A measure of the variation in price over time. Also a measure of the risk of a financial instrument.

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8
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2answers
464 views

Is the price of European put option monotone in volatility if we replace BM in Black-Scholes with a general Levy process?

Under the Black-Scholes model, we have the European put option is $\mathbb{E} [e^{-rt}(K-S_t)]$, where we take $\log(S_t)=X_t$ and $dX_t= \sigma dW_t - \dfrac{1}{2}\sigma^2 dt + rdt$. Here the option ...
5
votes
0answers
464 views

Risk Budgets with Target Portfolio Volatility

I'm working through the implementation of a risk budgeting approach as described in the recent Roncalli paper. The idea is that the portfolio manager sets a contribution of total portfolio volatility ...
2
votes
1answer
201 views

Which prices to use to compute realized volatility?

For computation of realized volatility, especially range based volatility, deal prices are commonly used. If Level I data available should the deals data still be used or another measures of spot ...
11
votes
1answer
772 views

So many volatility models. Any comparisons of them?

Are there any papers that make an explicit contrast/comparison of the following (or other) vol models in terms of the suitability for addressing some empirical problem? Wavelet multiresolution ...
1
vote
2answers
450 views

Relationship between European, American options volatility

Suppose, if the price of a European option (say a put) can be shown to be monotone in volatility (say for any maturity), does it follow that American options has to be monotone in volatility? ...
0
votes
1answer
280 views

Volatility of a rolling window strategy

What methods can be applied to determine the volatility of strategy using a rolling window? Using normal standard deviation would bias the results as the returns will be highly correlated. Although, ...
1
vote
0answers
83 views

How to measure if variance is greater at a certain time of day?

I'm not very fluent in the quant vernacular, so perhaps the nature of my question will be better illustrated as a hypothesis. One market has closed and another market elsewhere on Spaceship Earth is ...
2
votes
2answers
224 views

Time Varying Volatility

If stock returns ($r_t$) are not auto correlated why is that the squared term of the returns (volatility) exhibit serial correlation? Does heteroskedacity, by its nature, imply that time varying ...
3
votes
2answers
260 views

Transformation to reduce standard deviation without changing median

Consider some negative skew and high kurtosis return time-series $X_t$. I do not know the functional form of the pdf of $X_t$ and have about 150,000 data points. Suppose that I was to create an ...
10
votes
2answers
359 views

How to estimate the following model?

Suppose I have the following model: $$r_t=\sigma_t * \epsilon_t$$ where $r_t$ is the return at time t, $\sigma_t$ is the volatility, the model used to model this volatility is an exponentially ...
6
votes
3answers
775 views

Gamma vs. Volatility Risk

Original Question: What is the link between Gamma and the Volatility Risk? It leads me to ask: - What is the Volatility Risk definition and what are the good practices to measure it? Thinking about ...
3
votes
2answers
570 views

Fitting distributions to financial data using volatility model to estimate VaR

I want to fit a distribution to my financial data using a volatility model to estimate the VaR. So in case of a normal distribution, this would be very easy, I assume the returns to follow a normal ...
3
votes
2answers
272 views

Black-Scholes and Fundamentals

So basically $dS_t=\mu S_tdt+\sigma S_tdWt$ and $\mu=r-\frac12\sigma^2$ I have just been thinking about this later equation. This is very interesting because it ties together risk-free ...
0
votes
2answers
389 views

Why the implied volatilities calculated are so different

I Calculated facebook option(expired in 12/4/13) Implied Volatility with the Bisection Method. The program will be attached at the end. The results for different strike prices are so different: ...
5
votes
2answers
3k views

Square root of time

I am writing about VaR and I am wondering about the following: We can scale the VaR to different time horizons by using the square root of time, which means, that the volatility is adjusted by square ...
3
votes
0answers
180 views

Fitting a non linear AR + GARCH(1,1)-M model

I want to fit the following model to a time series: $$ y_{t}=\alpha_{0}+\alpha_{1}y_{t-1}+\alpha_{2}y_{t-1}^{2}+\lambda h_{t}+\varepsilon_{t} $$ $$ ...
4
votes
1answer
435 views

Stability of correlations and volatility

I had a discussion recently about the stability of volatilities and correlations. If we take for example stocks and bonds (think of DAX and Bund) then I have seen changing volatilities (something like ...
2
votes
0answers
163 views

EUR/PLN and EUR/USD delta-term-vol surface quoting convension

does anyone know for sure what is the FX market convension to quote delta-term pairs for EUR/PLN, for EUR/USD. I know that for EUR/PLN it should be delta p.a forward, for EUR/USD it should be delta ...
0
votes
1answer
208 views

compute FX forward from broker's data

assume I have following delta-term vol data from broker: ...
0
votes
1answer
175 views

volatility Table and BS formula

assume I have implied FX volatility Delta-Term table from broker. I have time noticed as 2M, 3M. what do I have to put into BS formula, is it 2/12 or "count the business days"/"daycount basis"? I am ...
2
votes
3answers
337 views

Logarithmic returns for realized variance?

I am wondering which method makes more sense when computing log returns. I am trying to compute log returns for realized variance, and I have the opening and closing prices for every minute. Since ...
5
votes
1answer
1k views

How to use Newey West covariance corrector?

I have implemented the following model: daily_vol(t+1) = A*daily_vol(t) + B*weekly_vol(t) + C*monthly_vol(t) + error where vol means volatility, and A, B, C are ...
3
votes
2answers
2k views

Why FX Vanilla Options are quoted in volatility

I've been curious why vanilla options are quoted (and traded) in terms of volatility. Considering that every financial institution has its own options pricing model, volatility as an input would cause ...
5
votes
1answer
736 views

Problems with dealing with GARCH models and intra-day data

Short question would be "Which type of model from GARCH family is most suitable for modeling 5-minute data returns ?" but I've added some story to it. Long time ago I was preparing my thesis, one ...
2
votes
0answers
355 views

Markov-Switching E-GARCH with R

I am looking for a R library for modeling a Markov-Switching E-GARCH process. In other questions at StackExchange related to GARCH models, the package rugarch is often mentionned. Do you recommend it ...
2
votes
1answer
146 views

How to calculate two-time scale variance?

I am having trouble understanding how to calculate two-time scale variance as I do not have a strong mathematical background. Suppose I want to calculate the TSRV at 5 min intervals. Do I calculate ...
2
votes
1answer
615 views

How to calculate implied volatility and greeks in Bull Put Spread option strategy?

Ok, obviously I am buying lower strike put and selling higher strike put. What is the recommended volatility and greeks to consider in my trade? Volatility: Average volatility between both legs? ...
3
votes
1answer
181 views

Why are there different estimators for stock volatility? (realized variance, RAV, etc)

I am very confused about why different volatility estimators (RV, RAV, BPV, etc) exist. If the goal is to find the best estimator for stock volatility, and volatility is latent, how do I know which ...
3
votes
3answers
429 views

Avoiding negative volatility when applying Heston model

When applying the Heston model to generate the sample volatility surface, some of the volatility value will be negative. I am just wondering what do practioners normally do with these negative value. ...
2
votes
2answers
659 views

Squared and Absolute Returns

I've always wondered why do one use squared or absolute returns to determine if volatility modeling is required for the return series? We understand that there are various tests for its ...
0
votes
1answer
105 views

Volatility Index Weighting Scheme

Among the several weighting schemes used for constructing volatility indices, which ones are the best for forecasting (realized) volatility? I've constructed a volatility index for emerging markets ...
5
votes
4answers
2k views

What are the advantages/disadvantages of these approaches to deal with volatility surface?

I would like to know if someone could provide a summarized view of the advantages and disadvantages of the approaches on the volatility surface issues, such as: Local vol Stochastic Vol ...
4
votes
0answers
306 views

Asymmetric Volatility Modeling (Interpretation)

I am currently writing a paper on asymmetric volatility modeling of brent, gold, silver, wheat, soybean and corn from 1986-2012 and divided them into 4 sub-sample periods (i.e. 1986-1991, 1991-1997, ...
3
votes
1answer
2k views

What is the “leverage effect” for stocks?

I've read the so-called "leverage-effect" for stocks models the fact that if a company is leveraged, its volatility should increase as the stock price moves lower and closer to the level of debt. Can ...
2
votes
0answers
281 views

Yield Curve Volatility

Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds. Each yield curve has its slope and its curvature, and they obviously change ...
1
vote
1answer
546 views

How to interpret/use VaR and Standard Deviation?

The parametric VaR is defined as follows: $$VaR=Z_a*Vol$$ Is this the best way to interpret how much risk is being taken on for a particular asset? How does one interpret volatility on its own if ...
2
votes
1answer
166 views

How to enumerate all the possible portfolios with a given target volatility?

Let's say I have $n$ assets and their returns are stored in a matrix $X \in \mathbb{R}^{m \times n}$ (i.e. I have $m$ returns for each of them. The covariance matrix of the returns is $\Sigma \in ...
2
votes
2answers
510 views

Should I use GARCH volatility or standard deviation in cross-sectional regression?

I want to do a cross-sectional study where the historical, medium-long run volatility of some return series (call it $R_t$) is included as a regressor. Which of the following two estimates of ...
3
votes
2answers
428 views

When gains are made: Overnight or during trading hours? What is the connection to volatility?

Falkenblog reports an interesting finding: All of the stock returns since 1993 are from overnight returns and cross-sectionally, volatility receives a positive overnight risk premium, a negative ...
3
votes
0answers
169 views

Measuring unbiased estimator for variance with RMSE?

The root mean squared error (RMSE) is considered by some to be the best measure of how good a variance estimate is. You often see it quoted as: $RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^n(\hat{\sigma_i} - ...
2
votes
1answer
172 views

How to group mutual funds by volatility?

I want to group Mutual Funds by their volatility. Ideally, I would like to end up with the mutual funds beings attached to different groups: High volatility Medium volatility Low Volatility My ...
1
vote
1answer
308 views

Why does $\hat{\epsilon}'\hat{\epsilon}$ of a factor model measure risk?

$\hat{\epsilon}'\hat{\epsilon}$ from the market model: $R_{it} - \hat{\alpha} - \hat{\beta}R_{mt} = \hat{\epsilon}$, or from a factor model such as the Fama-French 3 factor model, is often used in the ...
8
votes
2answers
627 views

Why do low standard deviation stocks tend to have superior future returns?

I've recently stumbled on something that really surprised me. These papers (1, 2) find that past standard deviation of returns is inversely related to future returns. That is, portfolio of low ...
7
votes
1answer
1k views

Conditional or unconditional volatility?

I am reading a paper (reference below) that states "The conditional volatility for each underlying security (or for a market index) can be estimated using the standard deviation of the stock’s ...
4
votes
1answer
369 views

Volatility models using Rugarch

I have estimated sGARCH, EGARCH and TGARCH, which some for particular models are significant. For others, the alpha remain insignificant using various innovations such as the skewed variants of the ...
2
votes
2answers
264 views

Construction of “vol of vol”

How do you construct something that lets you buy "vol of vol"? not necessarily for VIX, but any particular stock or index.
1
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0answers
77 views

How to trade risk-adjusted returns?

Why does dividing daily returns by daily range eliminates fat tails and results in an (almost) gaussian distribution? And how could that distribution be exploited to enter trades?
2
votes
3answers
770 views

Trading a synthetic replication of the VVIX (volatility of VIX)

In the same spirit as this question: Trading a synthetic replication of the VIX index. The VVIX tracks the volatility of the VIX. One cannot directly buy and sell the VVIX index and, as opposed to ...
4
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0answers
134 views

Rolling window Kendall's tau against APARCH(1,1) correlation

Assume you want to forecast the correlation matrix of a stocks' basket (say 15 ~ 20 stocks from different sectors); assume you need to forecast at $T$ days because you will use the forecast ouput with ...
1
vote
1answer
308 views

Unsystematic/Idiosyncratic/Firm-specific volatility/variance in the market model?

I was asked to use idiosyncratic volatility as a regressor in a cross-sectional regression upon cross-sectional returns as the dependent variable. Returns can be thought of as the raw log stock return ...