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

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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 ...
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431 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 ...
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230 views

Why is volatility said to be persistent?

Persistence in volatility of stock returns is one of the common 'stylized facts' when it comes to analyzing time series. However, I am wondering for theoretical arguments why (estimated) volatility ...
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758 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 ...
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2answers
316 views

HFT to blame for Flash Crashes?

Some people 1, 2, 3 claim that High Frequency Trading is partly to blame for the extreme volatilities in the markets yesterday (24. August 2015). Is that true? Is the amount HFTs move even enough ...
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5k views

Why FX Vanilla Options are quoted in volatility

I've been curious why vanilla options are quoted (and traded) in terms of volatility. Considering that every financial institution has its own options pricing model, volatility as an input would cause ...
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743 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 ...
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576 views

Why linear interpolation not appropriate for volatility surface construction?

We know linear interpolation is not appropriate for constructing a surface, but why? In the book, "Foreign Exchange Option Pricing: A Practitioners Guide", the author writes: native linear ...
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5answers
344 views

Can classical economics explain *any* of the so-called stylized facts of finance?

I am doing some reading on the (historical) emergence of the Black-Scholes implied volatility smile for index options (yes - post 87), and I stumbled across an economic paper attempting to explain the ...
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Can American options with no dividends and zero risk-free rate be treated as European?

Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
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6k views

Annualzing the log of daily returns riddle

Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or ...
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212 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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807 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 ...
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562 views

Tradable Volatility

VIX (spot) has very nice features, including mean reversion. We all know that we can't trade VIX (spot). The closest we can get is using front-month future contracts. The problem I have with that is ...
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1answer
3k 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 ...
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304 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 ...
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612 views

Do intraday volume and volatility share the same properties?

volatility clustering and mean reversion are very well known properties that one could use when trading. Traders, especially in options world, do take realized vol into account (e.g. by forecasting it ...
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2k 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 ...
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1answer
287 views

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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2k views

What does it mean to be “long or short in volatility”?

I've heard a question regarding pricing of european calls. The question is: Is the call long or short in volatility when it is (deep) OTM? What is the profile of the implied volatility? I ...
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8k views

What is the “leverage effect” for stocks?

I've read the so-called "leverage-effect" for stocks models the fact that if a company is leveraged, its volatility should increase as the stock price moves lower and closer to the level of debt. Can ...
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2answers
7k views

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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226 views

How is implied volatility derived?

How to compute Implied Volatility Calculation? The above link shows that there multiple ways to calculate implied volatility. My question is that for most of the common data sources like Bloomberg, ...
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263 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 ...
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124 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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311 views

Does it make sense to use upward and downward volatility in option pricing?

Historically stocks have a higher likelihood to increase in price than to fall in price. As such would it make sense to split a stocks volatility measurement into upward and downward components? For ...
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1answer
2k views

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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1answer
237 views

Density forecast of a GARCH model

I am currently working on developing a series of density forecasts and I am encountering some problems. I am working on weekly S&P 500 returns and the returns process is described as $r_{t} = \...
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454 views

Variance swap replication and variance vega

Noob here. I've been trying to gain a better understanding of variance swaps and what better way than to replicate it with a portfolio of better understood instruments. I have read the GS 1999 ...
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1answer
1k views

Problems with dealing with GARCH models and intra-day data

A Short question would be "Which type of model from GARCH family is most suitable for modeling 5-minute data returns ?" but I've added some story to it. A Long time ago I was preparing my thesis, one ...
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2answers
1k views

How to derive appropriate volatility for a binary option (with strike/term) from market data?

I am valuing a binary FX option (european) with a defined strike and term (2Y). I'm using a closed form solution based on Black-Scholes framework. How can I derive the appropriate volatility to use ...
6
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1answer
592 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
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1answer
741 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 ...
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140 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 caps....
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1answer
629 views

What research is available on the performance of convertible bond arbitrage models?

The basic principles of convertible bond arbitrage have been clear at least since Thorp and Kassouf (1967). For those who are not familiar, the arbitrage entails purchasing a convertible bond and ...
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847 views

Do low volatility stocks outperform high volatility stocks over the long run?

A recent article from Forbes seems to indicate that low volatility stocks outperform high volatility stocks over the long run. Does anyone have any supporting or contradicting evidence to this claim? ...
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3answers
2k views

Does the debt load affect the volatility of equity?

Does the debt load of a company have an impact on the stock price of a company and its volatility? Also, how does the market react to the announcement of a company issuing bonds?
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194 views

How to derive this approximation of the risk-neutral expectation of the variance?

On the paper Bollerslev, Tauchen and Zhou (2009 RFS) the authors say about equation (15): The corresponding model implied risk-neutral conditional expectation $$E^Q_t(\sigma^2_{r,t+1})=E_t(\...
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1answer
389 views

Is volatility for the next day forecastable? To any extent?

In a more general way: is there 1) a methodological approach to quantify the correctness of a model that produces a probability distribution for the, say, S&P 500 index return for the next ...
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1k views

How to avoid having negative volatility when applying Heston model?

When applying the Heston model to generate the sample volatility surface, some of the volatility value will be negative. I am just wondering what do practioners normally do with these negative value. ...
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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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Garch modelling on Stata

I would like to ask "how to do GARCH modelling on stata". Basically I want to estimate stock market volatility using daily data. I have one variable as return series, $r_t=\ln(\frac{P_t}{P_{t-1}})$. ...
5
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343 views

How to calculate volatility on intraday data?

I have several weeks of minute-by-minute stock data (start and end prices, volume). Everything I've read so far leads me to believe there isn't a standard method for volatility, which is leaving me ...
5
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2answers
856 views

How to use a realized kernel?

I've read that realized kernels are the thing to use for calculating daily volatility from high-frequency data. So I've got minute data, how do I actually use such a kernel? Will it give me minute-ly ...
5
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1answer
290 views

Reference on Electronic volatility trading [duplicate]

Possible Duplicate: Looking for a recommendation for a real life volatily trading book. I recently came in contact with a quant desk that traded volatility. The discussion only highlited my ...
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1answer
522 views

Why are there so many different ways of calculating historical volatility

There appears to be several ways of calculating volatility: Price volatility (of which there are several variants): close to close high low range average of open, high, low and close Log returns ...
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1answer
506 views

Black-Equivalent Volatility

Can Someone Explain to me what this term means, and how it's used?
5
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1answer
148 views

Which volatility to use to price options on futures contract?

I have some questions regarding pricing futures options and I just want to be sure that my thoughts are correct. I am trying to price options on futures for american & european style. In the ...
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1answer
3k views

How to use Newey West covariance corrector?

I have implemented the following model: daily_vol(t+1) = A*daily_vol(t) + B*weekly_vol(t) + C*monthly_vol(t) + error where vol means volatility, and A, B, C are ...
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793 views

Construction of “vol of vol”

How do you construct something that lets you buy "vol of vol"? not necessarily for VIX, but any particular stock or index.