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# 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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33 views

### how to model NGARCH using 5min frequency data?

NGARCH model using 5-min High-frequency data in R I wanted to analyze some 5 minute frequency data of stock market. My teacher asked me to use NGARCH to model, but I didn't know how to program.Here ...
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### Dorfleitner's Standard Deviation

Can someone please advise how to compute the following (as my results go into thousands): E.g. I have used and the result (for T=12) = 580103.7261 Thanks
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### What is the appropriate benchmark for a Long/Short VIX futures strategy?

Trying to figure out the benchmark for a L/S Vix futures stragegy, doesn't seem like only long or short Vix futures would be appropriate, any ideas? Thx
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### What is the annualized realized volatility of simulated Brownian motion paths?

I saw this following question in an exam. Take a Brownian motion simulation with drift 5% and annualized volatility of 20% for a period of 1 year. Then the annualized realized volatility of the ...
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### Constructing Volatility Smile from American Options

My question is about best practices for reconstructing volatility smiles for a fixed tenor from American option data. For simplicity/liquidity, I am currently considering options on SPY. I am ...
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### looking for a simple realistic parametric volatility model

Which parametric volatility is realistic to test quickly and qualitatively a model? I do not wish to fit market quotes but would like to have a non-trivial volatility with skew or smile to do some MC ...
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### Variance swap volatility - ATMF vol, Skew and Curvature

In a pure diffusion setting, it is a well known result that the volatility $\sigma_T$ of a fresh-start variance swap of maturity $T$ as seen of $t=0$ verifies \begin{align} \sigma_T^2 &= \Bbb{E}_0^...
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### Is it possible to compute implied returns from volatility?

If we assume that, broadly speaking: Assets in liquid markets are fairly priced to its value Volatility is predictable (volatility clustering, GARCH, etc) Investors are rewarded and earn a return for ...
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### Varswap replication product

I would like to ask about a product that some Flow desks sell : Varswap replication strategies. I know that it consists of weighted basket of calls and puts , however I would like to know how does it ...
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Suppose I am long spread option with underlying : rate A - rate B. The vega on the option would be positive. But if I want to compute the option vega with respect to individual rates, can I use the ...
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### Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
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### What is the best book to learn about local vs. stochastic volatility, modelling and pricing of Exotics?

I am starting to delve into the world of Exotics and I am trying to find a rigorous yet understandable book that covers both mathematically and qualitatively (especially mathematically) the following ...
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### stock specific volatility

I was unsure about the precise definition of "stock specific volatility". Used in this question "A stock has beta of 2.0 and stock specific daily volatility of 0.02. Suppose that yesterday's closing ...
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### Probability of stock closing over a certain price

A stock has beta of 2.0 and stock specific daily volatility of 0.02. Suppose that yesterday's closing price was 100 and today the market goes up by 1%. What's the probability of today's closing price ...
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### Is $\sigma_{1} = \frac{\sigma_{\tau}}{\sqrt{\tau}}$ suitable for volatility scaling?

It seems to be the de-facto method; and I see how we get it from log-normal assumption. However volatility scaling seems to be way more sensitive to $\tau$ than mean scaling -- as in two ~ 2 times (...
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One can trade vol swap to get exposure of the volatility of the underlying security in a 'clean' way. On the other hand, we know that vol swap, theoretically can be replicated by a dynamic position of ...
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### Swaption pricing and strategies

I am looking for resources (books, papers, websites, etc.) that deal with Vanilla and Exotic swaptions from a more advanced and quantitative perspective. I am interested in both the pricing side (e.g. ...
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### Implied volatility of Treasury options

For practitioners, does the concept of implied volatility also apply to (European) Treasury Options (whose underlying is Treasury Futures contracts)? For the standard individual stock vanilla ...
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### Interpretation conditional volatility plot

I have plotten the log differences of exchange rates and in the same plot, I show the conditional volatility $\sigma_t^2$. The conditional volatility follows approximately the same path, but is much ...
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### Interpolation of SVI Implied Volatility in parameter space

I am currently working with a slice-wise SVI parametrisation of the implied volatility surface. $\sigma^2(x,t) = a_t + b_t (\rho_t (x - m_t) + \sqrt{(x - m_t)^2 + \theta^2})$ Does anyone have ...
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### Calculation of the risk free rate

For portfolio management I need the risk-free to compute the sharpe ratio. I would like the use to rate on the 3 month treasury bill from the US. https://fred.stlouisfed.org/series/TB3MS#0 The ...
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### How to determine the risk-neutral measure in a Heston model?

To clarify, I'm quite familiar with the risk-neutral pricing framework, and I know one can efficiently Monte-Carlo a Heston model via the non-central $\chi^2$ distribution approach. But so far we're ...
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### What is the cause of a “broken” volatility surface?

I am currently working on a project for which I need the implied volatility surfaces, to estimate the value of plain-vanilla European options with different strikes (cannot be observed directly in the ...
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### Squared returns and volatility

Squared returns are considered pillars of GARCH/ARCH modelling and most used method for forecasting or studying volatility. Can you tell me how to calculate it from simple stock price. Is it better ...
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### Cross Effect in OLS

I am using cross effect in OLS regression for a time series problem for a multivariate regression. I want to quote reference for use of cross effect. Secondly, I want to explain why better to use ...
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### Forward Volatility vs Spot Volatility in Option Skew Models

My question is regarding Volatility Skew Models and their inputs. I have noticed that a vast majority of models take as an input the forward of the underlying (even in the case of stocks - where the ...
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### How can i fit the following regression in R? Why is the coefficient [second Columns] for R so low?

'Rwml' is the monthly log return So the first column is clear, I got nearly the same values, at least the same magnitude. But: If I regress on the variance, my input values are way too low to get a ...
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### What is the unconditional variance for a GARCH model?

I want to use a Matlab script to calculate Heston Nandi GARCH prices. I found an appropriate script online and it asks for the "unconditional variance" as an input. How do I calculate the appropriate ...
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### Black's Approximation - Discrete dividend for Put Options

I am currently trying to price and option chain for dividend paying stocks (american style exercise). I am able to calculate the Net Present Value (NPV) of dividends until maturity and then apply ...
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### Half life of Exponetial Weighted Moving Average

I am trying to apply a volatility strategy. I am reading a paper where the authors defined the volatility as: "Exponential Weighted Volatility of returns with a 1-year window and 3-month half-life" ...
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### GARCH volatility modeling, squared returns, and convergence

After reading some more of Volatility Trading, I decided to try to make a simple volatility model using daily log returns of an ETF I follow. It turns out "simple" is sort of relative. Unfortunately, ...
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### How to forecast monthly volatility with daily gjrGarch estimates

I'm currently writing a paper and need to regress the 22 days realized volatility of the following month on its GARCH estimate and the 126days realized volatility up to t=1 The paper im referring to ...
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### How to create a volatile market, by combining less volatile markets?

This might be against the law of gravity, but I'll give a try 🙂 Is there a way to combine two financial products $p_1$ and $p_2$, into a single product $p_c$ that is more volatile than its ...
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### What is the basis for the ansatz here? [duplicate]

I'm reposting this question: Jim Gatheral's ansatz I have the same question, but the answer given in the comment is no longer applicable since the link does not work.
The volatility $\sigma$ of an Ito process $dS_t = r S_t dt + \sigma S_t dW_t$ is not the square root of its variance. But you often hear that "volatility = standard deviation". What's going on here?...