Simple models for trading climate and weather risk

Size: px

Start display at page:

Download "Simple models for trading climate and weather risk"

Hillary Newton
6 years ago
Views:

1 Simple models for trading climate and weather risk Sébastien Chaumont, Peter Imkeller, Matthias Müller Humboldt-Universität zu Berlin Cours Bachelier, Paris, February 17, 26 Partially supported by the DFG research center MATHEON (FZT 86) in Berlin

SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 1 El Niño phenomenon of anomalously high surface temperatures of eastern South Pacific (Peru); randomly periodic, every 3-8 years around Christmas

2 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 1 El Niño phenomenon of anomalously high surface temperatures of eastern South Pacific (Peru); randomly periodic, every 3-8 years around Christmas El Niño, Dec 82, SOI=-2.48 normal, Dec 83, SOI=-.17 Southern Oscillation Index (SOI) SOI: air pressure difference Darwin (AUS) Tahiti El Niño: SOI small, east Pacific warm La Niña: SOI big, east Pacific cold Southern Oscillation Index

(Peru) strong precipitation in western Pacific (Indonesia) cold ocean: food

3 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 2 Climatic consequences El Niño conditions normal conditions strong precipitation in eastern Pacific (Peru) strong precipitation in western Pacific (Indonesia) cold ocean: food for big animals in surface layer warm ocean: food for big animals in deeper layers

4 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 3 Economic consequences: fishing Peruvian anchoveta catch rates Skipjack tuna catch rate = complementary economic interests: Peru-Indonesia

5 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 4 Economic consequences: farming Peru Rainfall data 2 Precipitation in Peru and El Niño Forest fires in Indonesia and El Niño = complementary economic interests: fisher- (rice) farmer in Peru

6 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 5 Periodically forced bi-stable temperature U(t, k) periodic in t, k = 1, k = 1, periodic motion of well depths V U (t) = K(t) 1 U (t) = K(t+1/2) U (t) 1 U (t) 1 v 1/2 1

7 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 6 Trajectories for potential diffusion X σ K small t X σ K big t X σ K good t

8 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 7 Bi-stable potential diffusion for numerical simulation bi-stable temperature curve resulting from the non-linear two-dimensional oscillator by Wang, Bacilon, Fang bi-stable temperature curve used in our numerical experiments Temperature. Model 2 K K 1

9 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 8 Risk exposure of different model agents fisher s income Income φ f (k) = exp( (k k) 2 ) H f = T φf (K s ) ds K 1 K 2 farmer s income Income φ r (k) = exp( (k k) 2 ) H r = T φr (K s ) ds K 1 K 2

10 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 9 farmer s optimal investment into Y, model B Optimal investment in risk-security, model B, t=.25 Optimal investment in risk-security, model B, t=.5 x49.dat x99.dat Optimal investment in risk-security, model B, t=.75 Optimal investment in risk-security, model B, t=1. x149.dat x199.dat

11 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 1 farmer s optimal investment into Y, model C Optimal investment in risk-security, model C, t=.25 Optimal investment in risk-security, model C, t=.5.2 x49.dat.2 x99.dat Optimal investment in risk-security, model C, t=.75 Optimal investment in risk-security, model C, t=.95.2 x149.dat.2 x199.dat

12 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 11 appreciation rate for trading with Y, models B and C

13 SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 12 Sources Title page Slide 1 diag.: diag.: SOI-Data: sensorlab.cnu.ac.kr/ cybercat/soi.dat Slide 2 Slide 3 diag.: diag.: diag.: Nature, vol. 389, 16 October 1997, Slide 4 Peru Rainfall Data: tao.atmos.washington.edu/data_sets/piura/ diag.: Slide 6 diag.: B. Wang, A. Barcilon, Z. Fang, J. Atmos. Sciences, 56, 1999, 5-23 Slide 7 diag.: walrus.wr.usgs.gov/globalhydrate/images/pacific.gif Slide 9 diag.: S. Slide 6 diag.: diag.: IFAD Photo by Franco Mattioli

Name: Date: Hour: Comparing the Effects of El Nino & La Nina on the Midwest (E4.2c)

Name: Date: Hour: Comparing the Effects of El Nino & La Nina on the Midwest (E4.2c) Purpose: Comparing the Effects of El Nino & La Nina on the Midwest (E4.2c) To compare the effects of El Nino and La Nina on the Midwest United States. Background Knowledge: The El Nino-Southern Oscillation