Modeling temperature and pricing weather derivatives based on subordinate Ornstein-Uhlenbeck processes

Kevin Z. Tong; Allen Liu; Kevin Z. Tong; Allen Liu

doi:10.3934/GF.2020001

Green Finance

2020, Volume 2, Issue 1: 1-19. doi: 10.3934/GF.2020001

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Research article

Modeling temperature and pricing weather derivatives based on subordinate Ornstein-Uhlenbeck processes

Kevin Z. Tong ^{1
,
,},
Allen Liu ²

1.
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada
2.
Enterprise Risk and Portfolio Management, Bank of Montreal, Toronto, ON, Canada

Received: 09 February 2020 Accepted: 26 February 2020 Published: 27 February 2020
JEL Codes: C02, G13

In this paper we employ a time-changed Ornstein-Uhlenbeck (OU) process for modeling temperature and pricing weather derivatives, where the time change process is a Lévy subordinator time changed by a deterministic clock with seasonal activity rate. The drift, diffusion volatility and jumps under the new model are all seasonal, which are supported by the observed temperature time series. An important advantage of our model is that we are able to derive the analytical pricing formulas for temperature futures and future options based on eigenfunction expansion technique. Our empirical study indicates the new model has the potential to capture the main features of temperature data better than the competing models.
- weather derivatives,
- eigenfunction expansion,
- stochastic time change,
- Lévy subordination,
- additive subordination
Citation: Kevin Z. Tong, Allen Liu. Modeling temperature and pricing weather derivatives based on subordinate Ornstein-Uhlenbeck processes[J]. Green Finance, 2020, 2(1): 1-19. doi: 10.3934/GF.2020001

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Abstract

In this paper we employ a time-changed Ornstein-Uhlenbeck (OU) process for modeling temperature and pricing weather derivatives, where the time change process is a Lévy subordinator time changed by a deterministic clock with seasonal activity rate. The drift, diffusion volatility and jumps under the new model are all seasonal, which are supported by the observed temperature time series. An important advantage of our model is that we are able to derive the analytical pricing formulas for temperature futures and future options based on eigenfunction expansion technique. Our empirical study indicates the new model has the potential to capture the main features of temperature data better than the competing models.

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