加密货币资产的奇异衍生品定价——蒙特卡洛视角

Mesias Alfeus, S. Kannan
{"title":"加密货币资产的奇异衍生品定价——蒙特卡洛视角","authors":"Mesias Alfeus, S. Kannan","doi":"10.2139/ssrn.3862655","DOIUrl":null,"url":null,"abstract":"In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discretely monitored window average lookback option, whose monitoring frequencies are randomly selected within the time to maturity, and whose monitoring price is the average asset price in a specified window surrounding the instant. We price these options whose underlying asset is the CCI30 index of various Cryptocurrencies, as opposed to a single cryptocurrency, with the intention of reducing volatility, and thus, the option price. We employ the Normal Inverse Gaussian (NIG) and Rough Fractional Stochastic Volatility (RFSV) models to the cryptocurrency market and using the Black-Scholes as the benchmark model. In doing so, we intend to capture the extreme characteristics such as jumps and volatility roughness for cryptocurrency price fluctuations. Since there is no availability of a closed-form solution for lookback option prices under these models, we utilize the Monte Carlo simulation for pricing and augment it using the antithetic method for variance reduction. Finally, we present the simulation results for the lookback options and compare the prices resulting from using the NIG model, RFSV model with those from the Black-Scholes model. We found that the option price is indeed lower for our proposed window average lookback option than for a traditional lookback option. We found the Hurst parameter to be H = 0.09 which confirms that the cryptocurrencies market is indeed rough.<br>","PeriodicalId":385335,"journal":{"name":"Cryptocurrencies eJournal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Pricing Exotic Derivatives for Cryptocurrency Assets - A Monte Carlo Perspective\",\"authors\":\"Mesias Alfeus, S. Kannan\",\"doi\":\"10.2139/ssrn.3862655\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discretely monitored window average lookback option, whose monitoring frequencies are randomly selected within the time to maturity, and whose monitoring price is the average asset price in a specified window surrounding the instant. We price these options whose underlying asset is the CCI30 index of various Cryptocurrencies, as opposed to a single cryptocurrency, with the intention of reducing volatility, and thus, the option price. We employ the Normal Inverse Gaussian (NIG) and Rough Fractional Stochastic Volatility (RFSV) models to the cryptocurrency market and using the Black-Scholes as the benchmark model. In doing so, we intend to capture the extreme characteristics such as jumps and volatility roughness for cryptocurrency price fluctuations. Since there is no availability of a closed-form solution for lookback option prices under these models, we utilize the Monte Carlo simulation for pricing and augment it using the antithetic method for variance reduction. Finally, we present the simulation results for the lookback options and compare the prices resulting from using the NIG model, RFSV model with those from the Black-Scholes model. We found that the option price is indeed lower for our proposed window average lookback option than for a traditional lookback option. We found the Hurst parameter to be H = 0.09 which confirms that the cryptocurrencies market is indeed rough.<br>\",\"PeriodicalId\":385335,\"journal\":{\"name\":\"Cryptocurrencies eJournal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cryptocurrencies eJournal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.3862655\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cryptocurrencies eJournal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3862655","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2

摘要

在本文中,我们开发了一种为加密货币定价回顾期权的方法。我们提出了一种离散监测的窗口平均回看期权,其监测频率是在到期日之前随机选择的,其监测价格是围绕该时刻的指定窗口内的平均资产价格。我们为这些期权定价,其标的资产是各种加密货币的CCI30指数,而不是单一的加密货币,目的是减少波动性,从而降低期权价格。我们将正态反高斯(NIG)和粗糙分数随机波动(RFSV)模型应用于加密货币市场,并使用Black-Scholes作为基准模型。在这样做的过程中,我们打算捕捉加密货币价格波动的极端特征,如跳跃和波动粗糙度。由于在这些模型下没有回溯期权价格的封闭形式解的可用性,我们利用蒙特卡罗模拟进行定价,并使用对偶方法进行方差减小。最后,给出了回溯期权的仿真结果,并比较了NIG模型、RFSV模型和Black-Scholes模型的定价结果。我们发现,我们提出的窗口平均回顾期权的期权价格确实低于传统的回顾期权。我们发现Hurst参数为H = 0.09,这证实了加密货币市场确实是粗糙的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Pricing Exotic Derivatives for Cryptocurrency Assets - A Monte Carlo Perspective
In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discretely monitored window average lookback option, whose monitoring frequencies are randomly selected within the time to maturity, and whose monitoring price is the average asset price in a specified window surrounding the instant. We price these options whose underlying asset is the CCI30 index of various Cryptocurrencies, as opposed to a single cryptocurrency, with the intention of reducing volatility, and thus, the option price. We employ the Normal Inverse Gaussian (NIG) and Rough Fractional Stochastic Volatility (RFSV) models to the cryptocurrency market and using the Black-Scholes as the benchmark model. In doing so, we intend to capture the extreme characteristics such as jumps and volatility roughness for cryptocurrency price fluctuations. Since there is no availability of a closed-form solution for lookback option prices under these models, we utilize the Monte Carlo simulation for pricing and augment it using the antithetic method for variance reduction. Finally, we present the simulation results for the lookback options and compare the prices resulting from using the NIG model, RFSV model with those from the Black-Scholes model. We found that the option price is indeed lower for our proposed window average lookback option than for a traditional lookback option. We found the Hurst parameter to be H = 0.09 which confirms that the cryptocurrencies market is indeed rough.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
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:481959085
Book学术官方微信