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计价物numeraire应该如何理解？ - 微观经济学 - 经管之家(原人大经济论坛)

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人大经济论坛 › 论坛 › 经济学论坛三区 › 微观经济学 › 计价物numeraire应该如何理解？

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关键词：Numeraire

如何理解

NUM

Era

Air

如何

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Numéraire - Wikipedia

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1Change of numéraire

2Numéraire in financial pricing

3See also

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From Wikipedia, the free encyclopedia

The numéraire (or numeraire) is a basic standard by which value is computed. In mathematical economics it is a tradable economic entity in terms of whose price the relative prices of all other tradables are expressed. In a monetary economy, one of the functions of money is to act as the numéraire, i.e. to serve as a unit of account and therefore provide a common benchmark relative to which the value of various goods and services can be measured against.

Using a numeraire, whether monetary or some consumable good, facilitates value comparisons when only the relative prices are relevant, as in general equilibrium theory. When economic analysis refers to a particular good as the numéraire, one says that all other prices are normalized by the price of that good. For example, if a unit of good g has twice the market value of a unit of the numeraire, then the (relative) price of g is 2. Since the value of one unit of the numeraire relative to one unit of itself is 1, the price of the numeraire is always 1.

Change of numéraire[edit]

In a financial market with traded securities, one may use a numéraire to price assets. For instance, let

(

)

{\displaystyle M(t)}

be the price at time t of $1 that was invested in the money market at time 0. The fundamental theorem of asset pricing says that all assets

(

)

{\displaystyle S(t)}

priced in terms of the numéraire (in this case, M), are martingales with respect to a risk-neutral measure, say

{\displaystyle Q}

. That is:

(

)

(

)

[

(

)

(

)

]

{\displaystyle {\frac {S(t)}{M(t)}}=E_{Q}\left[{\frac {S(T)}{M(T)}}\right]}

Now, suppose that

(

)

{\displaystyle N(t)>0}

is another strictly positive traded asset (and hence a martingale when priced in terms of the money market). Then we can define a new probability measure

{\displaystyle Q^{N}}

by the Radon–Nikodym derivative

(

)

(

)

(

)

(

)

(

)

(

)

{\displaystyle {\frac {dQ^{N}}{dQ}}={\frac {M(0)}{M(T)}}{\frac {N(T)}{N(0)}}={\frac {N(T)}{M(T)}}}

Then it can be shown that

(

)

{\displaystyle S(t)}

is a martingale under

{\displaystyle Q^{N}}

when priced in terms of the new numéraire

(

)

{\displaystyle N(t)}

[

(

)

(

)

]

[

(

)

(

)

(

)

(

)

]

[

(

)

(

)

]

(

)

(

)

[

(

)

(

)

]

(

)

(

)

(

)

(

)

(

)

(

)

{\displaystyle {\begin{aligned}&{}\quad E_{Q^{N}}\left[{\frac {S(T)}{N(T)}}\right]\\&=E_{Q}\left[{\frac {N(T)}{M(T)}}{\frac {S(T)}{N(T)}}\right]/E_{Q}\left[{\frac {N(T)}{M(T)}}\right]\\&={\frac {M(t)}{N(t)}}E_{Q}\left[{\frac {S(T)}{M(T)}}\right]\\&={\frac {M(t)}{N(t)}}{\frac {S(t)}{M(t)}}\\&={\frac {S(t)}{N(t)}}\end{aligned}}}

This technique has many important applications in LIBOR and swap market models, as well as commodity markets. Jamshidian (1989) first used it in the context of the Vasicek model for interest rates in order to calculate bond options prices. Geman, El Karoui and Rochet (1995) introduced the general formal framework for the change of numéraire technique. See for example Brigo and Mercurio (2001)[1] for a change of numéraire toolkit.

Numéraire in financial pricing[edit]

Determining an appropriate numéraire has foundation in several financial pricing models such as options and certain assets. Identifying a risky asset as numéraire has a correlation with the number of underlying assets to model. Underlying shifts are modelled by the following:

{\displaystyle Z_{i}:={\frac {X_{i}}{X_{0}}}}

(

)

→

(

)

{\displaystyle X=(X_{0},X_{1},...,X_{n})\to Z=(1,Z_{1},...,Z_{n})}

where 1 defines the numéraire.

Numeraire: What it is, History, How it Works

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如何理解计价单位（numeraire）? - 知乎

如何理解计价单位（numeraire）? - 知乎首页知乎知学堂发现等你来答切换模式登录/注册金融数学如何理解计价单位（numeraire）?一开始对计价单位的理解就是简单的，把计价单位当分母，就能把一个随机的payoff在此probability measure下变成鞅。可是当把股票，un…显示全部关注者22被浏览13,135关注问题写回答邀请回答好问题 4添加评论分享3 个回答默认排序黑猫Q形态金融工程学等 3 个话题下的优秀答主关注早上CNY有报价前水一个答案不才之前写过一个计价单位系列（内含目录）；论严谨程度，LPL水平是没有的，但是勉强自信有个LDL的水平，如果要学习概念凑活着看吧。不过题主显然需要的不是概念而是直觉，那我就讲点直觉。计价单位的含义出乎意料简单，就是字面意思——单位。相当于换了个币种去度量产品。那位啥这么简单的概念，到了衍生品里就那么虚假和复杂呢？因为你但你接受了一个单位做度量，就必须接受这个单位的全部这里的"全部"包括但不限于，价格，分布信息，定价核（贴现因子）……而这些”全部“信息，在deltaone产品或者收linear产品时很难体现出来的，而衍生品偏偏会体现或者需要那个”全部“。以和计价单位字面意思最接近的例子——外汇为例，对于结售汇这种简单的行为，以Ccy1还是Ccy2作为基准货币无非是汇率采用X还是1/X的区别但是但凡需要用到价格以外的其他信息，比如期望。那就不行了因为最简单的：\frac{1}{E[X]} \ne E[\frac{1}{X}] 同理，方差，衍生品价值，跨国贴现因子这些在Ccy1Ccy2和Ccy2Ccy1下就会有天壤之。而题主对”单位“这一概念理解崩塌最大的原因是刚刚开始接触需要接受单位全部信息这样的场景吧。Welcome to world of derivatives 发布于 2021-02-25 09:03赞同 42添加评论分享收藏喜欢收起宦文浩热死了！关注刚看完这一章，粗浅地答一下。首先，无套利是计价单位变换使用的基础条件。此时所有贴现资产过程在该市场的风险中性测度下是鞅，这个时候才能把其他资产看做是计价单位。例如Shreve金融随机分析里推导外币风险中性测度的思路就是，先通过本币货币市场，本币股票和购买外币货币市场再转回本币这三种资产组合的无套利得出本币风险中性测度所对应的布朗运动，再观察外币下的三种投资方案，就是在购买外币货币市场再转回本币的资产组合所计价的本币的三种资产（有点绕，建议看书），而由于本币的三种资产在本币风险中性测度下都是鞅，因而可以直接做计价单位变换，轻松将外币风险中性测度下的布朗运动通过哥萨诺夫定理导出。然后，计价单位变换可以简化计算。计价单位变换过以后的资产过程在新的测度下还是一个GBM。如果布朗运动都是独立的话，那么波动项不变，只是漂移项有点变化。但是采取不同的计价单位就可以把原先风险中性测度中的D(T)V(T)进行相当漂亮的化简。后续学了更多可能再补充吧…发布于 2021-08-09 17:01赞同 1添加评论分享收藏喜欢收起

Numeraire，为世界对冲基金提供动力的加密货币 - 知乎

Numeraire，为世界对冲基金提供动力的加密货币 - 知乎切换模式写文章登录/注册Numeraire，为世界对冲基金提供动力的加密货币李旭互联网声明：本文翻译于Numerai项目创始人Richard Craib的的2018-02-11的博文https://www.zhihu.com/video/955193447112564736在2017年，Numerai发布了一个新的API，允许全球的人们通过机器学习模型提交预测来为我们的对冲基金提供动力。2018年，我们专注于我们的加密货币Numeraire（NMR）。我们将使NMR更有价值，我们将大大增加使用它的数据科学家的数量。Numeraire的使用Numerai上的每个用户都有机会将NMR的token放在他们的预测上，以表达他们对模型的信心。如果他们的预测是好的，他们会赚钱，他们的NMR会返回。如果他们的预测很差，他们的NMR将被销毁。对我们来说，最重要的使用指标是NMR的最大收获者是否也是最大的持有者，即持币大户是用户。这正是Numerai正在发生的事情。如果你进入Numerai的排行榜，并根据NMR的职业收入排序，你可以看到，排名前15的NMR收获人员中，有7人当前持有NMR。因此，拥有最大NMR数量的参与者中有将近一半的人每周都会增持。我不知道会有哪个单一的加密货币项目，其中token被其最大的持有者如此广泛而频繁地使用。在Numerai上，持币大户是使用者（蓝色意味着当前持有NMR）这种用法的一个重要原因是Numerai没有将ICO中的token出售给无意使用它的投机者。相反，我们将它与Numerai上最优秀的数据科学家 - 最有可能使用它的人分享。在发布当天，NMR不仅可以使用，而且可以立即用于其接收者。自发布以来，我们的一些数据科学家每隔一周就会获取增持NMR。Numeraire效应我们之所以要求数据科学家将NMR押注在他们的模型上，是因为只有好的模型才会获益并增持。这也正在发生。当Numerai用户提交预测时，他们还会对测试集提交预测。用户在这个测试集上没有得到他们的性能反馈，他们甚至不知道我们的数据代表什么; 这确保了这个测试集的测试结果是严格的。我们基于测试集的反向测试分析了未持有模型与已持有模型的夏普比率。这是表现：未持有的模型的夏普比率：1.66持有NMR的模型的夏普比率：2.09我们的后验有很多参数，例如我们如何将模型组合在一起，我们如何优化投资组合，以及如何估算交易成本。通过上述夏普比率，我们假设我们对模型的权重相等，不承担交易成本，也不做任何优化。夏普中的这种差异意味着持有者的模型可以获得更多的回报，同时回测中的波动率更低。例如，对于相同的10％波动率，持有者的模型将获得20.9％，而未持有者模型只能获得16.6％ - 对于对冲基金来说是一个很大的差异。NMR是一个实用token的巨大成功案例。它被广泛持有并被持有人使用。 NMR达到了我们一年前发表的白皮书的确切预期结果。它设计精确的行为并提高Numerai模型的性能。5倍提高由于持有NMR是一个如此强大的信号，我们希望今年更加关注它。我们刚刚将放款支出增加到2000NMR + 6000美元。以目前二级市场的NMR价格计算，这一变化使预测锦标赛支出增加500％。从今天开始，获得NMR的唯一方法就是赚取并持有NMR。这意味着持有NMR变得更加有价值，更多的NMR现在将被用户拿着并持有增值。Numerai的总收入每月超过140,000美元，使其成为全球薪酬最高的数据科学竞赛。编辑于 2018-03-08 21:50对冲基金区块链(Blockchain)金融学赞同添加评论分享喜欢收藏申请

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Numeraire price today, NMR to USD live price, marketcap and chart | CoinMarketCap

raire price today, NMR to USD live price, marketcap and chart | CoinMarketCapCryptos: 2.2M+Exchanges: 722Market Cap: $2.52T0.26%24h Vol: $152.49B41.17%Dominance: BTC: 52.2% ETH: 18.1% ETH Gas: 53 Gwei Fear & Greed: 88/100CryptocurrenciesCryptocurrenciesRankingCategoriesGlobal ChartsHistorical SnapshotsBitcoin ETFsLeaderboardsTrendingRecently AddedGainers & LosersMost VisitedNFTOverall NFT StatsTop CollectionsUpcoming SalesOn Chain DataDex PairsChain RankingHot DEX PairsExchangesSpotDerivativesDEXCommunityFeedsTopicsLivesArticlesProductsPRODUCTSConverterCMC LabsTelegram BotAdvertiseCrypto APISite WidgetsCAMPAIGNSAirdropsDiamond RewardsLearn & EarnCALENDARSICO CalendarEvents CalendarLearnNewsAcademyResearchVideosGlossaryHalving: 43DWatchlistPortfolioSearch/Numeraire price NMR$38.16 10.58% (1d)Numeraire to USD ChartLoading DataPlease wait a moment. Add to watchlist Numeraire statisticsMarket cap 10.64%$239,272,575#275Volume (24h) 15.03%$30,315,950#283Volume/Market cap (24h) 12.67%Total value locked (TVL) $7,487,712Market cap / TVL 31.95536375Circulating supply 6,270,704 NMR57.01%Total supply 10,742,748 NMRMax. supply 11,000,000 NMRFully diluted market cap $419,729,325ContractsEthereum: 0x1776...b46671 Official linksWebsiteWhitepaperGitHubSocialsTwitterRedditTelegramRating · Based on 3 institutional ratings3.2 Network informationChain explorersSupported walletsUCID1732 NMR to USD ConverterNMRUSDPrice performance24h Low$33.24High$38.71All-time highJun 25, 2017 (7 years ago)$168.49-77.35%All-time lowNov 26, 2018 (5 years ago)$1.93+1879.46%See historical dataPopularityIn watchlists71,642x564th / 8.9KTagsAsset ManagementAI & Big DataDeFiShow allMore informationDo you own this project? Update Token Info Loading DataPlease wait a moment. Numeraire community Numeraire marketsALLCEXDEXSpotPerpetualFuturesAll pairsLoading data...Show full widthDisclaimer: This page may contain affiliate links. CoinMarketCap may be compensated if you visit any affiliate links and you take certain actions such as signing up and transacting with these affiliate platforms. Please refer to Affiliate DisclosureNumeraire news About NumeraireWhat Is Numeraire (NMR)?Numerai is an Ethereum-based platform allowing developers and data scientists to experiment and create machine learning models with improved reliability. The platform’s main goal is to bring decentralization to the data science field and allow developers to compete in creating effective machine learning prediction models.Founded in late 2015 in San Francisco, Numerai claims to be the first hedge fund to launch a cryptocurrency on the market. Unlike traditional hedge funds, however, Numerai relies on the data and predictions produced by tournament participants to participate in the stock market. They claim to be the first hedge fund to use machine learning so heavily in its investment strategy.Who Are the Founders of Numeraire?Richard Craib is the founder and CEO of Numerai. He graduated from the University of Cape Town in 2008 and later acquired one more bachelor’s degree from Cornell University, and spent a year in UC Berkeley. His professional career started with founding Numerai and has taken him to a Forbes 30 under 30 designee position.Richard Craib is often cited for his innovative approach to hedge fund management and the revolutionary idea to rely so heavily on artificial intelligence for stock price prediction. Not only that, Numerai has created one of the largest global data science tournaments.What Makes Numeraire Unique?Numerai and the Numeraire token are unique in terms of the idea behind their creation. This is reportedly the first cryptocurrency to be created and released by a hedge fund. One of the main benefits of the NMR token is that it is awarded to data scientists whose models perform well in the Numerai tournament. This means that the token becomes more valuable as more people enter the tournament and start competing.Not only that, but the models ventured for the tournament allow Numerai to actively participate in stock market trading based on the results revealed by participating projects. This innovative approach to stock trading makes Numerai one of the few hedge funds to rely significantly on AI-generated data predictions.How Many Numeraire (NMR) Coins Are There in Circulation?The maximum supply of NMR is 11,000,000 tokens. The supply cap for Numeraire was initially 21 million tokens; however, the platform announced that it is going to cut this maximum by more than half in 2019.In a 2018 press release, Numerai announced that three million NMR tokens will remain locked until 2028, and will be released as a reward incentive for tournament participants. The Numeraire token did not undergo an initial coin offering (ICO). Instead, Numerai decided to distribute 1 million NMR tokens among 12,000 platform users with the highest activity statistics.NMR tokens are burned on a weekly basis, as tournament participants who venture losing models and predictions lose their stake in the competition.How Is the Numeraire Network Secured?As an ERC-20 token, NMR is secured by the Ethereum proof-of-stake (PoS) consensus mechanism. This means that validators and block creators are selected based on the amount of NMR tokens they are currently staking. ERC-20 tokens are becoming increasingly popular as they offer higher versatility in terms of use. However, the Ethereum blockchain still provides the same level of protection as blockchains operating with other security protocols.Unlike other popular consensus mechanisms like proof-of-work (PoW), PoS does not rely on high consumption of electrical or computing power to create new tokens. This makes the consensus much more scalable and easily incorporated in different use cases.Where Can You Buy Numeraire (NMR)?Numeraire is growing in popularity, as the hedge fund performs better, and more data scientists are participating in the weekly tournament. If you are looking to trade NMR, there are a number of exchanges now offering the token.Coinbase Pro has the highest trading volume for NMR/USD as of February 2021. Other relevant exchanges with high trading volumes include Binance, DigiFinex, and Bilaxy.Read more about buying crypto here.Related Pages:Read more about Uniswap.Find out more about Tellor.Learn more about networks.Have a look at the CoinMarketCap blog. Numeraire analyticsLoading...Most Visited CryptocurrenciesRabbitXRBX$0.131412.44%DexCheckDCK$0.130832.59%RichQUACK.comQUACK$0.00000000133921.92%Solidus Ai TechAITECH$0.13692.17%Script NetworkSCPT$0.0310318.73%OpSecOPSEC$1.6030.60%MAGATRUMP$6.3719.20%Baby ElonBABYELON$0.0000000000178855.76%Niza GlobalNIZA$0.011795.38%BitcoinBTC$66,987.940.66%Super TrumpSTRUMP$0.00277542.71%Shiba InuSHIB$0.000031913.22%BabyBABY$0.00000156939.02%Childrens Aid FoundationCAF$0.32586.22%SolspongeSOLSPONGE$0.000000020732.47%EthereumETH$3,790.772.83%SolanaSOL$139.966.12%PepePEPE$0.00000684816.25%DogecoinDOGE$0.15339.61%Fetch.aiFET$2.6533.05%Global PricesNMR/USDUnited States Dollar$38.16NMR/EUREuro€35.02NMR/GBPPound Sterling£29.92NMR/CNYChinese Yuan¥274.65NMR/CADCanadian Dollar$51.50NMR/AUDAustralian Dollar$57.77NMR/JPYJapanese Yen¥5,637.21NMR/KRWSouth Korean Won₩50,731.55NMR/RUBRussian Ruble₽3,471.99NMR/INRIndian Rupee₹3,155.62NMR/BRLBrazilian RealR$188.46NMR/TRYTurkish Lira₺1,215.22NMR/PHPPhilippine Peso₱2,130.16People also watchGoldMint$0.0336960.73%Band Protocol$2.445.75%Uniswap$14.874.77%Firo$2.010.32%Chainlink$19.931.52%Oasis Network$0.17158.36%Blocknet$0.040890.78%yearn.finance$9,656.760.03%Solar$0.48694.81%MahaDAO$1.293.21%TrendingPepe$0.00000686315.59%dogwifhat$1.7915.14%Meme Ai$0.005971112.79%Fetch.ai$2.6634.76%Shiba Inu$0.0000320612.85%Numeraire Price Live DataThe live Numeraire price today is $38.16 USD with a 24-hour trading volume of $30,315,950 USD. We update our NMR to USD price in real-time. Numeraire is up 10.58% in the last 24 hours. The current CoinMarketCap ranking is #275, with a live market cap of $239,272,575 USD. It has a circulating supply of 6,270,704 NMR coins and a max. supply of 11,000,000 NMR coins.If you would like to know where to buy Numeraire at the current rate, the top cryptocurrency exchanges for trading in Numeraire stock are currently Binance, OKX, Bybit, UEEx, and DigiFinex. You can find others listed on our crypto exchanges page.CryptocurrenciesTokensNumeraireProductsCMC LabsChatGPT PluginCrypto APICrypto IndicesDoodlesSitemapAdvertiseCompanyAbout usTerms of usePrivacy PolicyCookie preferencesCookie policyCommunity RulesDisclaimerMethodologyCareersWe’re hiring!SupportRequest FormContact SupportFAQGlossarySocialsX (Twitter)CommunityTelegramInstagramFacebookRedditLinkedIn© 2024 CoinMarketCap. All rights reserved

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The New Palgrave Dictionary of Economics

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Numeraire

Michael Allingham2

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AbstractIn general equilibrium theory the price of one good in terms of another is interpreted as the amount of the second which can be exchanged for a given amount of the first. There is thus no essential role for a standard of value, or numéraire, though it is frequently helpful to introduce this. Such a numéraire is a commodity in terms of which, by convention, other commodities are valued.KeywordsMoneynumeraireJEL ClassificationsD0This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume

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BibliographyArrow, K.J., and F. Hahn. 1971. General competitive analysis. San Francisco: Holden Day.

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Clower, R.W. 1967. A reconsideration of the microfoundations of monetary theory. Western Economic Journal 6: 1–8.

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Walras, L. 1874–7. Eléments d’économie politique pure. Definitive ed., Lausanne: Corbaz, 1926. Trans. W. Jaffé as Elements of pure economics. London: George Allen & Unwin, 1954.

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Download referencesAuthor informationAuthors and Affiliations http://link.springer.com/referencework/10.1057/978-1-349-95121-5Michael AllinghamAuthorsMichael AllinghamView author publicationsYou can also search for this author in

In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_1514-2Download citation.RIS.ENW.BIBDOI: https://doi.org/10.1057/978-1-349-95121-5_1514-2Received: 13 January 2017Accepted: 13 January 2017Published: 17 March 2017

Publisher Name: Palgrave Macmillan, London

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Numeraire

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DOI: https://doi.org/10.1057/978-1-349-95121-5_1514-2

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25 November 2016

DOI: https://doi.org/10.1057/978-1-349-95121-5_1514-1

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