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Modeling and pricing of space weather derivatives

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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.

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Notes

  1. X-class flares (R3–R5) have a peak flux of >\(10^{-4}\) W/\({\text(m)}^2\). They are major events that can trigger planet-wide radio blackouts and long-lasting radiation storms, whereas M-class (R1–R2) flares are medium-sized with a peak flux of >\(10^{-5}\) W/\({\text(m)}^2\). They can cause brief radio blackouts that affect Earth’s polar regions. Minor radiation storms are sometimes followed by an M-class flare.

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Authors and Affiliations

  1. Institute of Physics, IGAM, University of Graz, Universitaetsplatz 5, 8010, Graz, Austria

    Birgit Lemmerer

  2. Department of Economics & Business, Saint Anselm College, Saint Anselm Drive 100, Manchester, NH, 03102, USA

    Stephan Unger

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  1. Birgit Lemmerer
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Correspondence to Stephan Unger.

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Appendix

Appendix

See Tables 3, 4, 5, 6, 7, 8 and 9.

Table 3 Finalized global Kp-index with 28 values (?)
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Table 4 Regression: 1st derivative of sunspots on option prices with Kp-barrier 7
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Table 5 Regression: 1st derivative of sunspots on option prices with Kp-barrier 8
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Table 6 Regression: 1st derivative of sunspots on option prices with Kp-barrier 9
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Table 7 Regression: weights of 1st derivative on option prices with Kp-barrier 7
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Table 8 Regression: weights of 1st derivative on option prices with Kp-barrier 8
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Table 9 Regression: weights of 1st derivative on option prices with Kp-barrier 9
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Lemmerer, B., Unger, S. Modeling and pricing of space weather derivatives. Risk Manag 21, 265–291 (2019). https://doi.org/10.1057/s41283-019-00052-0

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