GARCH-type volatility in the multiplicative quadrinomial tree method: An application to real options

Abstract

This article applies the multiplicative quadrinomial tree numerical method with non-constant volatility to assess a real option of abandonment, based on an estimate of the conditional volatility for WTI oil commodity prices and their respective equivalence in a GARCH-diffusion model. The methodology refers to the use of an estimate of type GARCH (1,1) and the numerical method through a quadrinomial tree. There are two main findings: 1) when employing the quadrinomial method, the value of the real option turned out to be greater than the value estimated through the traditional multiplicative binomial method, due to underestimation of the real value of volatility that occurs in a specific period according to the latter method; and 2) a methodological contribution that demonstrates plainly way the presence of non-constant conditional volatility as well as being able to value all types of options using stochastic volatility.