A stochastic optimal timing approach to modelling the transformation of agricultural systems subject to climate change

Greg Hertzler Todd Sanderson

Tim Capon

Peter Hayman

Ross Kingwell

The Australian wheat belt Source: Adapted from ABARES

APSIM simulations for South Australia Example gross margins for sheep and wheat

Geometric Brownian motion and the Ornstein-Uhlenbeck process

System dynamics (GPS)

Real Options for Adaptive Decisions (ROADs)

Option pricing equation

Shadow price of time

Opportunity cost of retaining the option instead of selling it and putting the money in the bank

Value of an expected change in the gross margin

Risk premium

Risk adjusted capital gains from retaining the option

Payoff functions

Gross margins with the obligation to continue

Gross margins with the option to exit

minus

Payoff of the option to exit

Payoff of the option to enter

The calculation of option values, the location of thresholds and expected times at thresholds

Step 1. Solve the option pricing equation for all possible times and gross margins.

Step 2. Assume the gross margin is fixed and search for the largest option price for that particular gross margin. Make note of the expected time before the switch.

Step 3. Repeat step 2 for all possible gross margins and identify the gross margin where the largest option price is no longer greater than the terminal value.

Transition probabilities (TRIPs)

Density functions

Cumulative probability distributions

Probabilities of crossing the entry threshold