Valuation models
Employee stock options
The Hull and White (2004) lattice with forfeiture on leaving before vesting, exercise on leaving after it and early exercise at a multiple of the strike, with dilution, expected life, the chance of exercise and the Black-Scholes values at full term and at the expected life for comparison.
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Results
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Methodology
Conventions
- Cox-Ross-Rubinstein tree. Shout: the holder may lock in the intrinsic value once, and keeps the upside.
- Employee stock options (Hull-White 2004): forfeited on leaving before vesting, exercised on leaving after.
- Early exercise once the share reaches the exercise multiple × strike; dilution N / (N + M).
References
- Hull and White, How to Value Employee Stock Options (2004)
- Thomas, Something to Shout About (1993)
- ASC 718 and IFRS 2
Formulas
- Shout value
- V_{shout} = e^{−rτ}(S − K) + BS(S, S, τ)
- ESO node
- V = (1 − e^{−λΔt}) max(S − K, 0) + e^{−λΔt} e^{−rΔt} E[V']