Advertisement

Modeling and pricing of space weather derivatives

  • Birgit Lemmerer
  • Stephan UngerEmail author
Original Article
  • 5 Downloads

Abstract

This article proposes a pricing model for space weather derivatives with payout depending on solar activity. By measuring the disturbance of the Earth’s magnetosphere, it is possible to price space weather derivatives which trigger a payoff if a certain level of energization is reached. Since energetic particles emitted by the Sun are a non-tradeable quantity, unique prices of contracts in an incomplete market are obtained using inverse transformation sampling as well as the market price of risk. We find a step-wise decline of option prices with increasing barriers of Kp-index values, a dependence of the option prices on the sunspot cycle, as well as reduced sensitivity of longer-dated maturities for higher Kp-index values.

Keywords

Space weather Geomagnetic storms Geomagnetic indices Space weather derivative Pricing Hedging Inverse transformation sampling 

Notes

Compliance with ethical standards

Conflicts of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

References

  1. Alaton, P., B. Djehiche, and D. Stillberger. 2002. On modelling and pricing weather derivatives. Applied Mathematical Finance 9 (1): 1–20.  https://doi.org/10.1080/13504860210132897.Google Scholar
  2. Baker, D.N. 2000. Effects of the Sun on the Earth’s environment. Journal of Atmospheric and Solar-Terrestrial Physics 62 (17–18): 1669–1681.Google Scholar
  3. Baker, D.N., and S.G. Kanekal. 2008. Solar cycle changes, geomagnetic variations, and energetic particle properties in the inner magnetosphere. Journal of Atmospheric and Solar-Terrestrial Physics 70 (2–4): 195–206.Google Scholar
  4. Baker, D.N., T.I. Pulkkinen, X. Li, S.G. Kanekal, et al. 1998. Coronal mass ejections, magnetic clouds, and relativistic magnetospheric electron events: ISTP. Journal of Geophysical Research 103 (A8): 17279–17292.Google Scholar
  5. Bala, R., P. Reiff, and C.T. Russell. 2015. Testing the estimated hypothetical response of a major CME impact on Earth and its implications to space weather. Journal of Geophysical Research: Space Physics 120 (5): 3432–3443.Google Scholar
  6. Barnard, L., and M. Lockwood. 2011. A survey of gradual solar energetic particle events. Journal of Geophysical Research 116: A5.Google Scholar
  7. Bartels, J., N.H. Heck, and H.F. Johnston. 1939. The three-hour-range index measuring geomagnetic activity. Terrestrial Magnetism and Atmospheric Electricity 44 (4): 411.Google Scholar
  8. Boberg, F., P. Wintoft, and H. Lundstedt. 2000. Real time Kp predictions from solar wind data using neural networks. Physics and Chemistry of the Earth Part C 25 (4): 275–280.Google Scholar
  9. Boteler, D.H. 2001. Space weather effects on power systems, AGU. Geophysical Monograph Series 125: 347–352.Google Scholar
  10. Bothmer, V., and I.A. Daglis. 2007. Space weather: Physics and effects, XXXVIII, 1-438. New York: Springer.Google Scholar
  11. Brody, D.C., J. Syroka, and M. Zervos. 2002. Dynamical pricing of weather derivatives. Quantitative Finance 2 (3): 189.Google Scholar
  12. Cao, M. and J. Wei. 2003. Pricing weather derivatives: An equilibrium approach, Working paper, The Rotman Graduate School of Management, The University of Toronto, Ontario.Google Scholar
  13. Choi, H.S., J. Lee, K.S. Cho, Y.S. Kwak, et al. 2011. Analysis of GEO spacecraft anomalies: Space weather relationships. Space Weather 9: S06001.Google Scholar
  14. Cliver, E.W., V. Boriakoff, and K.H. Bounar. 1996. The 22-year cycle of geomagnetic and solar wind activity. Journal of Geophysical Research 101 (A12): 27091–27109.Google Scholar
  15. Corby, P. M., F.D. Fox. 2002. System, method, and computer program product for valuating weather-based financial instruments, U.S. patent application No. 6,418, 417 B1.Google Scholar
  16. Costello, K. A. 1997. Moving the Rice MSFM into a real-time forecast mode using solar wind driven forecast models, Ph.D. dissertation, Rice Univ., Houston, Texas.Google Scholar
  17. Davis, M. 2001. Pricing weather derivatives by marginal value. Quantitative Finance 1: 305–8.Google Scholar
  18. Elliott, H.A., J.-M. Jahn, and D.J. McComas. 2013. The Kp-index and solar wind speed relationship: Insights for improving space weather forecasts. Space Weather 11 (6): 339–349.Google Scholar
  19. Ferguson, D.C., S.P. Worden, and D.E. Hastings. 2015. The space weather threat to situational awareness, communications, and positioning systems. IEEE Transactions on Plasma Science 43 (9): 3086–3098.Google Scholar
  20. Forbes, K.F., and O.C. St. Cyr. 2012. Did geomagnetic activity challenge electric power reliability during solar cycle 23? Evidence from the PJM regional transmission organization in North America. Space Weather 10 (5): 1.Google Scholar
  21. Gehred, P. A., W. Cliffswallow, and J. D. Schroeder III, 1995, A comparison of USAF Ap and Kp indices to Gottingen indices, Tech. Memo. ERL SEL-88, NOAA, Silver Spring, Md.Google Scholar
  22. Gopalswamy, N. 2006. Solar connections of geoeffective magnetic structures. Journal of Atmospheric and Solar-Terrestrial Physics 70 (17): 2078–2100.Google Scholar
  23. Gopalswamy, N. 2006. Properties of interplanetary coronal mass ejections. Space Science Reviews 124 (1–4): 145–168.Google Scholar
  24. Gosling, J.T., S.J. Bame, D.J. McComas, and J.L. Phillips. 1990. Coronal mass ejections and large geomagnetic storms. Geophysical Research Letters 17: 901–904.Google Scholar
  25. Hathaway, David H., Robert M. Wilson, and Reichmann J. Edwin. 1993. The shape of the Sunspot cycle. Solar Physics 151: 177–190.Google Scholar
  26. Jewson, S., and A. Brix. 2005. Weather derivative valuation. Cambridge: Cambridge University Press.Google Scholar
  27. Kahler, S.W. 1992. Solar flares and coronal mass ejections. Annual Review of Astronomy and Astrophysics 30: 113–141.Google Scholar
  28. Kataoka, R. 2013. Probability of occurrence of extreme magnetic storms. Space Weather 11 (5): 214–218.Google Scholar
  29. Kilpua, E.K.J., N. Olspert, A. Grigorievskiy, M.J. Kaepylae, et al. 2015. Statistical study of strong and extreme geomagnetic disturbances and solar cycle characteristics. The Astrophysical Journal 806 (2): 272.Google Scholar
  30. Love, J.J., E.J. Rigler, A. Pulkkinen, and P. Riley. 2015. On the lognormality of historical magnetic storm intensity statistics: Implications for extreme-event probabilities. Geophysical Research Letters 42 (16): 6544–6553.Google Scholar
  31. Lloyd’s of London. 2013. Solar storm risk to the North American electric grid. London: Lloyd’s of London.Google Scholar
  32. McPherron, R.L. 1991. Physical processes producing magnetospheric substorms and magnetic storms. Geomagnetism 4: 593–739.Google Scholar
  33. Menvielle, M., and A. Berthelier. 1991. The K-derived planetary indices—description and availability. Reviews of Geophysics 29: 415–432.Google Scholar
  34. Moreno, M. and D. Whitehead. A quick guide to weather derivatives, speedwell weather, http://www.speedwellweather.com/PDF/Consultancy/ A%20Quick%20Guide%20to%20Weather%20Derivatives.pdf. Accessed 02 Feb 2018.
  35. O’Brien, T.P. 2009. SEAES-GEO: A spacecraft environmental anomalies expert system for geosynchronous orbit. Space Weather 7: S09003.Google Scholar
  36. Oughton, E., J. Copic, A. Skelton, V. Kesaite, Z.Y. Yeo, S.J. Ruffle, et al. 2017. Helios solar storm scenario. Cambridge: Cambridge Centre for Risk Studies.Google Scholar
  37. Petrovay, K. 2010. Solar cycle prediction. Living Reviews in Solar Physics 7: 6.Google Scholar
  38. Richards, T., M. Manfredo, and D. Sanders. 2004. Pricing weather derivatives. American Journal of Agricultural Economics 86 (4): 1005–1017.Google Scholar
  39. Riley, P. 2012. On the probability of occurrence of extreme space weather events. Space Weather 10 (2): 1.Google Scholar
  40. Rostoker, G. 1972. Geomagnetic indices. Reviews of Geophysics and Space Physics 10: 935–950.Google Scholar
  41. Schwenn, R. 1983. The average solar wind in the inner heliosphere: Structures and slow variations. Washington: NASA Conference Publication.Google Scholar
  42. Schwenn, R. 2006. Space weather: The solar perspective. Living Reviews in Solar Physics 3 (1): 72.Google Scholar
  43. Snyder, C.W., M. Neugebauer, and U.R. Rao. 1963. The solar wind velocity and its correlation with cosmic-ray variations and with solar and geomagnetic activity. Journal of Geophysical Research 68: 6361.Google Scholar
  44. St. Cyr, O.C., S.P. Plunkett, D.J. Michels, S.E. Paswaters, et al. 2000. Properties of coronal mass ejections: SOHO LASCO observations from January 1996 to June 1998. Journal of Geophysical Research 105 (A8): 18169–18186.Google Scholar
  45. Vita-Finzi, C. 2008. The sun, a user’s manual, 119. New York: Springer.Google Scholar
  46. Waheed, M., P. Khan, S. Tripathi, et al. 2015. Long term evolution of geomagnetic activity under the influence of 11 year cyclic variations in solar activity during solar cycle 23 and 24. International Journal of Innovative Research in Science, Engineering and Technology 4: 18585–18590.Google Scholar
  47. Wing, S., J.R. Johnson, J. Jen, C.-I. Meng, et al. 2005. Kp forecast models. Journal of Geophysical Research: Space Physics 110 (A4): 1.Google Scholar
  48. Wystup, Uwe. 2006. FX options and structured products, 2nd ed, 94–101. Hoboken: Wiley.Google Scholar
  49. Zeng, L. 2000. Pricing weather derivatives. Journal of Risk Finance 2: 72–8.Google Scholar
  50. Zhang, J., I.G. Richardson, D.F. Webb, N. Gopalswamy, et al. 2007. solar and interplanetary sources of major geomagnetic storms (Dst \(\le -100\) nT) during 1996–2005. Journal of Geophysical Research: Space Physics 112: A10.Google Scholar

Copyright information

© Springer Nature Limited 2019

Authors and Affiliations

  1. 1.Institute of Physics, IGAMUniversity of GrazGrazAustria
  2. 2.Department of Economics & BusinessSaint Anselm CollegeManchesterUSA

Personalised recommendations