波动率
波动率和标准差的关系
波动率和标准差的关系
波动率和标准差是两个经济学和金融学中常用的概念，它们之间有着密切的关系。
波动率是指资产价格在一定时间内的波动程度，而标准差则是衡量数据集合中各数据值偏离平均值的程度。
波动率和标准差之间的关系可以通过以下公式进行计算：
波动率= 标准差/ 平均值
这个公式表明，波动率和标准差之间的关系是正比的。
也就是说，当标准差增加时，波动率也会增加；反之，当标准差减少时，波动率也会减少。
在金融市场中，波动率和标准差的计算通常是基于历史数据进行的。
通过对历史数据的分析，可以得出资产价格的平均值和标准差，从而计算出波动率。
波动率的大小反映了市场对资产价格波动的预期，因此在投资决策中具有重要的参考价值。
总之，波动率和标准差是经济学和金融学中非常重要的概念，它们之间的关系是密切的。
通过对波动率和标准差的计算和分析，可以更好地理解市场的波动性和风险，从而做出更加明智的投资决策。
波动率计算公式
波动率计算公式
波动率计算公式是：波动率＝［有重要意义的第二高（低）点一有重要意义的第一高（低点）］／两高（低）点间的时间。
波动率计算公式预测是根据历史的数据。
进一步来说的话，新股就需要经过一段时间的运动观察之后，才可以进行相应的预测。
重要的低点是判断的关键，如果点选错了，那么就没有了计算的意义。
在选择重要高低点的时候也是需要注意跟时间周期的结构相符合，月线、周线的高低点并不一定要符合日线、小时线的要求。
波动率计算公式介绍
波动率也是分为上升趋势中的波动率和下跌趋势中的波动率计算方法。
上升趋势中的波动率计算是需要在上升趋势中进行选取的，使用底部和底部之间的距离，然后除以两个底部之间相隔的时间。
而在下跌趋势的波动率计算需要取在下跌趋势中，顶部和顶部之间的距离，然后除以两个顶部之间的时间间隔。
使用这个当作坐标的刻度绘制出1x1图形。
波动率
波动率研究一、波动率概念波动率是金融资产价格的波动程度，是对资产收益率不确定性的衡量，用于反映金融资产的风险水平。
波动率越高，金融资产价格的波动越剧烈，资产收益率的不确定性就越强；波动率越低，金融资产价格的波动越平缓，资产收益率的确定性就越强。
二、波动率的分类1、隐含波动率隐含波动率是将市场上的权证交易价格代入权证理论价格模型，反推出来的波动率数值。
从理论上讲，要获得隐含波动率的大小并不困难。
由于期权定价模型(如BS模型)给出了期权价格与五个基本参数(标的股价、执行价格、利率、到期时间、波动率)之间的定量关系，只要将其中前4个基本参数及期权的实际市场价格作为已知量代入定价公式，就可以从中解出惟一的未知量，其大小就是隐含波动率。
因此，隐含波动率又可以理解为市场实际波动率的预期。
2、历史波动率历史波动率是指投资回报率在过去一段时间内所表现出的波动率，它由标的资产市场价格过去一段时间的历史数据（即St的时间序列资料）反映。
这就是说，可以根据{St}的时间序列数据，计算出相应的波动率数据，然后运用统计推断方法估算回报率的标准差，从而得到历史波动率的估计值。
显然，如果实际波动率是一个常数，它不随时间的推移而变化，则历史波动率就有可能是实际波动率的一个很好的近似。
3、预测波动率预测波动率又称为预期波动率，它是指运用统计推断方法对实际波动率进行预测得到的结果，并将其用于期权定价模型，确定出期权的理论价值。
因此，预测波动率是人们对期权进行理论定价时实际使用的波动率。
这就是说，在讨论期权定价问题时所用的波动率一般均是指预测波动率。
需要说明的是，预期波动率并不等于历史波动率，因为前者是人们对实际波动率的理解和认识，当然，历史波动率往往是这种理论和认识的基础。
除此之外，人们对实际波动率的预测还可能来自经验判断等其他方面。
4、已实现波动率已实现波动率是针对频率较高的数据计算的一种波动率，又称为日内波动率或高频波动率。
高频数据是指以小时、分钟或秒为采集频率的数据。
1_波动率的计算
1_波动率的计算波动率是评估资产价格或市场波动性的一种方法，通常用来衡量资产的风险程度。
它是股票、债券、期货、外汇等金融资产价格日常波动的统计指标，并且是方差或标准差的一种度量。
波动率的计算有不同的方法，下面将介绍两种常用的计算方法：历史波动率和隐含波动率。
1.历史波动率计算：历史波动率是通过观察资产过去一段时间的价格变动，计算资产未来可能的价格波动的一种方法。
常见的历史波动率计算方法有简单波动率和对数收益率波动率。
1.1简单波动率计算：简单波动率又称为历史波动率，是指计算资产价格的每日变动的标准差，进而得出未来价格可能的波动幅度。
步骤：1.收集一段时间内的资产价格数据，通常是收盘价。
2.计算每日价格的变动，即当天价格与前一天价格之间的差值。
3.计算这些每日变动的平方，得到方差。
4.将方差求和，然后除以天数，得到波动率的平方，再开平方根，得到波动率。
计算公式：波动率=√(方差之和/天数)1.2对数收益率波动率计算：对数收益率波动率是对资产价格取对数之后计算的波动率，它是用来解决价格波动随时间变化而变动的问题，并更好地符合实际情况。
步骤：1.收集一段时间内的资产价格数据，通常是收盘价。
2.计算对数收益率，即每天收益率的对数，可以使用自然对数或对数收益率公式。
3.计算对数收益率的标准差，并进行年化处理，得到对数收益率波动率。
计算公式：波动率=对数收益率标准差×√天数×√(年度交易天数) 2.隐含波动率计算：隐含波动率是根据期权价格计算的，它反映了市场参与者对未来价格波动的预期。
步骤：1.收集目标资产的期权合约价格。
2.使用期权定价模型（如布莱克-斯科尔斯期权定价模型）来计算隐含波动率。
3.通过对期权价格的归一化，将价格转化为波动率。
隐含波动率是从事期权交易的投资者对未来波动率的预期，因此它反映了市场对资产未来可能波动的看法。
总结：波动率是评估资产价格或市场波动性的一种方法，对于投资者来说是非常重要的风险指标。
波动率计算的三种方法
波动率计算的三种方法波动率是金融市场中常用的一个指标，用来衡量资产价格的波动程度。
波动率的计算方法有很多种，其中常用的有三种：简单波动率、历史波动率和隐含波动率。
一、简单波动率简单波动率是最常用的一种波动率计算方法。
它基于历史价格数据，通过计算价格的标准差来衡量价格的波动程度。
简单波动率的计算公式为：波动率 = 标准差 / 平均价格其中，标准差是一种统计学上常用的指标，用来衡量数据的离散程度。
平均价格是指一段时间内的价格均值。
简单波动率的计算方法比较简单，容易理解和应用。
但是它只考虑了历史数据，没有考虑到市场的预期和未来的变化，因此可能存在一定的局限性。
二、历史波动率历史波动率是基于历史价格数据计算的波动率。
它通过计算一段时间内价格的对数收益率的标准差来衡量价格的波动程度。
历史波动率的计算公式为：波动率 = 标准差 / 平均对数收益率其中，对数收益率是指价格的对数变化。
历史波动率考虑了历史数据的波动情况，相对于简单波动率更加准确。
但是它也存在一个问题，就是对历史数据的依赖性较强，可能无法准确反映未来的波动情况。
三、隐含波动率隐含波动率是市场参与者对未来波动率的预期。
它是通过期权的市场价格反推出来的，可以被视为市场对未来波动的一种估计。
隐含波动率的计算方法比较复杂，需要使用期权定价模型来计算。
隐含波动率的计算方法相对于前两种方法更加复杂，但它可以提供更准确的预测。
因为它是市场参与者对未来波动的共识，反映了市场的预期。
波动率是衡量资产价格波动程度的重要指标。
常用的波动率计算方法有三种：简单波动率、历史波动率和隐含波动率。
每种方法都有其优缺点，应根据实际情况选择合适的方法进行计算和分析。
在使用波动率进行投资决策时，还需要考虑其他因素的影响，做出准确的判断和预测。
波动率
预测波动率
又称为预期波动率，一般指运用统计推断方法对实 际波动率进行预测得到的结果，并可将其用于资产定 价模型(例如期权定价模型)，确定出资产的理论价值。 因此，预测波动率是人们对权证进行理论定价时实际 使用的波动率。目前，常用的计算预测波动率的方法 基本上是一些统计方法，包括建立各类模型进行预测 与推断，除此之外，人们对实际波动率的预测还可能 来自经验判断等其他方面。
VL
2 由于权重之和为1，因此
n VL u
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2 n1
1
GARCH (1,1)
令 ， GARCH (1,1) 模型可以表示成 L
V
和
u
2.指数平滑法： 2 2 2 估计公式： t t 1 (1 )rt 1
t (1 ) r
2 i 1
i 1 2 t i
说明： 为衰退因子， ,J.P.Morgan riskmetrics 系统建议 随资料周期改变，并给出一个规范值，日数 据为0.94，月数据为0.97.
其他高频波动率
很大意义上是对已实现波动率的优化。高频数据包 含了关于市场微观结构的信息，且频率越高，包含信 息越多，而低频数据中，几乎不包含市场微观结构的 信息。传统的经济理论通常认为市场是有效的：没有 交易成本，没有摩擦，当前价格反映了所有信息、是 资产的有效价格，已实现波动率即是基于资产的真实 价格来估计的。
简单： 加权：
t [1/ (M 1)] (rt i
2 i 1
2 M
M
rt j
j 1
M
M
)2
rt j
j 1 M
t [1/ (M 1)] t i (rt i
波动率
定义sn为第n-1天和第n天的日波动率，即在第 n-1天末进行估值 定义Si为市场变量在第i天的取值 定义 ui= ln(Si/Si-1)
m 1 2 n2 ( u u ) m 1 i 1 n i
1 m u un i m i 1
风险管理中的简化式
定义 ui 为 (Si−Si-1)/Si-1 假设 ui 的平均值为0(这种假设的前提是每 一天市场变化期望值远远小于市场变化的 标准差) 用m替换m-1(这种做法将我们的波动率从无 偏差估计转换为最大似然估计,具体做法将 在第九节指出)
金融风险管理，第九章，闫海峰，南京财经大学金融学院，2011
9.36
方差目标法
增加GARCH(1,1)模型稳定性的方法之一是 应用方差目标法 令长期平均波动等于相同的方差 仅有其余的两个参数需要估计
金融风险管理，第九章，闫海峰，南京财经大学金融学院，2011
9.37
最大似然估计法
在最大似然估计方法中，我们选择合适 的参数以使得观测值发生的概率最大。
金融风险管理，第九章，闫海峰，南京财经大学金融学院，2011
9.38
例1
观察一个实验，在进行的十次实验中假设 某个事件为随机事件，那么这个事件发生 一次的概率是多少呢？ 计算的结果是： p(1 p)9 使得表达式取得最大值的极大似然估计值: p=0.1
金融风险管理，第九章，闫海峰，南京财经大学金融学院，2011
令第i个区间的回报为xi= ㏑(Si/Si-1),
式中,i=1,2, …,n.
xi的标准差估计式s为
标准差估计式的推导
随机变量X的标准差定义为：
波动率和方差
波动率和方差
波动率和方差是用于衡量数据集或金融资产价格变动的统计指标。
尽管两者有某种程度的联系，但它们有着不同的定义和应用。
下面是对波动率和方差的简要说明：
波动率：波动率是用于衡量数据集或金融资产价格变动的波动程度的指标。
波动率可以分为历史波动率和隐含波动率两种常见形式。
•历史波动率：历史波动率是根据过去价格数据计算得出的波动率。
它可以通过计算价格序列的标准差或方差来衡量
数据的波动程度。
•隐含波动率：隐含波动率是从期权定价模型中反推出来的预期未来波动率。
它表示市场对未来的波动性有着什么样
的预期。
隐含波动率主要在期权交易中使用，用于确定期
权合理的价格。
方差：方差是统计学中用于衡量数据集的离散程度的指标。
它描述了数据点与平均值之间的差距。
方差的计算涉及将每个数据点与平均值的差值的平方相加，然后求平均。
方差可用于衡量数据集的散布程度。
在金融领域，方差经常被用来衡量金融资产回报率或股票价格的变动范围。
具有较高方差的资产被认为具有更大的风险，因为它们更容易在一段时间内发生价格波动。
总结一下，波动率和方差都是用于度量数据集或金融资产
价格变动的指标。
波动率是对价格波动程度的度量，而方差是对数据集或金融资产回报率的离散程度的度量。
波动率可以通过历史波动率和隐含波动率来计算，方差则是通过计算数据点与平均值的差值的平方来得出的。
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