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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7answers
33k views

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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1answer
3k views

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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5answers
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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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4answers
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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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1answer
914 views

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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3answers
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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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1answer
565 views

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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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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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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1answer
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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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1answer
881 views

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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Estimating implied volatility of an index component with no vanilla options market

There are liquid vanilla options trading on an index of 20 equity components. The question is how to price an option on one of the index components, knowing that there are no options trading on that ...
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1answer
356 views

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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1answer
1k views

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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1answer
4k views

volatility input for black scholes formula

I am not a mathematician but want to try and understand the BS model for option pricing. I get the intuitive sense of it but am unable to figure out calculation of volatility (as an input). Some ...
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3answers
209 views

Why is $dS/S$ an estimate of realized volatility?

For one period, $dS/S$ is an estimate of realized volatility, which we can annualize by dividing with $\sqrt{\Delta t}$. But.... why? How is $dS/S$ an estimate of volatility? Volatility is, to me, ...
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1answer
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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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1answer
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Which volatility as input in Black Scholes formula?

I am trying to price an option on an Index using Black Scholes formula. I estimated the daily volatility $\sigma_{day}$. My question is should I use an annual volatility based on the business days of ...
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1answer
547 views

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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1answer
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Correctly applying GARCH in Python

Problem: Correct usage of GARCH(1,1) Aim of research: Forecasting volatility/variance. Tools used: Python Instrument: SPX (specifically adjusted close prices) Reference material: On Estimation of ...
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5answers
16k 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 (Heston/SVI) ...
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3answers
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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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2answers
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Regime-Switching Model for detecting market shifts

I'm always wondering whether anyone has utilized regime-switching models successfully in forecasting or trading. Academia has long discussed this topic in-depth, such as using Regime Switching ...
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8answers
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What is the difference between volatility and variance?

How do volatility and variance differ in finance and what do both imply about the movement of an underlying?
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3answers
9k views

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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5answers
11k views

Why is the VIX futures market usually in a state of contango?

I'm a VIX newbie and I'm trying to understand why the VIX futures market is usually in a state of contango. All I can figure is that the sellers of VIX futures contracts demand high "prices" (because ...
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2answers
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How to forecast expected volatility from high-frequency equity panel data?

I'm wading through the vast sea of literature on realized volatility estimation and expected volatility forecasting (see, e.g. Realized Volatility by Andersen and Benzoni, which cites 120 other papers,...
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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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2answers
6k views

How to annualize intra-day volatility on minute data?

I am trying to convert minute based volatility into annualized volatility in such a way that both are comparable. $Vol_{min} * \sqrt(t)$ does not seam to get them into the same scale if I annualize ...
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2answers
5k views

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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2answers
3k 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 ...
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2answers
4k views

SPX options vs VIX futures trading

Forward volatility implied by SPX options, and that of VIX futures get out of line. If there existed VIX SQUARED futures they could easily be replicated (and arbitraged) with a strip of SPX options. ...
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2answers
760 views

Ideas about Stochastic volatility models

I am currently working on comparing different models for modelling the volatility and then pricing vanilla options (I use option prices on real stocks in order to calibrate my models and then I ...
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5answers
8k views

What is a regime switch?

I've come across the term regime switch in volatilities when reading about the modelling of interest rates but could not find a definition for a regime switch and what a regime is. Can somebody give ...
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3answers
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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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1answer
730 views

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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2answers
6k views

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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2answers
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Constructing an approximation of the S&P 500 volatility smile with publicly available data

Besides of the VIX there is another vol datum publicly available for the S&P 500: the SKEW. Do you know a procedure with which one can extrapolate other implied vols of the S&P 500 smile with ...
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2answers
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Why is the vega of an at the money option so insensitive to movements in volatility? I.e, why do ATM options have such little Vomma?

I've been trying to understand why at the money options have very little vomma. I was reading and came across a graph that showed vega as volatility changes and I couldn't grasp how the relationships ...
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2answers
4k views

GJR-GARCH Model In R

Any idea how to estimate GJR-GARCH models in R? Is there any particular library like fGarch that supports such models?
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2answers
833 views

SKEW and VIX relations?

My question is about the CBOE published index VIX and SKEW. To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston model....
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1answer
2k views

Implied Volatility Surface - log forward moneyness

I'm reading this paper by Fengler (2005) and have came across the below snippet. context: Implied volatiltiy surface plot has 3 dimensions IV, Strike, Time to Maturity. Author replaced Strike with ...
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3answers
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Which volatilities should I use for Quanto Options?

Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate. How can I read the "right" volatilies ...
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1answer
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Estimating the historical drift and volatility

I want to forecast prices $S(t)$ of some asset based on historical daily values. I want to use the geometric Brownian motion given by an SDE: $$dS=\mu S t + \sigma S dB,$$ where $B$ is a Brownian ...
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2answers
791 views

Expected value of Black-Scholes

(Apologies for any formatting mistakes) Within the Black Scholes model, given that you are estimating the volatility from historical data - and all other parameters assumed exact - one usually ...
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2answers
2k views

Mid-curve swaption

I would like to know how the mid-curve swaption could inform us about forward volatility. In my understanding it is a swaption on a forward starting swap. Let us say the midcurve swaption expires ...
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1answer
534 views

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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3answers
484 views

Construction of VIX and VVIX

I just read the CBOE's Whitepapers for VIX and VVIX and notice that they are constructed in the same way, i.e. a range of calls and puts on the respective underlyings (S&P500 in case of VIX, and ...
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2answers
335 views

Proof of approximation formulas for implied volatilities

I am trying to calibrate a local volatility model to observed implied volatility smiles (not surfaces!, just a smile given for fixed maturity). I ran into the following approximation, and thought I ...