk-free rate of 4% per year. With no taxes or transaction costs, what lower bound on holding value follows from $C\ge S-Ke^{-r\tau}$, and how does it compare with immediate exercise? (Answer: The lower bound is approximately $\$17.33$, versus an immediate exercise payoff of $\$15.00$.)
An employee’s vested option has $S=\$32$ and $K=\$20$. Assume zero interest, no taxes or transaction costs, and immediate exercise-and-sale is possible. If the employee waits, departure occurs at month 6 with probability 0.25, when the share price is $\$26$ and exercise is allowed for 30 days. Otherwise the employee stays to expiration; then the share price is $\$50$ with probability 0.40 and $\$15$ with probability 0.60. Compare immediate proceeds with expected proceeds from waiting. (Answer: Immediate proceeds are $\$12$; expected waiting proceeds are $\$10.50$, so immediate exercise and sale produce more in this simplified expected-proceeds comparison.)

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