An economic scenario generator for embedded derivatives in South Africa

IF 0.1 Q4 BUSINESS, FINANCE
A. Levendis, E. Maré
{"title":"An economic scenario generator for embedded derivatives in South Africa","authors":"A. Levendis, E. Maré","doi":"10.4314/saaj.v22i1.4","DOIUrl":null,"url":null,"abstract":"It is well known that interest rate risk is a dominating factor when pricing long-dated contingent claims. The Heston stochastic volatility model fails to capture this risk as the model assumes a constant interest rate throughout the life of the claim. To overcome this, the risk-free interest rate can be modelled by a Hull-White short rate process and can be combined with the Heston stochastic volatility model to form the so-called Heston-Hull-White model. The Heston-Hull-White model allows for correlation between the equity and interest rate processes, a component that is important when pricing long-dated contingent claims. In this paper, we apply the Heston-Hull-White model to price Guaranteed Minimum Maturity Benefits (GMMBs) and Guaranteed Minimum Death Benefits (GMDBs) offered in the life insurance industry in South Africa. We propose a further extension by including stochastic mortality rates based on either a continuous-time Cox-Ingersoll-Ross short rate process or a discrete-time AR(1)-ARCH(1) model. Our findings suggest that stochastic interest rates are the dominating factor when reserving for GMMB and GMDB products. Furthermore, a delta-hedging strategy can help reduce the variability of embedded derivative liabilities.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.1000,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"South African Actuarial Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4314/saaj.v22i1.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0

Abstract

It is well known that interest rate risk is a dominating factor when pricing long-dated contingent claims. The Heston stochastic volatility model fails to capture this risk as the model assumes a constant interest rate throughout the life of the claim. To overcome this, the risk-free interest rate can be modelled by a Hull-White short rate process and can be combined with the Heston stochastic volatility model to form the so-called Heston-Hull-White model. The Heston-Hull-White model allows for correlation between the equity and interest rate processes, a component that is important when pricing long-dated contingent claims. In this paper, we apply the Heston-Hull-White model to price Guaranteed Minimum Maturity Benefits (GMMBs) and Guaranteed Minimum Death Benefits (GMDBs) offered in the life insurance industry in South Africa. We propose a further extension by including stochastic mortality rates based on either a continuous-time Cox-Ingersoll-Ross short rate process or a discrete-time AR(1)-ARCH(1) model. Our findings suggest that stochastic interest rates are the dominating factor when reserving for GMMB and GMDB products. Furthermore, a delta-hedging strategy can help reduce the variability of embedded derivative liabilities.
南非嵌入式衍生品的经济情景生成器
众所周知,利率风险是长期或有债权定价的主要因素。赫斯顿随机波动模型未能捕捉到这种风险,因为该模型假设在整个索赔期内利率不变。为了克服这一点,无风险利率可以通过赫尔-怀特短期利率过程来建模,并可以与赫斯顿随机波动模型相结合,形成所谓的赫斯顿-赫尔-怀特模型。赫斯顿-赫尔-怀特模型考虑了股权和利率过程之间的相关性,这是为长期或有债权定价时的重要组成部分。本文运用Heston-Hull-White模型对南非人寿保险行业提供的保证最低到期收益(gmmb)和保证最低死亡收益(gmdb)进行定价。我们提出了一个进一步的扩展,包括基于连续时间Cox-Ingersoll-Ross短期利率过程或离散时间AR(1)-ARCH(1)模型的随机死亡率。我们的研究结果表明,随机利率是GMMB和GMDB产品储备的主导因素。此外,delta对冲策略可以帮助降低嵌入衍生品负债的可变性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
South African Actuarial Journal
South African Actuarial Journal BUSINESS, FINANCE-
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信