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 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 2 1-1 Southern Oscillation Index 1866-21 188 19 192 194 196 198 2
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
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
SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 4 Economic consequences: farming Peru Rainfall data 2 Precipitation in Peru and El Niño 15 1 5 82 83 84 85 86 87 88 89 9 91 92 93 94 95 96 97 Forest fires in Indonesia and El Niño = complementary economic interests: fisher- (rice) farmer in Peru
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) 1 1 1 U (t) 1 U (t) 1 v 1/2 1
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
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 2.5 1 1.5 2 K 1
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
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.2.2.1.1 -.1 -.1 -.2 -.2 -.3 -.3-4 -3-2 -1 1 2 3 4-4 -3-2 -1 1 2 3 4 Optimal investment in risk-security, model B, t=.75 Optimal investment in risk-security, model B, t=1. x149.dat x199.dat.2.2.1.1 -.1 -.1 -.2 -.2 -.3 -.3-4 -3-2 -1 1 2 3 4-4 -3-2 -1 1 2 3 4
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.15.15.1.1.5.5 -.5 -.5 -.1 -.1 -.15 -.15 -.2 -.2 -.25 -.25-4 -3-2 -1 1 2 3 4-4 -3-2 -1 1 2 3 4 Optimal investment in risk-security, model C, t=.75 Optimal investment in risk-security, model C, t=.95.2 x149.dat.2 x199.dat.15.15.1.1.5.5 -.5 -.5 -.1 -.1 -.15 -.15 -.2 -.2 -.25 -.25-4 -3-2 -1 1 2 3 4-4 -3-2 -1 1 2 3 4
SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 11 appreciation rate for trading with Y, models B and C
SIMPLE MODELS FOR TRADING CLIMATE AND WEATHER RISK 12 Sources Title page Slide 1 diag.: www.ems.psu.edu/weatherworld/features/witn98.html diag.: www.cdc.noaa.gov/map/clim/sst_olr/old_sst/sst_8283_anim.shtml SOI-Data: sensorlab.cnu.ac.kr/ cybercat/soi.dat Slide 2 Slide 3 diag.: www.jam-web.de/el-nino/k1.php diag.: www.fao.org/fi/fifacts/plots/lamer/lat2.asp diag.: Nature, vol. 389, 16 October 1997, 715-717 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.: www.photolib.noaa.gov/fish/images/big/fish2167.jpg diag.: www.ifad.org/photo/region/pl/pe.htm#, IFAD Photo by Franco Mattioli