{"title":"Modelling Temperature Using CARMA Processes with Stochastic Speed of Mean Reversion for Temperature Insurance Pricing","authors":"M. Darus, C. M. I. C. Taib","doi":"10.47836/mjms.16.2.07","DOIUrl":null,"url":null,"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.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Malaysian Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47836/mjms.16.2.07","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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.
期刊介绍：
The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.
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