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8.6 Monte Carlo models
Publication date: 31 Jul 2022
us Stock-based compensation guide
A Monte Carlo simulation model assumes that the underlying entity's stock price follows a Geometric Brownian Motion stochastic process. Geometric Brownian Motion is an accepted methodology for simulating the expected future path of stock prices. Stock prices are simulated at regular intervals (daily, monthly, annually) depending on award conditions and precision of estimate desired.
A large number of sample paths are simulated, and a fair value of the award is determined for each sample path outcome based on the payout value of the award discounted to the grant date. The fair value of the award is estimated as the average value of the fair values calculated for each sample path.
Like a lattice or Black-Scholes model, it is first necessary to develop assumptions for the initial stock price, volatility, risk-free rate, dividend yield, and any other pertinent factors given the awards' terms.
A discussion of the theoretical underpinnings of the Monte Carlo simulation is outside the scope of this guide. However, we note that best practices have developed for the use of Monte Carlo simulation and the use of such models (with the assistance of an outside valuation specialist) is now commonplace.
A fairly large number of companies issue awards that contain (sometimes complex) market conditions. Valuation of these award types generally requires the use of a Monte Carlo simulation.
PwC. All rights reserved. PwC refers to the US member firm or one of its subsidiaries or affiliates, and may sometimes refer to the PwC network. Each member firm is a separate legal entity. Please see www.pwc.com/structure for further details. This content is for general information purposes only, and should not be used as a substitute for consultation with professional advisors.
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