Employee Stock Options

Henderson, Vicky; Sun, Jia

doi:10.1002/9780470061602.eqf03015

Cited by 1 publication

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“…Indeed, there are a number of papers in this vein, notably Carpenter et al (), Grasselli and Henderson (), Henderson (), Leung and Sircar (), and Rogers and Scheinkman (), all of whom study American option pricing under utility indifference for single or multiple identical options. (There is also a long literature in finance focussing on one‐period or binomial models typically without partial hedging; for a discussion and references, see the survey of Henderson and Sun . The first treatment of employee stock options in a utility indifference framework with partial hedging was Henderson who considered European style payoffs.)…”

Section: Employee Stock Optionsmentioning

confidence: 99%

Portfolios of American Options Under General Preferences: Results and Counterexamples

Henderson

Sun²,

Whalley

2012

Mathematical Finance

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We consider the optimal exercise of a portfolio of American call options in an incomplete market. Options are written on a single underlying asset but may have different characteristics of strikes, maturities, and vesting dates. Our motivation is to model the decision faced by an employee who is granted options periodically on the stock of her company, and who is not permitted to trade this stock. The first part of our study considers the optimal exercise of single options. We prove results under minimal assumptions and give several counterexamples where these assumptions faildescribing the shape and nesting properties of the exercise regions. The second part of the study considers portfolios of options with differing characteristics. The main result is that options with comonotonic strike, maturity, and vesting date should be exercised in order of increasing strike. It is true under weak assumptions on preferences and requires no assumptions on prices. Potentially the exercise ordering result can significantly reduce the complexity of computations in a particular example. This is illustrated by solving the resulting dynamic programming problem in a constant absolute risk aversion utility indifference model. KEY WORDS: American options, utility indifference pricing, employee stock options.

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