Download presentation

Presentation is loading. Please wait.

Published byKaden Nickel Modified about 1 year ago

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

2

3

4
Greg Hertzler Todd Sanderson

5
Tim Capon

6
Peter Hayman

7
Ross Kingwell

8

9

10

11

12

13

14

15
The Australian wheat belt Source: Adapted from ABARES

16

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

18
Geometric Brownian motion and the Ornstein-Uhlenbeck process

19

20
System dynamics (GPS)

21

22

23

24

25
Real Options for Adaptive Decisions (ROADs)

26
Option pricing equation

27

28

29

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

41

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

50

51

52

53

54

55

56

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google