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

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17
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7answers
4k views

Why is volatility mean-reverting?

We all know it does mean revert. The question is why. What's making volatility mean-revert? Is it some sort of cyclical behaviour of option traders? The way it's calculated? Why?
16
votes
6answers
15k views

What's the difference between volatility and variance?

How do they differ in what they imply about an underlying's (or any variable's) movement?
16
votes
2answers
2k views

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 ...
15
votes
5answers
3k views

Skew arbitrage: How can you realize the skewness of the underlying?

It's not clear to me how to realize skewness. In other words, how do you implement skew arbitrage? There seems to be no well-known recipe like in volatility arbitrage. Volatility arbitrage (or ...
12
votes
4answers
8k views

Why are GARCH models used to forecast volatility if residuals are often correlated?

The answers to this question on forecast assessment suggest that if the sequence of residuals from the forecast are not properly independent, then the model is missing something and further changes ...
12
votes
3answers
624 views

How to price a volatility-index option?

There exist several volatility indices, such as the CBOE Volatility Index (VIX). There are also options on such indicies. What is the best way to price a volatility-index option? Is there a simple ...
12
votes
2answers
2k views

statistical arbitrage option overlay strategies / volatility trading

Here's an interesting trading puzzle that I would love to get the community's input on. Let's say there exists an alpha signal that does a good job of sorting equities expected excess returns over ...
11
votes
6answers
2k views

Why does the VIX index have *any* correlation to the market?

It appears that the log 'returns' of the VIX index have a (negative) correlation to the log 'returns' of e.g. the S&P 500 index. The r-squared is on the order of 0.7. I thought VIX was supposed to ...
11
votes
7answers
1k views

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 ...
11
votes
4answers
2k views

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 ...
11
votes
1answer
718 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 ...
11
votes
2answers
713 views

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 ...
11
votes
2answers
307 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 ...
10
votes
5answers
3k views

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 ...
10
votes
1answer
2k views

How do I compare implied and historic volatility?

what would you suggest are the starting points for comparing, in an easy, visual way, implied and delivered volatility surfaces? I'd like to see what the differences are between the historic surfaces, ...
10
votes
2answers
402 views

Exploiting breakdowns in correlation of estimated volatility

In the attached image I have a plot of the rolling correlation of 90-day historic volatility (using the Garman Klass estimator based on Sinclair's Volatility Trading) of JPM v. the S&P. As can be ...
10
votes
1answer
326 views

Is Arithmetic Return Bias Basis of Low Vol Anomaly?

An observation in capital markets is that the connection between return and risk (measured as volatility) is not that straightforward (at least not as modern portfolio theory assumes). One interesting ...
9
votes
5answers
6k views

Why would an investor trade a variance swap over a volatility swap?

Why would an investor trade a variance swap over a volatility swap? Is it simply related to the leverage involved in a Var (i.e. sigma-squared) or is there something else to it?
9
votes
3answers
557 views

better estimator of volatility for small samples

One commonly used sample estimator of volatility is the standard deviation of the log returns. It is indeed a very good estimator (unbiased, ...) when the sample is large. But I don't like it for ...
9
votes
1answer
368 views

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 ...
9
votes
1answer
525 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 ...
9
votes
3answers
3k views

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 $\sqrt{(days/252)}$ $*volatility*mean*$ $\log(mean)$. ...
9
votes
1answer
323 views

Appropriate measure of Volatility for economic returns from an asset?

I am doing research on uncertainty analysis and risk assessment for oil field development. For doing economic forecast and valuation I use Real Options theory, which is almost similar to theory used ...
9
votes
1answer
494 views

Can VIX be interpreted as a proxy for instantaneous volatility?

BJO06 (Table 2) estimate the following Cox-Ingersoll-Ross model for market variance, $\sigma^2_t$: $\mathrm{d}\sigma^2_t = (\alpha_0 + \alpha_1\sigma^2_t)\mathrm{d}t + ...
8
votes
2answers
740 views

Analytical relationship between a covariance matrix and cross-sectional dispersion

Given an expected returns vector and a covariance matrix, one can perform a joint draw and measure the average cross-sectional variation as the standard deviation across returns for a particular joint ...
8
votes
3answers
1k views

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 ...
8
votes
2answers
510 views

Extensions of Black-Scholes model

For the Black-Scholes model my feeling is that the volatility parameter is like sweeping stuff under the rug. Are there models which improve on the volatility aspect of Black-Scholes by adding other ...
8
votes
1answer
359 views

What are the main differences in Jump Volatility and Local Volatility

Is a JV model simply Local Vol + Jump Diffusion? If so, it seems logical that an existing JV model be able to be used for valuation of both Vanilla and Exotic options. Is this true? Does a Local ...
8
votes
2answers
613 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 ...
8
votes
1answer
299 views

What are the major characteristics of natural gas volatility and options?

Seasonality is a big deal in the natural gas markets. My understanding is that they are broadly divided into summer and winter, with seasonality in both price and the volatility. What does this ...
7
votes
2answers
945 views

What does the VIX formula measure and how does it work?

I have read the CBOE's white paper on the VIX and a lot of other things, but I need to honestly say, I don't really get it, or I am missing something important. In semi-layman's terms, is the VIX ...
7
votes
2answers
2k 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. ...
7
votes
2answers
218 views

Extrapolating implied volatilities to small time

Could anyone please direct me to literature or methods for extrapolating the implied volatility surface towards small expiry? I'm looking to price very short time to expiry binary options (e.g. 5 ...
7
votes
1answer
934 views

How should I estimate the implied volatility skew term when calculating the skew-adjusted delta?

I'm trying to come up with the implied volatility skew adjusted delta for SPY options. I'm working with the following formula: Skew Adjusted Delta = Black Scholes Delta + Vega * Vol Skew Slope. I ...
7
votes
1answer
428 views

What is the best method to compute project volatility in Real Option Valuation?

There are few methods like Copeland-Antikarov, Herath-Park, Cobb-Charnes etc. to compute project volatility, however these methods compute upward biased volatility. What is the best method I could ...
7
votes
2answers
426 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 ...
6
votes
6answers
8k 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 ...
6
votes
2answers
2k 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 ...
6
votes
4answers
698 views

How to hedge against lack of volatility

Say you have a trading system that works best when markets are most volatile. What would be the best way to hedge against lack of volatility ? For example, 2008, 2009 was highly volatile and it has ...
6
votes
3answers
1k views

What really drives option implied volatility?

A common and oft repeated belief regarding options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of an expected ...
6
votes
3answers
218 views

How to measure investors' “experienced” volatility?

In asset allocation, you usually send reports to your clients where you will report the volatility of its portfolio. Assuming you only have monthly returns, you will compute volatility over a ...
6
votes
2answers
368 views

The T+H Problem in Factor model forecasts

Suppose we train on M individuals consisting of T observations (i.e. TxM design matrix). The dependent variable is one-year return for each security (H = horizon of one year). In a factor model ...
6
votes
2answers
558 views

Varswap Basis - What is it in practice?

What is the varswap basis? I am not completely sure what this number represents. Is it the basis between the estimated future realized volatility and the vol surface implied volatilty at a specified ...
6
votes
1answer
82 views

Model calibration to illiquid assets when pricing options with long maturities

Let us assume one is interested in pricing an option with a very long maturity (up to 20 or 30 years) on a liquid underlying. The market won't have liquid quotes for the higher maturities. Still you ...
6
votes
1answer
342 views

How sensitive are vertical spreads to changes in implied volatility?

How sensitive are vertical spreads to changes in volatility / implied volatility in the money, at the money, and out of the money? I'm thinking for 1 point spreads this would be very small / neutral ...
6
votes
1answer
957 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 ...
6
votes
1answer
205 views

Why does the price of a derivative not depend on the derivative with which you hedge volatility risk?

I'm trying to derive the valuation equation under a general stochastic volatility model. What one can read in the literature is the following reasoning: One considers a replicating self-financing ...
6
votes
1answer
138 views

Should we apply practical constraints on the distribution of monte carlo paths?

to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out ...
6
votes
0answers
1k views

Volatility-Based Envelopes

I am following an article by Mohamed Elsaiid (MFTA) about Volatility-Based Envelopes - a quite new technical indicator he has introduced, that is being used by Bloomberg. My goal is to get a simple ...
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 ...