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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Variance replication using options
I would like to understand the intuition behind the following question:
Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying?
A variance swap ...
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Option Pricing for Illiquid case
I am currently studying crypto options trading and have observed that there is often a lack of liquidity for options (such as BTC Options) on various exchanges, including Binance. In many cases, there ...
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How to calculate historical intraday volatility?
Sorry for what must be a beginner question, but when I went to write code I realized I didn't understand exactly how historical volatility, or statistical volatility, is defined. Wikipedia tells me "...
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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 (Heston/SVI)
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Understanding Yang-Zhang Volatility Estimator
I am using TTR in R and I am trying to understand the Yang Zhang volatility estimator (without drift). The following equations seem to imply a single value:
$$
\sigma = \sqrt{{\sigma_o^2}+k\sigma_c^2+...
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Probability of an Option maturing In-the-money vs. Volatility
How will the probability of an option ending up in the money change if the volatility of the underlying stock increases?
Intuitively, I think the answer to this is that if volatility goes up the ...
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Is the VIX more similar to a volatility swap or a variance swap?
I am reading the following paragraph on the VIX wikipedia article and I find it confusing:
The VIX is calculated as the square root of the par variance swap rate for a 30-day term[clarify] ...
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Continuous delta hedge formula
When we buy a call and continuously delta hedge using some implied volatility $\sigma_i$, what is the formula for our aggregate profit given that the actual realized volatility is $\sigma_r$?
Say $...
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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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Value of Call Option as Volatility goes to Infinity
Why would the value of a call option go infinity as volatility goes to infinity?
I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
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Where can I find caplet implied volatility data?
I am looking for caplet implied volatility data for Libor-EUR. Is there any online data base etc. available to get such data? Does ...
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What exactly is meant by "microstructure noise"?
I see that term tossed around a lot, in articles relating to HFT, and ultra high frequency data.
It says at higher frequencies, smaller intervals, microstructure noise is very dominant.
What is ...
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Volatility pumping in practice
The fascinating thing about volatility pumping (or optimal growth portfolio, see e.g. here) is that here volatility is not the same as risk, rather it represents opportunity. Additionally it is a ...
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What is the importance of alpha, beta, rho in the SABR volatility model?
I just read that SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the ...
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How to calculate future distribution of price using volatility?
I want to create a lognormal distribution of future stock prices. Using a monte carlo simulation I came up with the standard deviation as being $\sqrt{(days/252)}$ $*volatility*mean*$ $\log(mean)$. ...
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What is the equation for Garman-Klass volatility?
I want to calculate realized/historical volatility for the underlying products of various options using the Garman-Klass estimator, but I can't see to find an equation, although I know it involves ...
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Does the unconditional variance implied by a GARCH equal the sample variance?
In the MATLAB default settings for GARCH estimation they say "presample conditional variance is the sample average of the squared disturbances of the offset-adjusted response data y". Am I right in ...
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Why is the GARCH intercept supposed to be strictly positive?
Maybe it's a simple question but I don't really understand why it is theoretically required. Let's take the standard GARCH(1,1)
$$\sigma^2_{t+1}=\omega+\alpha\epsilon^2_{t}+\beta\sigma^2_{t}$$
In most ...
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If the volatility of pounds/euros = .2 do we know anything about the volatility of euros/pounds?
I think the question here is what we know about $\mathrm{Var}\left(\frac1X\right)$. Is this the right question to ask, and if so is there anything that can be said?
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Option Price vs. Implied Volatility
I was doing an exercise on investigating the relationship between European Call option price and its volatility. I was asked to compute $\frac{\partial^2C}{\partial \sigma^2}$ and find out the domain ...
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how to do interpolation in the term structure of volatility surface?
everyone~ I am a newbee in the quantitative finance and I meet a problem in working out an equity option volatility surface.
We use the reasonable market data to derive the implied volatility, then ...
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Pricing VIX Futures
In a 2006 paper Zhang and Zhu propose a model for VIX and VIX Futures based on Heston.
I am struggling in understanding how they get equation 6 and 8 (where they define the parameters).
Can anyone ...
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Daily realized volatility and true daily volatility
Can someone help if I am thinking correctly?
If $R(t,i)$ is the i'th log-return for $i = 1\ldots,M$ of day $t$ for $t = 1\ldots,T$.
Can I assume that the daily realized volatility (denoted $RV(t)$) is ...
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Realized Variance (realized volatility)
I'm confused about realized variance. I roughly know the theory around Ito Calculus and quadratic variation and integrated volatility so I understand what realized variance measures (even though as ...
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Historical volatility on bloomberg API
Is there a way to obtain the historical volatility of a stock from the bloomberg API? I would be looking for the data in the HVT table. Actually 3-months historical volatility from now would be enough....
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Is there a HAR that deals with the leverage effect?
The EGARCH is a special GARCH model that treats the leverage effect of the volatility. The HARV does not make a distinction between negative and positive returns. Is there a special HARV that deals ...
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Probability of exercise in the Black-Scholes Model
What's the intuition behind the fact that the limit of $\mathcal{N}(d_2)$, i.e. the (risk-neutral) probability of exercise, in the Black-Scholes Model tends to $0$ when the volatility tends to ...
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Paradox in option expiry as volatility goes to infinity
As volatility goes to infinity, the delta of a call option goes to 1. The delta approximates the probability that the option expires in the money. So it seems that the probability of expiring in the ...
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Understanding out-of-sample performance metrics for Realized Volatility
I fitted several models on a realized volatility process and then proceeded to obtain out-of-sample results. I'm struggling to interpret these results apart from to tell model A seems better than ...
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How to forecast volatility using high-frequency data?
There is a large literature covering volatility forecasts with high-frequency tick data. Much of this has surrounded the concept of "realized volatility", such as:
"Realized Volatility and ...
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Looking for a recommendation for a real life volatily trading book.
Recently I started working in an algotrading company as a programmer.
After I studied that subject a little in the university and read a book or two in that field I gained a little knowledge in that ...
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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 ...
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Why is realized volatility typically lower than implied volatility?
A number of quantitative finance textbooks mention something along the following lines, without further explanation:
A typical feature of implied volatility from stock index options is that it is ...
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How does volatility affect the price of binary options?
In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's ...
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Derivation of VIX Formula
I've read a lot of derivations about VIX formula. I can say it is -adjusted- fair strike of variance swap. But I can't see how it goes from variance swap rate to VIX formula. In particular I can't see ...
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How to calibrate a volatility surface using SVI
I've read the following paper by Gatheral and Jacquier and have several question regarding the calibration of a volatility surface in a arbitrage free way and some theoretical aspects. Let me first ...
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Volatility arbitrage - how is the profit extracted?
Is there any paper that describes in detail how the profit is extracted in directional volatility bet (vol arb)? I mean in the case that I bet the realized volatility will be lower than currently ...
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Does your Parkinson volatility ratio work as Taleb explained?
According to Dynamic Hedging: Managing Vanilla and Exotic Options (Taleb, 1997), the Parkison volatility estimator has several meaningful properties. It is defined
$$P=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\...
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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 ...
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One dimensional analog of cleansing a correlation matrix via random matrix theory
The general idea of cleansing a correlation matrix via random matrix theory is to compare its eigenvalues to that of a random one to see which parts of it are beyond normal randomness. These are then ...
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Transition Between Volatility Regimes
Emanuel Derman wrote a great paper in 1999 about volatility regimes and the adjustments the market makes during these periods (sticky strike, sticky implied tree, sticky delta, etc).
Has any ...
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How do you estimate the volatility of a sample when points are irregularly spaced?
I was looking again at this question which basically haunts every quant I believe, and I was thinking about the effect of these gaps when computing volatility of the series.
Let's define the problem ...
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SSR definition in Bergomi in relation to sticky strike and sticky delta
In Bergomi [Stochastic Vol Modelling] (Sec. 2.5.2), in the section on surface dynamics, the following definition of the "Skew Stickiness Ratio" (SSR) is made:
$$ SSR = \dfrac{1}{\mathcal{S}_T}\frac{d\...
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How is the formula for the VEV (VaR-equivalent volatility) in the PRIIP document derived?
The recent regulation (page 32) on PRIIPs requires to compute a VaR-equivalent volatility defined as
$$\mbox{VEV}=\frac{\sqrt{3.842-2\ln \mbox{VaR}}-1.96}{\sqrt{T}}$$
Does anyone have an idea how ...
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Mixed local-stochastic volatility model in Quantlib
At a conference the speaker mentioned that it is a standard approach today to use a mix of local and stochastic volatility model in equity, FX and interest rates.
Can you please suggest the most ...
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Is there anywhere I can read the paper, "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves"
Hello there was a paper published by: M. Arslan, G. Eid, J. El Khoury and J. Roth titled "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves" (2009).
I believe they ...
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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 ...
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Intuitive Explanation for Volatility Smile for Equity
I am trying to understand the intuitive reasoning for why volatility is more for deep OTM/ITM put/call then ATM..(why Simles for equity) Why ATM will not have more volatility as deep OTM/ITM option ...
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Local vol, stochastic vol, implied vol
I've been studying volatility modelling over past the few days; in particular, the connections between local vol, stochastic vol, implied vol. I've been reading Gatheral's book "The volatility surface"...
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How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)?
In markets, many instruments are quoted in volatility, but how we can tell what kind of volatility is this? Is it normal volatility, or lognormal volatility. because it affect our hedging positions.
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