# A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock Options

## TL;DR

This paper introduces a comprehensive framework for valuing employee stock options that considers multiple exercises, job termination risk, and contractual features, using advanced numerical and analytical methods.

## Contribution

It presents a novel top-down valuation approach incorporating multiple exercises, termination risk, and a new maturity randomization method with analytic formulas.

## Key findings

- Job termination risk significantly affects ESO valuation.
- Exercise intensity and contractual features impact ESO costs.
- The proposed methods improve valuation accuracy and computational efficiency.

## Abstract

We propose a new framework to value employee stock options (ESOs) that captures multiple exercises of different quantities over time. We also model the ESO holder's job termination risk and incorporate its impact on the payoffs of both vested and unvested ESOs. Numerical methods based on Fourier transform and finite differences are developed and implemented to solve the associated systems of PDEs. In addition, we introduce a new valuation method based on maturity randomization that yields analytic formulae for vested and unvested ESO costs. We examine the cost impact of job termination risk, exercise intensity, and various contractual features.