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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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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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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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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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Can increase in volatility reduce the price of a deeply in-the-money European put?

Hull states that option prices increase with an increase in volatility. I think that statement could be false in a specific scenario: when we are considering a deeply in-the-money European put ...
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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(\sigma^...
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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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What's volatility timing?

I'm new and i'm starting studying finance. My english level is not so good. Could you explain me please, what is volatility timing? Thanks to all
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Vol swaps Vol of vol

I an quite unfamiliar with those products and would like to understand why they require a vol of vol model for pricing. The variance swap is replicated (assuming no cash dividends) with a delta hedged ...
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Predict probability of returns: How does changing volatility affect the return pdf?

I am trying to predict the future probability of stock returns based on the return distribution. Therefore I calculate the returns as $\frac{P(t)}{P(t-1)}$ for the whole daily data and fit a ...
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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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Question on Local Volatility

In Gatheral's book The Volatility Surface (Wiley, 2006), a local volatility model is defined as... $$ dS_t =S_t \mu_tdt + S_t \sigma(S_t, t)dZ $$ The famous Dupire Equation is given by... $$ \sigma^2(...
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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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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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How to apply the “Knapsack Problem” to minimise a portfolio's volatility?

Suppose I have a stock selection universe of 100 stocks. I have estimated the covariance matrix of this 100 stocks. I would like to create an equaly-weighted basket of 5 stocks which has the lowest ...
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Science behind options pricing into Earnings event

I am wondering about studies regarding the uncanny options pricing into public company's earnings reports. The phenomenon being that the price of a straddle before earnings costs near exactly the ...
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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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Why do we fit volatility surfaces implied from a option pricing model to the empirical data?

As far as I understand volatility surface. It is made of 2 components, the volatility skew/smile and the volatility term structure. Together they form something like Implied volatility is ...
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Replicating Log Contract - Errors Introduced by Jumps

In the GS Research Note about Volatility Swaps, it is shown that you can replicate a pure variance exposure (hedge) with only vanilla calls and puts, primarily thanks to the Carr-Madan formula of ...
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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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Uncertain volatility

Recently, I have encountered something called "uncertain volatility". Is it a popular concept in QF? Do practitioners use it nowadays? What are its pros and cons compared to e.g more familiar ...
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657 views

VXV vs. VIX futures: arbitrage opportunities?

At a first glance, VXV and VIX futures should not be compared at all: VXV is an underlying index, whilst VIX futures are derivatives written on a different underlying index, that is, VIX. As instance,...
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Negative high frequency intraday volatility - Zhou estimator

To estimate high frequency tick data stock intraday volatility, I have read Robert Almgren's notes7.pdf http://www.cims.nyu.edu/~almgren/timeseries/notes7.pdf where he talks about the bias free ...
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How to calculate implied volatility smile of basket using correlations?

For a basket, the realized volatility can be calculated using: $$\sqrt{\sigma_1^2 + \sigma_2^2 + 2 \sigma_1 \sigma_2 \rho}$$ If I have the volatility surface of two underlyings S1,S2 (strike space). ...
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Time-independent local volatility

Suppose somebody provides us with a surface of European call prices $C(\tau,K)$ where $\tau$ stands for time-to-maturity and $K$ for the strike. By Dupire's results, there is a unique local volatility ...
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How to compare volatility models?

What are the most popular ways to compare volatility models? Suppose I wanted to compare the forecasting accuracy of a GARCH(1,1) model with the historic 30 day volatility. What method should I use?
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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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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.
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Volatility swap hedge

What are the hedging methods for volatility swap (rather than variance swap)? What are the possibilities of setting up a static, semi-static or dynamic hedging? I am aware of but have not yet read ...
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441 views

The Heston Solution For European Option - Jim Gatheral

I have this equation (Eq. (2.4) "The Volatility Surface - A Practitioner's Guide" by Jim Gatheral (Ed. 2006)): $$-\frac{\partial C(v, x, \tau)}{\partial \tau}+\frac{1}{2}v \frac{\partial^2 C(v,x,\tau)}...
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DCC GARCH: specifying ARCH and GARCH parameter matrices in STATA

The command in STATA to estimate the DCC model of two variables is: mgarch dcc ( x1 x2=, noconstant) , arch(1) garch(1) distribution(t) $$ \begin{bmatrix} h_1{...
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Nested volatility

The introduction VIX options makes the concept of "volatility of volatility" a real life concept. The idea of "nested volatility" seems interesting, and I am wondering if there are any academic ...
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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 ...
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Calibrating Hull-White using volatility data

I would like to calibrate Hull-White model using volatility data.I am using [Park (2004)] paper as a reference. He suggests to minimize the following objective function: where the first term is ...
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Volatility of a rolling window strategy

What methods can be applied to determine the volatility of strategy using a rolling window? Using normal standard deviation would bias the results as the returns will be highly correlated. Although, ...
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How to determine the risk-neutral measure in a Heston model?

To clarify, I'm quite familiar with the risk-neutral pricing framework, and I know one can efficiently Monte-Carlo a Heston model via the non-central $\chi^2$ distribution approach. But so far we're ...
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Comparing historical to implied volatility

As title states, I am trying to compare historical to implied volatility of a stock. I approximate the single implied volatility (30 days forward) of the stock by first finding 2 series that ...
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Options on Volatility Control Index

I have two question. Does an option on volatility control index exist? If I google it, it seems like there is such an option, but I can't find the option on any of exchanges. So this is my first ...
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Fitting a non linear AR + GARCH(1,1)-M model

I want to fit the following model to a time series: $$ y_{t}=\alpha_{0}+\alpha_{1}y_{t-1}+\alpha_{2}y_{t-1}^{2}+\lambda h_{t}+\varepsilon_{t} $$ $$ h_{t}=\beta_{0}+\beta_{1}\varepsilon_{t-1}^{2}+\...
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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 compute the realised intraday volatility?

I'm in the position to calculate a non-parametric volatility estimator for 15 and 30 minutes intervals of the SPY. I got data sampled on second resolution. However, I checked plenty of papers but, as ...
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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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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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What is the difference between squared returns and variance?

I am trying to calculate 1-day ahead volatility forecasts using the exponentially weighted moving average, however I am unsure on how to read the formula provided within Risk-Metrics Technical ...
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Delta Neutral / Gamma Neutral Positions

I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ...
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Trading spot volatility

I am reading a paper that very briefly talks about some volatility arbitrage strategies. It's so brief that I do not exactly understand how it works. It says one of the strategy is based on "short ...
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Effect of volatility on the delta of a call option

In the book 'Dynamic Hedging', Nassim Taleb writes: ...
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pricing using dupire local volatility model

I am reading about Dupire local volatility model and have a rough idea of the derivation. But I can't reconcile the local volatility surface to pricing using geometric brownian motion process. If I'm ...
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Is there a better way to price options than with historical volatility?

I know that annualized historical volatility calculated with closing prices is a much rougher estimate than implied volatility for the correct "volatility" parameter in options pricing models. ...