How does real option value compare with Faustmann value when log prices follow fractional Brownian motion?

摘要

Analysis of an extended price series from 1973 to 2016 for New Zealand A grade export logs confirms that the price series is not I(0) stationary. The rejection of the unit root test suggests that it is also not I(1). It is estimated that log prices are fractionally integrated with A grade prices being I(0.78) and the natural logarithm of A grade prices being I(0.83). The implication is that log prices should be modelled using fraction Brownian motion (FBM) rather than geometric Brownian motion (GBM) or as a stationary autoregressive process.