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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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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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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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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Why are my GARCH forecasts biased?

I've run an ARMA(1, 1)-GARCH(1, 1) model with normal density on log returns for twelve stocks. I computed the one-step-ahead out of sample forecast for daily volatility on a rolling windows for 500 ...
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implied volatility and strike price

Assume for simplicity that the expiration time of an option is $1$ the initial stock price is $1$ and there is no dividend yield and the risk free return is $0$. How is it possible to show that the ...
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Callable bond price sensitivity to Hull-White volatility changes

I'm using classic Hull-White model for short term interest rate dynamic: $$dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$$ (Notation is quite intuitive, anyway I am using the same as Wikipedia ...
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Asymmetric Volatility Modeling (Interpretation)

I am currently writing a paper on asymmetric volatility modeling of brent, gold, silver, wheat, soybean and corn from 1986-2012 and divided them into 4 sub-sample periods (i.e. 1986-1991, 1991-1997, ...
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Measure how different forecasted volatility is from realized volatility

Hi Quantitative Finance Stack Exchange, I'm looking for an opinion on a simple question. Suppose I use a Garch(1,1) model to make a volatility forecast. At time $t$, I have realized volatility $\...
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Calculating volatility of inhomogeneous time series

I am reading an article by Zumbach and Müller whose name is Operators on Inhomogeneous Time Series. This is interesting in general, but my main goal is to learn a good and efficient method to ...
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EUR/PLN and EUR/USD delta-term-vol surface quoting convension

does anyone know for sure what is the FX market convension to quote delta-term pairs for EUR/PLN, for EUR/USD. I know that for EUR/PLN it should be delta p.a forward, for EUR/USD it should be delta ...
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How to price the american options using local volatility

I have given with a surface of american option prices $C_{am}(T, K)$. From these american option prices the implied volatility surface is deduced. Now I want to find the local volatility $\sigma(s,t)$...
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Whats the big deal between volatility and the risk free rate?

I am trying to understand asset price volatility. Many of the news articles I read link how stock market volatility is linked to asset price volatility? To give an example, in Mike Mackenzie's (...
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Spread in Option Quotes

Let's take a look at market-maker's option quote in vol terms: 8.5 / 9.5. In that example bid-ask spread equals 1.0 point of vol. Can anybody clarifying how market-maker choose amount of spread in ...
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Volatility Parametrization Libor Market Model - Underspecified Model?

Does the volatility parametrization that I have chosen give an underspecified model? Which volatility parametrization in the Libor Market Model would suit the best for the particular case described ...
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How can a beginner trader make use of 'volatility of volatility'

For a beginner option trader in equity options, how can he use this metric that is provided by his broker/data vendor? How can he use this metric to gain an added understanding of the option pricing/...
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Rolling window Kendall's tau against APARCH(1,1) correlation

Assume you want to forecast the correlation matrix of a stocks' basket (say 15 ~ 20 stocks from different sectors); assume you need to forecast at $T$ days because you will use the forecast ouput with ...
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Real time stock volatility

Is there any need for real time weighted volatility on a tick by tick basis for equities? If you had that access to that, what could you do with it?
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What is the longest number of consecutive days that options implied volatility has stayed “extremely high” for any particular underlying?

Curious as to whether or not there is any sort of all time record. Any index, future, or stock will do. Volatility must be well above the average 1 year volatility for all periods.
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Volatility of a stock basket

to determine the volatility of a basket of stocks, I often use the following formula: $\sigma_{basket}=\sum_{i}\sum_{j}w_i w_j \sigma_i \sigma_j \rho_{ij}$ where the $\sigma$ are the constituents' ...
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Intuitive description of the Spillover Index by Diebold and Yilmaz

I am struggling to grasp the steps outlined in the 2009 paper by Diebold & Yilmaz, which introduces the framework for a spillover index. The final expression for a spillover index for a two ...
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How rapidly should estimated volatility and volume change for estimating market impact in small markets?

The cost of market impact is usually modeled as: $$ \Delta{P} = \delta \sigma (\frac{Q}{V})^{1/2} $$ Where: $ \Delta{P} $ is the change in price of the asset caused by the transaction size $Q$ $\...
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Simulation of a DCC-GARCH

I want to simulate some exchange rates with a DCC GARCH. I know the package rmgarch but I want to code the simulation my self. The following are the main equations ...
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Derivation of the Pnl of a Delta Hedged Straddle and Risk Reversal

In the link below, in the text it states the following equations: Delta-hedged straddle P&L = Volatility Risk-premium ×| Straddle Vega | and Delta-hedged risk-reversal P&L: ...
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volatility term structure calibration

As is well known in order to calibrate an interest rate model (i.e. hull-white, LMM) i need to use the current market yield curve and volatility. But in the case I want to calibrate the model in a ...
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Equity Options - “How do I build a forward simulation model with regards to shocks in spot pricing and IV?”

I am trying to build a "What-If" Portfolio, consisting of a total of 20 options, across different tenors, strikes (delta), but on the same security. Simply put, the objective is for me to test the ...
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118 views

Realized volatility vs Fundamental volatility

What is the difference between the realized volatility (also called historical volatility) and the fundamental volatility?
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How do the units compare inside the (rate - 0.5*sigma-squared) correction?

Usually, I find the units of the mean and the standard deviation of a distribution to be (quite obviously) the same. Can anyone come up with a really simple explanation (for MBA students, some of ...
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Variance swap “fast” models

As far as I understand, Variance Swap (VS for short) function as follows : no payment when entering the contract at maturity the VS buyer pays a strike $K^2$ and is paid (by the VS seller) the ...
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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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When to use SV or a GARCH model

So i have been searching for this answer for a question if there is a rule or something that would say when to use GARCH type model or use an stochastic volatility model to predict the volatility of ...
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Derivation of variance of Zhou (1996) volatility estimator

Does anyone know how to derive the Variance of Bin Zhou's volatility estimator (Theorem 1) in 'High-Frequency Data and Volatility in Foreign-Exchange Rates' (1996) Zhou 1996 Any help would be ...
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Reasoning for Bloomberg's short rate volatilty calculation

Bloomberg, in its documentation, explains that it calculates the short rate volatility for its Hull White implementation by multiplying the e.g. 10y IRS rate (divided by 100) by the 10y cap vol. Why? ...
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Yield Curve Volatility

Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds. Each yield curve has its slope and its curvature, and they obviously change ...
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Measuring unbiased estimator for variance with RMSE?

The root mean squared error (RMSE) is considered by some to be the best measure of how good a variance estimate is. You often see it quoted as: $RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^n(\hat{\sigma_i} - \...
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How to trade risk-adjusted returns?

Why does dividing daily returns by daily range eliminates fat tails and results in an (almost) gaussian distribution? And how could that distribution be exploited to enter trades?
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What is the relation between return volatility and return rank volatility, and how can I control the latter?

I have no experience in finance, but I've been playing around with a virtual portfolio. I'm trying to control the "rank volatility" distribution - that is, the volatility of a stock's daily rank in ...
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GARCH(1,1) one-step ahead volatility forecast biased, higher than Parkinson's HL volatility

I am trying to create one-step ahead forecasts for the S&P500 using a GARCH(1,1) model. I am using the rugarch package in R. As you can see, the forecasted points are consistently higher than the ...
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General assumptions for var swap replication

I've seen claims that the standard static-hedge for a plain vanilla variance swap holds so long as the underlying doesn't jump, but every derivation I have seen begins by assuming the asset follows a ...
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stochastic volatility and smile

Can we say that the volatility smile contain for sure stochastic volatility information ? If yes why ? Saying that BlackScholes does not explain the smile does not necessary mean there is an ...
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Vega for long long-term ATM call and short short-term ATM call

You are long a long-term ATM call and short a short-term ATM call. The ratio is adjusted to make the total vega zero. If before expiry of the short-term option, spot is again at the strike price. ...
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Estimating daily volatility of unevenly/irregularly spaced time series data

Say I have time-series data that is unevenly spaced, with anything between 4-50 hours of spacing in between. The data comes from a trading account history, which has captured the balance of the ...
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target correlation for portfolio

Given a long / short equity portfolio, I want to have some net long exposure. My portfolio volatility is fixed to a target, so in trying to have a certain beta to the market, the only thing I can ...
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volatility for multiple time series

I have time series data for a total of 4 stocks and want to analyze the volatility of those. Moreover I want to demonstrate that they have the same volatility. As a response variable I would use log ...
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Why is Bachelier implied volatility more skewed than the Black-Scholes implied volatility?

I found the following explanation in a paper by Grunspan (see attached paper page 6) but have trouble understanding it: By differentiating Formula (3) with respect to m, it turns out that the ...
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Frequency Arbitrage

We know that the volatility is lower when the sampling period is longer, for example $\sigma_{7days} < \sigma_{1day}$, Then I came across this strategy that I cannot quite understand how to exploit ...
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Looking for material on volatility forecasting with a focus on market/news events

I'm hoping someone can direct me towards any books/papers that approach volatility forecasting from the perspective of market specific events (fed meetings, USDA reports, OPEC announcements etc). From ...
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Unconditional variance of an E-GARCH model

I am attempting to calculate the unconditional variance of an E-GARCH model: $$\log(h_{t+1}) = \beta_{0} + \beta_{1}\log(h_{t}) + \beta_{2}\left[|\varepsilon_{t} - \lambda| + \gamma(\varepsilon_{t} - \...
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GARCH Option Pricing Model (Duan 1995)

I am trying to replicate Duan's results from his 1995 Paper, "The GARCH Option Pricing Model". I have written this code in Python myself, and using his parameters I consistently seem to obtain results ...
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326 views

Trading strategies for increased realized volatility

Suppose once every 2-3 weeks I have a way to select a few equities that are likely to exhibit higher realized volatility in the future month (relative to the past month). Historically, the average ...
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When is implied volatility greater than realized volatility?

Assume it to be known that the volatility of a stock at any point in time is $\sigma(t)$. My question is, if we have a number of options priced using some implied volatilities $\sigma_1, ..., \...