Mitigating geographical basis risk of weather derivatives using spatial-temporal regime-switching temperature model

Samuel Asante Gyamerah; Philip Ngare; Dennis Ikpe; Samuel Asante Gyamerah; Philip Ngare; Dennis Ikpe

doi:10.3934/math.2019.4.1274

AIMS Mathematics

2019, Volume 4, Issue 4: 1274-1290. doi: 10.3934/math.2019.4.1274

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Mitigating geographical basis risk of weather derivatives using spatial-temporal regime-switching temperature model

1.
Pan African University, Institute for Basic Sciences, Technology, and Innovation, Kenya
2.
University of Nairobi, Kenya
3.
African Institute for Mathematical Sceinces, South Africa

Received: 14 June 2019 Accepted: 14 August 2019 Published: 02 September 2019
MSC : 91G10, 91G20, 60G20, 60G15

In this paper, geographical basis risk in weather derivative design and pricing is mitigated by using spatial-temporal pricing models. A two-state regime-switching temperature model is constructed and extended to multi-dimensional locations that are highly correlated in temperature. The "normal" and "shifted" regime of this model are characterized by a heteroscedastic Ornstein-Uhlenbeck process and a Brownian motion with mean different from zero respectively. The correlation between the driving noise in each regime is assumed to be a function of the space between the locations and increases with decreasing space. A weight is assigned to each location in the temperature basket. However, a location with a higher risk is assigned a larger weight and vice versa. The weightings in the temperature basket gave considerable importance to farming locations having greater exposure to temperature risk. The further the farming location from the weather station, the larger the weight. With this spatial-temporal weather derivatives pricing model, the holder of a weather derivative contract will have the opportunity to select the most appropriate composite of weather stations with their desired weight that can reduce geographical basis risks.
- agriculture risk management,
- weather derivatives,
- regime-switching model,
- geographical basis risk,
- spatial-temporal model
Citation: Samuel Asante Gyamerah, Philip Ngare, Dennis Ikpe. Mitigating geographical basis risk of weather derivatives using spatial-temporal regime-switching temperature model[J]. AIMS Mathematics, 2019, 4(4): 1274-1290. doi: 10.3934/math.2019.4.1274

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Abstract

In this paper, geographical basis risk in weather derivative design and pricing is mitigated by using spatial-temporal pricing models. A two-state regime-switching temperature model is constructed and extended to multi-dimensional locations that are highly correlated in temperature. The "normal" and "shifted" regime of this model are characterized by a heteroscedastic Ornstein-Uhlenbeck process and a Brownian motion with mean different from zero respectively. The correlation between the driving noise in each regime is assumed to be a function of the space between the locations and increases with decreasing space. A weight is assigned to each location in the temperature basket. However, a location with a higher risk is assigned a larger weight and vice versa. The weightings in the temperature basket gave considerable importance to farming locations having greater exposure to temperature risk. The further the farming location from the weather station, the larger the weight. With this spatial-temporal weather derivatives pricing model, the holder of a weather derivative contract will have the opportunity to select the most appropriate composite of weather stations with their desired weight that can reduce geographical basis risks.

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