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Greg Hertzler Todd Sanderson

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.

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Greg Hertzler Todd Sanderson

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

  2. Greg Hertzler Todd Sanderson

  3. Tim Capon

  4. Peter Hayman

  5. Ross Kingwell

  6. The Australian wheat belt Source: Adapted from ABARES

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

  8. Geometric Brownian motion and the Ornstein-Uhlenbeck process

  9. Ornstein-Uhlenbeck process

  10. System dynamics (GPS)

  11. Hawker Hawker

  12. Orroroo Orroroo

  13. Clare Clare

  14. Real Options for Adaptive Decisions (ROADs)

  15. Option pricing equation

  16. Shadow price of time

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

  18. Value of an expected change in the gross margin

  19. Risk premium

  20. Risk adjusted capital gains from retaining the option

  21. Payoff functions

  22. Gross margins with the obligation to continue

  23. Gross margins with the option to exit

  24. minus

  25. Payoff of the option to exit

  26. Payoff of the option to enter

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

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

  29. 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.

  30. 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.

  31. Transition probabilities (TRIPs)

  32. Density functions

  33. Cumulative probability distributions

  34. Probabilities of crossing the entrythreshold

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