Employee stock options (ESOs) are equity instruments that may be granted to senior employees as part of their remuneration and bonus arrangements. These may be intended to incentivise and reward employees, make remuneration packages competitive and align executive decision making to the goals of the company’s shareholders. There are many different possible designs for the structure of an ESO, some quite complex. Typically ESOs are granted to the employee conditionally subject to a set of hurdles that must be met on the vesting date. The hurdles may be market based or may be non market based. After the vesting date the ESO usually has American style exercise rights up to the final maturity date. Exercise may be triggered by financial considerations or happen automatically in the event of death or ill health of the employee. In this thesis we consider a particular type of ESO with a three asset market based hurdle. The accounting standards such as IFRS2 and AASB2 require public companies to report the costs of providing these ESOs initially and at each reporting date using a fair value approach. The valuations are usually provided by actuaries, mathematicians and finance specialists. Due to the complexity of ESO design, valuation is often done using Monte-Carlo (MC) simulation approaches rather than by developing complex analytic formulae. Due to the variety of structures, there is no standard analytic formula that applies generally and analytic or numerical valuations must be developed on an adhoc basis. This paper adopts the Hull and White [21] exercise multiple approach to model voluntary early exercise behaviour of ESO holders and extends the Kyng et al. [28] approach to incorporate attrition induced early exercise to an ESO with a three asset hurdle. This paper explores the use of hybrid numerical methods for ESO valuation using MC simulations combined with either analytic formulae or binomial lattice methods via a series of numerical experiments and utilizing various methods to improve the convergence of these numerical methods. We provide analytic formulae for the version of the ESO that does not allow for early exercise, derived using the Skipper and Buchen [37] method. These formulae allow us to test the hybrid numerical methods for convergence and accuracy     «

Employee stock options (ESOs) are equity instruments that may be granted to senior employees as part of their remuneration and bonus arrangements. These may be intended to incentivise and reward employees, make remuneration packages competitive and align executive decision making to the goals of the company’s shareholders. There are many different possible designs for the structure of an ESO, some quite complex. Typically ESOs are granted to the employee conditionally subject to a set of hurdles...     »