Regime-Switching Risk: To Price or Not to Price?

T. Siu
{"title":"Regime-Switching Risk: To Price or Not to Price?","authors":"T. Siu","doi":"10.1155/2011/843246","DOIUrl":null,"url":null,"abstract":"Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"35 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Stochastic Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2011/843246","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 25

Abstract

Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.
政权转换风险:价格还是不价格?
政权转换的风险应该被定价吗?这也许是在马尔可夫的、制度转换的布莱克-斯科尔斯-默顿模型下为或有债权定价时需要解决的重要“规范性”问题之一。我们使用最小相对熵方法来解决这个问题。首先,我们利用双鞅的鞅表示来表征等价鞅测度的正则空间,该正则空间可以看作是包含扩散风险和状态切换风险的最大等价鞅测度空间。然后,我们证明了通过最小化等效鞅测度与真实世界概率测度之间的相对熵来选择正则空间上的最优等效鞅测度不需要对状态切换风险进行定价。最优度量也证明了在制度转换市场中使用埃舍尔变换进行期权估值是合理的。
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
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:604180095
Book学术官方微信