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Volatility is a statistical measure of the dispersion of returns on a specific security or market index. Usually measured by the standard deviation or variance of returns. In most cases, the higher the volatility, the riskier the security.
Volatility is a statistical measure of the dispersion of returns on a specific security or market index. Usually measured by the standard deviation or variance of returns. In most cases, the higher the volatility, the riskier the security.
In securities markets, volatility is often associated with large movements in prices. For example, when the stock market continues to rise or fall by more than 1% over a period of time, it is called a volatile market.
The volatility of an asset is a key factor when pricing options contracts.
Volatility generally refers to the risk or uncertainty associated with the magnitude of changes in a security's value.
High volatility means that a security’s value may be spread over a wider range. This means that over short periods of time, the price of a security can fluctuate significantly, either up or down. Low volatility means that the value of the security does not fluctuate much and tends to be stable.
One way to measure an asset's movement is to quantify daily returns (the percentage of daily price changes). Historical volatility is based on historical prices and represents the variability in asset returns. This value is unitless and expressed as a percentage.
While variance is used to capture the dispersion of an asset's returns around a mean, volatility is a measure of variance bounded over a specific time period. Therefore, we can report daily, weekly, monthly or annualized volatility. It is useful to think of volatility as annualized standard deviation.
Volatility is usually calculated using variance and standard deviation (standard deviation is the square root of the variance). Since volatility describes movement over a specific time period, simply multiply the standard deviation by the square root of the time period:
Among them:
For simplicity, let’s assume our monthly stock closing price is
<!-- @@@ -->2, and so on. To calculate variance, follow these five steps.
Next, take the square root of the variance to get the standard deviation, which results in
<!-- @@@ -->The values 1 to $10 are not randomly distributed on the bell curve, but are evenly distributed. Therefore, the expected percentages of 68%-95%-99.7% do not hold true. Nonetheless, traders often take advantage of standard deviation because price return data sets tend to resemble something closer to a normal distribution (bell curve).
TIP: Stock price volatility is considered mean-reverting, meaning that periods of high volatility tend to moderate, while periods of low volatility increase, swinging around some long-term mean.
Implied volatility (IV), also known as expected volatility, is one of the most important metrics for options traders. As the name suggests, it allows traders to gauge how volatile the market will be in the future.
This concept also provides traders with a way to calculate probabilities. It should be noted that this is not science and therefore does not predict the future direction of the market.
Unlike historical volatility, implied volatility comes from the price of the option itself and represents expectations for future volatility. Because it is implicit, traders cannot consider past performance as an indicator of future performance. Instead, they must estimate the option's potential in the market.
Note: Implied volatility is a key characteristic of options trading.
Historical volatility (HV), also known as statistical volatility, assesses the volatility of the underlying security by measuring price changes over a predetermined time period. When historical volatility increases, the price of a security can also move more than normal. At this point, a change in the market is usually expected. If historical volatility declines, it means uncertainty has been removed and markets return to normal.
This calculation can be based on intraday changes, but is usually based on the change from one close to the next. Historical volatility can be measured between 10 and 180 trading days, depending on the expected length of options trading.
Volatility is a key variable in option pricing models, estimating how much the underlying asset's returns will fluctuate before the option expires. Volatility as a percentage coefficient in option pricing formulas is derived from daily trading activity, and the method used to measure volatility will affect the value of the coefficient used.
Volatility is also used to price option contracts using models such as the Black-Scholes model or the binomial tree model. The more volatile the underlying asset, the higher the option premium because volatility gives the option a greater chance of being in the black at expiration.
Options traders try to predict the future volatility of an asset, so the price of an option in the market reflects its implied volatility.
IMPORTANT NOTE: The greater the volatility, the generally higher the market price of options contracts.
A measure of a particular stock's relative volatility relative to the market is its beta. Beta approximates the overall volatility of a security's returns relative to the returns of a related benchmark, typically the S&P 500 Index. For example, a stock with a beta of 1.1 rises 110% when the benchmark rises 100%.
Conversely, a stock with a beta of 0.9 rises 90% when the benchmark rises 100%.
Market volatility can also be observed through the Volatility Index (VIX), which is a quantitative measure of stock market volatility.
CBOE created the VIX as a measure of expected 30-day volatility in the U.S. stock market, based on real-time quotes for call and put options on the S&P 500 Index. It effectively measures the sentiment of investors and traders regarding the future direction of the market or a specific security. A high VIX reading means increased market risk.
Traders can trade the VIX using a variety of options and exchange-traded products, or use the VIX value to price certain derivatives.
Investors may find periods of high volatility unsettling, as prices may fluctuate wildly or drop suddenly. Long-term investors are advised to ignore short-term fluctuations and maintain established strategies. This is because stock markets tend to rise in the long run. At the same time, emotions like fear and greed can be amplified in volatile markets, undermining long-term investment strategies.
Some investors may use volatility as an opportunity to add to their portfolio by buying when prices are relatively cheap.
You can also use hedging strategies to deal with volatility, such as buying protective puts to limit downside losses without selling any shares. Note, however, that when volatility is higher, the price of put options also increases.
Let’s say an investor is building a retirement portfolio. Since she will retire within the next few years, she wants to find stocks with low volatility and solid returns. She considered two companies:
A more conservative investor might choose Company ABC because it is less volatile and its short-term value is more predictable.
Volatility is a statistical measure of the dispersion of data around its mean over a specific time period. It is calculated by multiplying the standard deviation by the square root of the number of time periods, T. In finance, it represents this dispersion of market prices, presented on an annualized basis.
Volatility is often used to describe risk, but this is not always correct. Risk involves the chance of suffering a loss, while volatility describes the magnitude and speed of price movements. Risk increases if increased price volatility also increases the likelihood of loss.
Whether volatility is good or bad depends on what kind of trader you are and your risk tolerance. For long-term investors, volatility can mean trouble, but for day traders and options traders, volatility often means trading opportunities.
If volatility is high, it means prices are moving quickly and dramatically (either up or down).
VIX is the CBOE Volatility Index, a measure of short-term volatility in the broader market, as measured by the implied volatility of 30-day S&P 500 options contracts. The VIX generally rises when stocks fall and falls when stocks rise. Also known as the "fear index," the VIX serves as an indicator of market sentiment, with higher values indicating greater volatility and investor fear.
Volatility is how much and how quickly prices move over a specific period of time. In the stock market, increased volatility is often a sign of investor fear and uncertainty. This is why the VIX is sometimes called the "fear index."
At the same time, volatility also provides day traders with opportunities to enter and exit positions. Volatility is also an important component of options pricing and trading.
TheQuantHackers is a cutting-edge community composed of a group of people from the world's top universities and quantitative finance practitioners, dedicated to exploring the infinite possibilities in the fields of artificial intelligence (AI) and quantification (Quant). Our team members come from world-renowned universities such as the University of Cambridge, Oxford University, Harvard University, ETH Zurich, Peking University, and the University of Science and Technology of China. Our external consultants come from first-class companies such as Microsoft, HSBC, Citadel, Man Group, Citi, Jump Trading, and top domestic private equity companies.10。例如，第一个月为
波动性是衡量特定证券或市场指数收益分散程度的统计指标。通常通过收益的标准差或方差来衡量。在大多数情况下，波动性越高，证券的风险越大。
在证券市场中，波动性通常与价格的大幅波动相关联。例如，当股票市场在一段时间内持续上涨或下跌超过1%时，被称为波动市场。
资产的波动性是定价期权合约时的关键因素。
波动性通常指与证券价值变动幅度相关的风险或不确定性。
高波动性意味着证券的价值可能会在更大范围内分布。这意味着在短时间内，证券的价格可能会大幅波动，向上或向下。低波动性则说明证券的价值波动不大，趋于稳定。
测量资产变动的一种方式是量化每日收益（每日价格变化的百分比）。历史波动性基于历史价格，代表资产收益的变异程度。这一数值是无单位的，以百分比表示。
虽然方差用于捕捉资产收益围绕平均值的分散情况，但波动性是特定时间段内界定的方差度量。因此，我们可以报告每日、每周、每月或年化的波动性。把波动性视作年化标准差是有益的。
波动性通常使用方差和标准差（标准差是方差的平方根）来计算。由于波动性描述的是特定时间段内的变动，因此只需将标准差乘以时间段的平方根即可：
其中：
为简单起见，假设我们的月度股票收盘价为$2.87。这是风险的度量，显示了价值相对于平均价格的分散程度，给交易者一个价格可能偏离平均水平多远的印象。
如果价格是从正态分布中随机抽样的，那么约68%的数据值将落在一个标准差内。95%的数据值将落在两个标准差内（在我们的例子中为2 × 2.87），而99.7%的所有值将落在三个标准差内（3 × 2.87）。
在这种情况下，10的值并不是在钟形曲线上随机分布的，而是均匀分布。因此，预期的68%-95%-99.7%的百分比并不成立。尽管如此，交易者常常利用标准差，因为价格收益数据集往往类似于更接近正态分布（钟形曲线）的标准。
提示： 股票价格的波动性被认为是均值回归的，这意味着高波动性时期往往会逐渐缓和，而低波动性则会增加，围绕某个长期均值波动。
隐含波动性（IV），也称为预期波动性，是期权交易者最重要的指标之一。顾名思义，它使交易者能够判断市场在未来将会多么动荡。
这个概念同样为交易者提供了一种计算概率的方法。需要注意的是，这并不是科学，因此不预测市场未来的走向。
与历史波动性不同，隐含波动性来自期权本身的价格，并代表对未来波动性的预期。由于是隐含的，交易者不能将过去的表现视为未来表现的指标。相反，他们必须估计期权在市场上的潜力。
注意： 隐含波动性是期权交易的关键特征。
同样被称为统计波动性的历史波动性（HV）通过衡量预定时间段内的价格变动，来评估基础证券的波动。当历史波动性上升时，证券的价格也会比正常情况下波动得更大。这时，通常会预期市场将发生变化。如果历史波动性下降，则意味着不确定性已经消除，市场会恢复正常。
这种计算可以基于日内变动，但通常是基于一个收盘价到下一个收盘价的变化。根据期权交易的预期时长，历史波动性可以在10至180个交易日之间测量。
波动性是期权定价模型中的关键变量，估计在期权到期之前，基础资产收益波动的程度。波动性作为期权定价公式中的百分比系数来源于日常交易活动，测量波动性的方法将影响所用系数的价值。
波动性同样用于使用如布莱克-肖尔斯模型或二项树模型等模型为期权合约定价。基础资产越波动，期权溢价越高，因为波动性使期权在到期时进入盈利状态的概率更大。
期权交易者试图预测资产未来的波动性，因此市场上期权的价格反映了其隐含波动性。
重要提示： 波动性越大，期权合约的市场价格普遍越高。
一个特定股票相对于市场的相对波动性度量是其贝塔（Beta）。贝塔值近似表示证券收益相对于相关基准（通常使用标准普尔500指数）收益的整体波动性。例如，贝塔值为1.1的股票在基准涨幅100%时上涨110%。
相反，贝塔值为0.9的股票在基准上涨100%时上涨90%。
市场波动性也可以通过波动率指数（VIX）来观察，这是对股票市场波动性的定量度量。
芝加哥期权交易所创建VIX，作为衡量美国股票市场预期30天波动性的指标，基于标准普尔500指数看涨和看跌期权的实时报价。它有效地衡量了投资者和交易者对市场或特定证券未来走向的投注情绪。VIX的高读数意味着市场风险加大。
交易者可以利用各种期权和交易所交易产品来交易VIX，或利用VIX值为某些衍生产品定价。
投资者可能会发现高波动时期令人不安，因为价格可能会剧烈波动或突然下跌。建议长期投资者忽略短期波动，保持既定策略。这是因为从长远来看，股票市场往往会上涨。同时，像恐惧和贪婪这样的情绪在动荡市场中可能会被放大，从而破坏长期投资策略。
一些投资者可能会利用波动性作为机会，通过在价格相对便宜时买入来增加投资组合。
您还可以使用对冲策略来应对波动性，例如购买保护性看跌期权，以限制下行损失而无需卖出任何股票。但请注意，当波动性较高时，看跌期权的价格也会增加。
假设一位投资者正在构建退休投资组合。由于她将在接下来的几年内退休，因此她希望寻找波动性低且收益稳健的股票。她考虑了两家公司：
一位更加保守的投资者可能会选择ABC公司，因为它的波动性较小，短期价值更加可预测。
波动性是衡量在特定时间段内数据围绕其均值的分散程度的统计指标。它的计算方式是将标准差乘以时间周期数的平方根T。在金融学中，它代表市场价格的这种分散，按年化基础呈现。
波动性通常用于描述风险，但这并不总是正确。风险涉及遭受损失的几率，而波动性则描述价格波动的幅度和速度。如果价格波动的增加也同时增加了损失的可能性，那么风险也会随之升高。
波动性是否好坏取决于您是什么样的交易者以及您的风险承受能力。对长期投资者而言，波动性可能意味着麻烦，但对日内交易者和期权交易者而言，波动性往往意味着交易机会。
如果波动性高，意味着价格在迅速且剧烈地变动（无论是上涨还是下跌）。
VIX是芝加哥期权交易所的波动率指数，衡量更广泛市场的短期波动性，通过30天标准普尔500期权合约的隐含波动性来测量。VIX一般在股票下跌时上升，而在股票上涨时下降。也被称为“恐慌指数”，VIX可以作为市场情绪的一个指标，较高的数值表明更大的波动性和投资者的恐惧感。
波动性是价格在特定时间段内变动的幅度和速度。在股市中，波动性的增加往往是投资者恐惧和不确定感的表现。这也是波动指数VIX有时被称为“恐慌指数”的原因。
与此同时，波动性也为日内交易者提供了进出仓位的机会。波动性也是期权定价和交易的重要组成部分。
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