文档介绍：Monte Carlo Estimation of Project Volatility for Real Options Analysis
Pedro Manuel Cortesão Godinho
Grupo de Estudos ários e Financeiros (GEMF)
ABSTRACT
Volatility is a fundamental parameter for option valuation. In particular, real
options models require project volatility, which is very hard to estimate accurately
because there is usually no historical data for the underlying asset. Several authors have
used a method based on Monte Carlo simulation for estimating project volatility. In this
paper we analyse the existing procedures for applying the method, concluding that they
will lead to an upward bias in the volatility estimate. We propose different procedures
that will provide better results, and we also discuss the business consequences of using
upwardly biased volatility estimates in real options analysis.
1
1. INTRODUCTION
Real options analysis has led to very important theoretical advances in the field
of project valuation. However, its practical application to real life projects presents
some serious difficulties that have hindered its ess. Estimating underlying asset
volatility is one of the most important problems faced by practitioners wanting to use
real options models. Sometimes, the only significant source of uncertainty for the
project is the price of modity and, in such cases, market data can be used to
estimate volatility (for example, Kelly, 1998, and Smit, 1997). However, most projects
contain multiple sources of uncertainty, and historical data do not exist for some
significant sources of volatility. For such projects, it may be useful to estimate the
volatility for the project without options, and use the project without options as the
underlying asset for the analysis (see Copeland and Antikarov, 2001, for example).
Some authors have tackled the problem of estimating the volatility of the project
without options. Davis (1998) provides a closed-form expression for t