Pricing Employee Stock Options under Stochastic Volatility

25 Pages Posted: 10 Jan 2013

Date Written: January 10, 2013


We employ a refined tree method to value employee stock options (ESOs) in the stochastic volatility model of Heston. Our setting covers risk-averse employees maximizing expected utility where we in particular focus on subjective option valuation, personal market beliefs and stochastic volatility. We formulate theoretical results on ESO valuation independently of a specific pricing model and utilize a recombining tree algorithm to value the American-style derivatives. We focus on the utility functions employed to numerically determine subjective option values and their impact on the valuation. We perform sensitivity analysis for various parameters, where we in particular examine the impact of the vesting period and an exercise constraint. We state market, objective and subjective ESO values and discuss their impact on possible contract designs.

Keywords: Heston model, employee stock options, subjective market beliefs, tree model, performance hurdle

JEL Classification: G00, G12, G13, G30

Suggested Citation

Sayer, Tilman, Pricing Employee Stock Options under Stochastic Volatility (January 10, 2013). Available at SSRN: or

Tilman Sayer (Contact Author)

Advanced Logic Analytics

United Kingdom

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