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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. Example gross margins for sheep and wheat. - PowerPoint PPT Presentation
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CRL seminar presentation
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 beltSource: Adapted from ABARES
APSIM simulations for South Australia
Example gross margins for sheep and wheatGeometric Brownian motion and theOrnstein-Uhlenbeck process
Ornstein-Uhlenbeck process
System dynamics (GPS)
Hawker
Hawker
Orroroo
Orroroo
Clare
Clare24
Real Options for AdaptiveDecisions (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 exitPayoff of the option to enter
The calculation of option values, the location of thresholds and expected times at thresholdsStep 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 distributionsProbabilities of crossing the entry threshold