Malaysian Journal of Mathematical Sciences, May 2022, Vol. 16, No. 2
Modelling Temperature Using CARMA Processes with Stochastic Speed of Mean Reversion for Temperature Insurance Pricing
Darus, M. and Taib, C. M. I. C.
Corresponding Email: imran@umt.edu.my
Received date: 20 September 2021
Accepted date: 5 January 2022
Abstract:
In this paper, we present a continuous time autoregressive moving average (CARMA) model
with stochastic speed of mean reversion. This model allows the mean reversion rates to behave
stochastically and governed by an Ornstein-Uhlenbeck process. We provide closed-form
solution to the CARMA with stochastic speed of mean reversion and formulate the price of temperature
insurance using spot-forward relationship framework. We demonstrate the insurance
pricing based on the cumulative average temperatures (CAT) index by simulating the temperature
variations. We found that our proposed model may explain the temperature evolution well
and the price of CAT-based index insurance looks reasonable.
Keywords: stochastic process; continuous autoregressive moving average processes; mean reversion; temperature model; temperature insurance.
