A stochastic optimal timing approach to modelling the
transformation of agricultural systems subject to climate change
Slide 2 Slide 3 Slide 4 Greg Hertzler Todd Sanderson Slide 5 Tim
Capon Slide 6 Peter Hayman Slide 7 Ross Kingwell Slide 8 Slide 9
Slide 10 Slide 11 Slide 12 Slide 13 Slide 14 Slide 15 The
Australian wheat belt Source: Adapted from ABARES Slide 16 Slide 17
APSIM simulations for South Australia Example gross margins for
sheep and wheat Slide 18 Geometric Brownian motion and the
Ornstein-Uhlenbeck process Slide 19 Slide 20 System dynamics (GPS)
Slide 21 Slide 22 Slide 23 Slide 24 Slide 25 Real Options for
Adaptive Decisions (ROADs) Slide 26 Option pricing equation Slide
27 Slide 28 Slide 29 Slide 30 Shadow price of time Slide 31
Opportunity cost of retaining the option instead of selling it and
putting the money in the bank Slide 32 Value of an expected change
in the gross margin Slide 33 Risk premium Slide 34 Risk adjusted
capital gains from retaining the option Slide 35 Payoff functions
Slide 36 Gross margins with the obligation to continue Slide 37
Gross margins with the option to exit Slide 38 minus Slide 39
Payoff of the option to exit Slide 40 Payoff of the option to enter
Slide 41 Slide 42 The calculation of option values, the location of
thresholds and expected times at thresholds Slide 43 Step 1. Solve
the option pricing equation for all possible times and gross
margins. Slide 44 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. Slide 45
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. Slide 46 Transition probabilities
(TRIPs) Slide 47 Density functions Slide 48 Cumulative probability
distributions Slide 49 Probabilities of crossing the entry
threshold Slide 50 Slide 51 Slide 52 Slide 53 Slide 54 Slide 55
Slide 56
