OPT_EXEC Function (Gnumeric)
Use Gnumeric OPT_EXEC to apply an executive-option forfeiture factor, with annual intensity, time-unit cautions and tested synthetic examples.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
OPT_EXEC multiplies a generalized European option value by an exponential survival factor. The stated model assumes that an executive forfeits the option on leaving the company. It is a particular theoretical adjustment, not a complete employee-equity valuation, compensation entitlement or current accounting standard.
Syntax and units
=OPT_EXEC(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry,lambda)
All eight arguments are required. Use “c” or “p”, positive spot and strike, positive remaining time, an annual decimal discount rate, positive annualized decimal volatility, and an explicit decimal cost of carry. lambda is the departure/forfeiture intensity in reciprocal time units. It is not directly a cumulative probability.
The inspected help labels time in days while describing annualized rate inputs. The implementation performs no day-to-year conversion: it passes time directly to the European-option calculation and uses EXP(−lambda×time). With annual rates, annual volatility and annual lambda, supply time in years. A time of 1 in the fixtures below means one year; it does not mean one day.
Reproducible zero- and positive-forfeiture controls
=OPT_EXEC("c",100,100,1,0.05,0.2,0.05,0)
=OPT_EXEC("c",100,100,1,0.05,0.2,0.05,0.1)
The independently expected results are approximately 10.4505835722 and 9.4560790564. The first has survival factor EXP(0)=1, so it equals the generalized European call value. The second multiplies that price by EXP(−0.1), approximately 0.9048374180.
The associated one-year forfeiture probability is 1−EXP(−0.1), approximately 9.5162582%, not exactly 10%. An annual intensity of 0.1 and a one-year probability of 10% are different parameterizations. If your source supplies a probability, it cannot be inserted unchanged as lambda without checking the model conversion.
A reusable assumption table
Place flag, spot, strike, years, rate, volatility, carry and lambda in A2:H2. Then use =OPT_EXEC(A2,B2,C2,D2,E2,F2,G2,H2). Label H1 Annual forfeiture intensity, not Probability. Hold the underlying pricing assumptions fixed when comparing intensities so the change can be attributed to the exponential factor.
The expected European component was independently computed by numerical integration of the discounted lognormal payoff. The adjustment was then calculated as a separate exponential factor. This separates the base-pricing control from the additional executive-option assumption instead of comparing two unexplained outputs.
Advanced interpretation
For a cumulative survival probability p over a specified positive horizon t, the constant intensity consistent with this factor is −LN(p)/t, provided 0<p<=1 and the same time units are used. This algebraic conversion does not establish that a constant-intensity model is appropriate for a particular employee or award.
For nonnegative lambda and a positive time horizon, the factor is at most one. Negative lambda would amplify the base value, which does not describe ordinary forfeiture survival. The implementation does not act as a comprehensive business-rule validator, so validate this condition in your input model.
Errors, model limits and troubleshooting
The underlying formula uses logarithms, square roots and division by volatility×sqrt(time). Avoid nonpositive spot/strike and zero time/volatility in this positive-domain tutorial. The OPT_EXEC wrapper returns its computed floating-point value directly rather than explicitly translating every invalid calculation in the same way as OPT_BS; error details outside the tested domain are not certified here.
The function does not include vesting schedules, tax consequences, individual exercise behavior or detailed employment terms. If the output appears inconsistent, first check the units of time and lambda, the explicit carry input, and whether the baseline option itself matches your intended model. A native calculation confirms software behavior for the synthetic cases, not the suitability of an employee valuation.
Evidence and compatibility
Gnumeric ssconvert 1.12.57 under C.UTF-8 recalculated the exact literal examples on October 17, 2026. The OptionControls fixture recorded F8 = 10.450583572185565; F9 = 9.4560790564254. These agree with the independent expectations within 10^-7, including finite-difference sensitivity error. Cell-driven layouts are instructional equivalents, not separate GUI tests. Other boundary/error statements are source-derived. Official Gnumeric 1.12.57 implementation was retrieved October 17, 2026; independent calculations use discounted-payoff quadrature and the explicitly stated derivative or survival relationships. Original introduction and last functioning release are not established. No GUI screenshot or execution of another release is claimed. These derivatives functions are registered as Gnumeric-specific; verify recalculation after export rather than relying on cached values in another application.