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

4. Greg Hertzler Todd Sanderson

5. Tim Capon

6. Peter Hayman

7. Ross Kingwell

15. The Australian wheat belt Source: Adapted from ABARES

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

18. Geometric Brownian motion and the Ornstein-Uhlenbeck process

20. System dynamics (GPS)

25. Real Options for Adaptive Decisions (ROADs)

26. Option pricing equation

30. Shadow price of time

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

32. Value of an expected change in the gross margin

33. Risk premium

34. Risk adjusted capital gains from retaining the option

35. Payoff functions

36. Gross margins with the obligation to continue

37. Gross margins with the option to exit

38. minus

39. Payoff of the option to exit

40. Payoff of the option to enter

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

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

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.

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.

46. Transition probabilities (TRIPs)

47. Density functions

48. Cumulative probability distributions

49. Probabilities of crossing the entry threshold