Valuation of Executive Stock Options Using a Closed-Form Formula

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Executive stock options usually have complex payoffs. To price them, we often use the binomial tree method or Monte Carlo simulations.

… a lattice model can be designed to accommodate dynamic assumptions of expected volatility and dividends over the option’s contractual term, and estimates of expected option exercise patterns during the option’s contractual term, including the effect of blackout periods. Therefore, the design of a lattice model more fully reflects the substantive characteristics of a particular employee share option or similar instrument. Nevertheless, both a lattice model and the Black–Scholes–Merton formula, as well as other valuation techniques that meet the requirements … can provide a fair value estimate that is consistent with the measurement objective and fair-value-based method. Read more

Recently, Hsiao et al. [1] derived a close-form solution to a particular class of executive stock options.

This study derives a closed-form approximate solution for Bermudan reset executive stock options with cash dividends. The complicated payoff characteristic of this exotic option is caused by its particular stylistic features, including the reset mechanism, cash dividends, early exercises, and increasing volatilities. Using the integral representation method, a closed-form approximate solution was successfully derived. Moreover, this study discusses how specific critical factors affect executive stock option values and arrives at some interesting results by way of a numerical calibration.

 

References

[1]  Y.L. Hsiao, L.L. Chen, C.J. Ting,  The Valuation of Executive Stock Option Using the Integral Representation Method, Journal of Mathematical Finance, 2020, 10, 431-447

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