# Questions tagged [volatility]

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

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### Derivation of optimal portfolio weights using Risk Budgeting approach

In Thierry Roncalli's book Introduction to Risk Parity and Budgeting (2013), he gives an example of particular solutions to the Risk Budgeting portfolio such as for the $n=2$ asset case. The risk ...
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1 vote
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### what does correlation $\rho$ means in surface SVI?

Why does everyone say $\rho$ is correlation in Surface SVI? $w = \frac{\theta_t}{2}(1+\rho\psi(\theta_t)k + \sqrt{(\psi(\theta_t)k+\rho)^2+1-\rho^2})$, with $\rho \in [-1,1]$ This paper says it is ...
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### Does the expected return increase with variance for stocks? [duplicate]

I took a historical dataset of ~2600 stocks and computed the 30-day returns for non-overlapping windows, for a 9 year period. For the returns, I computed the mean and variance. Then I plotted the mean ...
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### What is the Fair Strike in a Var/Vol Swap and how does it relate to its price? [closed]

I am a student trying to price volatility and variance swaps. People who price those two products usually try to get the "fair strike", and don't seem to care about the price. However, I ...
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### How to calculate expected value for an underlying contract and expected value for an option?

In Sheldon Natenberg's Options Volatility & Pricing, he writes: There is an important distinction between an option position and an underlying position. The expected value for an underlying ...
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### Barrier on realized volatility

I am trying to understand the risk exposures of vanilla options that also have a European barrier on realized volatility. For example, the option could knock out if the realized volatility over the ...
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### How to use Ta-Lib to calculate the ewmstd?

I am trying speed up below code for faster speed, df = df.ewm(span=lookback).std() I wrote a numba version but it is very slow in large dataset ...
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### Using Daily or Annual Volatility to Price an Option

From Joshi's Quant Interview book: The statistics department from our bank tells you that the stock price has followed a mean reversion process for the past 10 years, with annual volatility of 10% and ...
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### How does Bloomberg calculate Interest Rate Caps/Floors with Black Scholes Merton Model and Volatility set as "Normal"?

While valuing Interest Rate Caps/Floors in Bloomberg, I saw that we have an option for selecting both Model and Volatility. So, my question is how exactly does Bloomberg value the cap/floor, when we ...
575 views

### Is there a way to use normal volatility in the Black–Scholes–Merton model to value interest rate caps? [duplicate]

I am trying to understand if there is a version of the Black–Scholes–Merton model that can use Normal volatilities instead of Lognormal volatilities while valuing interest rate caps and floors?
1 vote
170 views

### Estimation of the Vech HAR model (Multivariate HAR)

I am trying to use the Vech-HAR (the mulitvariate HAR) model in order to forecast some covariances. I have been looking into the model proposed by Chiriac Modelling and forecasting multivariate ...
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### Is variance swap long volatility of volatility?

In JPM's note on variance swaps, on page 29, they say "... a long variance swap is also long volatility of volatility". In Bennett's book Trading Volatility, on page 115, he says "... a ...
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### Understanding volatility of volatility in realized roughness

In the paper Buy Rough Sell Smooth by Glasserman and He (2018), on page 5 equation (8) they define an estimate of the volatility of volatility ν, by setting $\log(ν)= β_1/2$. I would like to ...
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### Calibration of Local or Stochastic Volatility Models to Prices vs Implied Volatilities

As the title suggests, what is the difference between calibrating an option pricing model (say the Heston model) to market option prices instead of computing their implied volatilities using Black-...
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### What is the reason for adding 0.5 variance when calculating the ATM DNS of an option?

Why is an Option ATM DNS (Delta Neutral Straddle) strike calculated using exponential value of (rate + 0.5 variance) * t. For ATMF (At the money forward), the rate time is used as the value in ...
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### Incorporating idiosyncratic risk as a pricing factor with GMM

Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing an augmented CAPM or a multifactor model with an additional factor: the ...
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### Shape of FX Volatility Surface

I'm familiar with the volatility surface for equity options with the smile/skew dynamic and flattening with increased maturity, and the explanation/intuition behind its shape. However, today I came ...
248 views

### Appropriate way to combine alternative volatility estimates

I have a number of different annualized realized volatility estimates (for the same point in time) that I'd like to combine. Is a simple average over these appropriate? Or should I do this in the ...
1 vote
121 views

### How is variance derived in BS?

The realized variance under classical Black Scholes where the stock price process follows a GBM is given as $$V_T = \frac1T\int_0^T\sigma_s^2ds\qquad (1)$$ however, the texts I have been reading do ...
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### What is the process for using OLS on time series models (HAR like)

I am reading about HAR models for realised variance and they all seem to use WLS or OLS to calculate the parameters. Now I understand how that works if you just use say the 10 years of AAPL intraday ...
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387 views

### Volatility surface

When fitting/calibrating a option model like heston to option data, what are some useful data handling to do? The basic thing is to remove all options with no trade/volume, but how many maturities ...
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### What does implied volatility say about the underlying?

Here's a question that's been on my mind on-and-off for some time now. It's well known that Black-Scholes is an unsuitable model for pricing in the current (post 80s) market as it fails to capture the ...
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### bid volatiliy interpolation

I had a bid volatility data that had a concave shape. my question is how can I extrapolate for the the extreme strikes, and does the bid volatility goes to zero when strike->0 and strike-> ...
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### Compute monthly realized variance for Fama-French factor

I need to compute monthly realized variance from daily data for Fama-French factors. Knowing that Fama-French factors is the difference of return between different type of stocks, for example SMB ...
158 views

### What is wrong with my HAR model - constantly increasing?

I am trying to code the HAR (and eventually the HARQ) from Bollerslev et al 2016 and Corsi 2009. $$RV_t = \beta_0 +\beta_1 RV^d_{t-1} + \beta_2 RV^W_{t-1}+\beta_3 RV^M_{t-1}+u_t$$ Bollerslev ...
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### Reference Request Adjusting implied/historical volatility for earnings

Wanted a reference request for any source has discussed how to clean/adjust historical volatility/ historical implied volatility time series for Earnings. The RV/IV time series data have a lot of ...
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### Volatility model for pricing of Down-In Put options

What is the best volatility model to price Down-In Puts (DIP) under several stress scenarios (e.g downward movement of underlying price by -5%, -10%, -15%)? Please note that I got the market prices ...
1 vote
138 views

### Impact of stochastic rates on varswaps and volswaps

Let us consider that we are looking at issuing some varswaps or volswaps on some FX rate. By longer term I mean something longer than 3 months. Different from this time two years ago, now the interest ...
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746 views

### Compute monthly realized variance from daily data

I am confused about the correct formula to compute monthly realized variance from daily data. What is the first sigma in the picture: sum or average? I mean, after subtracting each observation from ...
1 vote
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### Identify upcoming stock price gaps in Implied Volatiltiy (quant / standardized approach)?

What you often obeserve in implied volatiltiy are higher levels of implied volatility for upcoming events like earnings or presentation of pharma data. For a human being which collects manual the ...
115 views

### Standard deviation of the difference between a time series and its EMA?

I have a time series $Q={\{q_t\}}$ of known standard deviation $\sigma$, and its EMA of parameter $\alpha$ : $\{EMA_t(\alpha)\}$. My question is : I'm looking for a formula that would give the ...
1 vote
218 views

### Standard deviation of annual returns formulas return all different values

I am trying to build a monte-carlo simulator for predicting the possible future values of a portfolio. I have daily historical prices for several assets but I don't know how to correctly estimate ...
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### Can the break-even of a straddle be lower than the implied move?

Let us consider a two day option: 1 day having a baseline vol of 16% 1 day having an event for which we want to find the implied move, higher than 16% Is it possible that the price of the straddle ...
490 views

### Assessing the GARCH model out-of-time

I have fitted two competing GARCH models, one GARCH(1,2) model and another EGARCH(1,1,1) both with t-distributed errors, on the ...
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### Comparing Volatility [closed]

Sorry for asking beginner level question. I want to compare Volatility of two different years of Nasdaq. I thought to compute true range (TR) on daily data and then average out TR values of this year ...
1 vote
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### Multistep ahead forecasts in GARCH equations

If my one step ahead forecasts from GARCH(1,1)-X are: $$\hat{h}_{t+1} = \hat{\alpha}_0 + \hat{\alpha}_1 \hat{u}^2_t + \hat{\beta}_1 \hat{h}_t + \hat{\psi} X_t$$ Where ...
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### How VIX ETF Rolls to follow the SP 500 VIX Index

I was reading the Methodology that S&P uses in order to construct VIX index VIX S&P Methodology If I understood it right, the VIX Short-Term Futures Index works as follows: Notice that both ...
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### VIX intraday Data (minute by minute) [duplicate]

I'm looking for an open source that provides intraday data (minute by minute). I wasn't able to find one so far. Any suggestions? Thank you.
73 views

### Idiosyncratic risk (t statistic)

I am working on idiosyncratic volatility analysis and I would like to control for size characteristics following the method used in the paper "The Cross-Section of Volatility and Expected Returns&...
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2k views

### RiskMetrics Half-Life and Decay Factor Settings

I have been reading about the RiskMetrics methodology. I read that RiskMetrics recommend a lambda of 0.94 for daily data and 0.97 for monthly data. I would like to convert these numbers to half-lives. ...
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### W-shaped Event Vol and Butterfly Arbitrage

I came across the Vola Dynamics page about the W-shaped vol before an event: https://voladynamics.com/marketEquityUS_AMZN.html I'm a bit confused by "this term does not have any butterfly ...
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### Why is Implied Volatility more important than skew for put spread pricing?

It is said on page 26 of the book "Trading Volatility: Trading Volatility, Correlation, Term Structure and Skew" by Bennett (2014) that: A rule of thumb is that the value of the OTM put ...
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### Simple Black-Scholes alternatives

I work at an accountancy firm and we use Black-Scholes to value equity in private companies that has option like features. The equity we typically value is akin to deeply out of the money European ...
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### Student-t measure of return volatility and time scaling

I have a series of price returns of an asset (4 days worth of data). They are relatively high-frequency. My ultimate goal is to calculate realized volatility, but using a student's t-distribution. I ...
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### How does autocorrelation bias annualizing variance?

I read somewhere that autocorrelation prevents someone from annualizing variance. But how does it bias it? Let's say you have daily returns. If autocorrelation is high, should that overstate or ...
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### Volatility Modelling negative GJR-GARCH-X coefficient

I have estimated GARCH and GJR-GARCH with several exogenous variables. Some of the exogenous variables have negative coefficients that are statistically significant. For instance, I can write my GJR-...
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### How do I estimate volatility for MPR historical data

How can I estimate volatility with historical data for Monetary Policy Rate (MPR) to use in a short rate model? I could use regular techniques like simple standard deviation or max likelihood, but the ...
1k views

### Daily vs Monthly vs. other return for volatility calculation?

I thought I read/heard somewhere that annualized volatility, using monthly returns vs daily returns is usually lower. With that said, I can't seem to find any papers on this. Does anyone have any ...
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