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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74 views

Are intraday volatility estimators useful for close-to-close predictions

I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the ...
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4answers
192 views

Identifying “logical” segments on trading charts

The chart below is the 15-minute EURUSD from earlier today. The blue lines represent dividers between three subjective but reasonable segments that can easily be made out by the eye. I would ...
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CBOE Skew Index Intuition

I was recently reading (and very much struggling to understand) the CBOE white paper on their Skew Index (CBOE Link), I thought it might be useful as I'm trying to better understand volatility skews. ...
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199 views

Volatility Managed 6 Factor Model (Fama French) - Does it make sense?

after weeks of intense research and in spite of the current situation, I decided to ask the following question to some experts (you): I would like to develop/investigate a volatility managed six ...
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50 views

Relation between volatility and exercise timing of American Options

Hopefully someone can help me with intuition. Suppose that we have a stock whose value evolves per the geometric brownian motion $dX_t=X_t\mu dt+X_t\sigma dW_t$, for $\sigma>0$, $\mu\in\mathbb{R}$ ...
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1answer
242 views

Local volatility and Stochastic Volatility

Please help me understand similarity and differences between local volatility and Stochastic Volatility both intuitively and mathematically.
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79 views

Can variance change over time?

I'm working on a toy project that involves fantasy basketball, I know this is the quantitative finance stackexchange, but it seemed like the best place to ask this question. My goal is to make ...
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125 views

Local volatility Formula and How To use it

I'm new to Volatility Modelling, so the content of this question may be completely wrong and th question naive. I'm reading "The volatility surface" by Gatheral. I'm trying to get a sense of the first ...
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48 views

TSRV parameters selection

I'm thinking about how to select the $J$, and particularly, $K$ parameters for the Two Scale Realized Volatility estimation? I cannot find any reference for that in the original paper - there it says $...
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61 views

HAR-RV model for predicting 1-min volatility

I would like to use HAR-RV model (Heterogenous AutoRegressive - Realized Volatility) to predict a 1 minute realised volatility using the HAR model. As regressors I intend to use RV of previous minute, ...
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49 views

how to model NGARCH using 5min frequency data?

NGARCH model using 5-min High-frequency data in R I wanted to analyze some 5 minute frequency data of stock market. My teacher asked me to use NGARCH to model, but I didn't know how to program.Here ...
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87 views

Is it possible to compute implied returns from volatility?

If we assume that, broadly speaking: Assets in liquid markets are fairly priced to its value Volatility is predictable (volatility clustering, GARCH, etc) Investors are rewarded and earn a return for ...
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53 views

Is $\sigma_{1} = \frac{\sigma_{\tau}}{\sqrt{\tau}}$ suitable for volatility scaling?

It seems to be the de-facto method; and I see how we get it from log-normal assumption. However volatility scaling seems to be way more sensitive to $\tau$ than mean scaling -- as in two ~ 2 times (...
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1answer
188 views

In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
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125 views

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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68 views

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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69 views

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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115 views

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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127 views

Fitting a forecasting S&P500 roll volatilities

I have a time series of S&P500 prices, for which I have calculated log-returns and roll-volatility. My goal is to forecast daily realized volatility and test a straddle strategy based on it (I ...
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51 views

Negative theta in Log-linear stochastic volatility model

I was asked to simulate the following geometric Brownian motion to get paths for the SPX stock price. the process follows a Log-Linear stochastic volatility. $dS_t = \mu S_tdt+e^VS_tdW_1 $ where ...
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65 views

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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1answer
198 views

Autocall Calibration

I'm trying to price autocalls. In theory my pricing method is ok (I followed Bouzoubaa's book procedure) but I'm not sure I read anything on calibration of autocalls. Basically my question is what ...
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46 views

DCCfit speed up formula

I am estimating the covariance matrix by using GARCH DCC model with function dccfit from package rmgarch. My code is something like: library(rugarch) library(rmgarch) ...
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274 views

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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63 views

What does multifrequency volatility mean?

I came across the term "multifrequency volatility" while reading the book "Multifractal Volatility: Theory, Forecasting, and Pricing" (2008) by Calvet and Fisher. Can anyone help me understand what ...
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48 views

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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292 views

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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702 views

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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1answer
260 views

Are “stylized facts” based on reliable evidence?

A highly cited article "Empirical properties of asset returns: stylized facts and statistical issues" by R. Cont use the Figure 8. below to illustrate the well-known phenomenon of volatility ...
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374 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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181 views

Relative Value Trading of American Style Options on Futures, Calcuating hedging ratios?

I am interested in Relative Value Trading of American style options on futures and have not found a whole lot of literature on it. The best resource I have discovered so far is a few pages in Colin ...
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211 views

OHLC Covarianc Estimation

Is there an R package which can estimate a covariance matrix using OHLC (Open/High/Low/Close) share prices for upwards of 40 shares using the Yang & Zhang method using daily data? I google ...
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727 views

GARCH filtering and extreme value theory

We are evaluating a model for risk management based on extreme value theory using peaks over threshold and markov chain monte carlo methods. In doing this, we are firstly fitting a GARCH (we have ...
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416 views

How to calibrate volatility surface for Interest Rate Cap&Floor pricing

I'm using Black model to do interest rate Cap & Floor pricing. The volatility is determined by using the bootstrapping methodology. However, afterwards, how should I do the calibration, or ...
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109 views

Testing for the presence of a positive or negative gamma effect

I am currently analyzing a statistic that I believe will have the effect of hedgers having a positive or negative gamma position in certain stocks. In the case where I believe hedgers have positive ...
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75 views

robust regions in grid search

I have a strategy f that takes parameters x,y (for x,y taking values in integer ranges). I get two grids (of returns and volatility values) from computing f(xi,yi) for integer ranges x1 <= xi <= ...
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100 views

How to measure if variance is greater at a certain time of day?

I'm not very fluent in the quant vernacular, so perhaps the nature of my question will be better illustrated as a hypothesis. One market has closed and another market elsewhere on Spaceship Earth is ...
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1answer
781 views

Instantaneous Volatility Estimator

Suppose a Stock follows an Itô process with instantaneous volatility $\sigma(S(t),t)$. Precisely $$dS(t)=\mu S(t)dt+\sigma(S(t),t)S(t)dW(t)$$ I have a historical data for the values of $S(t)$.How ...
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2answers
108 views

Jump diffusion simulation

I want to simulate a geometric Brownian motion and we assume that the volatility of the stock can take just two values $\sigma_1=0.2$ and $\sigma_2=0.8$. We also assume that the jumps up from lower ...
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155 views

1 Factor Hull And White Swaption Calibration

I'm trying to calibrate a Hull and White model with constant volatility, mean reversion and theta such that the model can reproduce the initial Term Structure. I'm using this python code adapted from &...
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32 views

Relationship between risk and return for GBM and riskless bond

Suppose we have $S$, a stock following geometric Brownian motion ($dS_t = S_t (\mu dt + \sigma dZ_t)$ for $Z =$ Brownian motion) and $B$, a zero coupon bond with rate $r$, i.e. $dB_t = rB_t dt$. In ...
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1answer
54 views

using bid ask prices to imply bid ask volatilities

Let's say i have bid / ask feed of an option prices (across strikes and expiries, calls and puts), what is the accurate way of implying out vols from these bid / asks For eg; to get the bid vol, ...
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64 views

Silly question: Why don't traders look at the sqrt(Var[ABC] - Var[XYZ]) when looking at gaps?

As you know, variances are additive but volatilities are not. If that is the case and I open a long position on product ABC at an implied vol of 28% and a short position on product XYZ at an implied ...
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26 views

Applying GARCH to Panel Data

I have a panel consisting of some quantity - say earnings/cash flows/or something similar. I am interested in forecasting the volatility that is inherent to that respective measure. In a single time ...
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69 views

Fast Monte Carlo of Local Volatility Model

I want to compute option prices via a Monte Carlo simulation. The model implemented is a Markov process, following the SDE : d X_t = alpha * dt + beta^(1/2) * d W_t ...
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48 views

garch(1,1) Annualised Volitility with python

I am trying to calculate the annualized Volatility of given returns for a stock with Garch(1,1) on python using a code I found online. The value I should be getting is around 27, but the value I am ...
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29 views

Volatility forecast on SPX option expiration day

I am looking for methods and papers on forecasting SPX option at-the-money implied volatility or realized volatility within its expiration day. What are some stylized facts and forecasting methods?
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62 views

Interpretation of Volatility of Volatility (VVIX)

Recently I came across the VVIX index (also known as VIX of VIX), which represents the 30 day implied (expected) Volatility of the VIX Index. I studied CBOE's Whitepaper for the VIX, which explains ...
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53 views

Modelling volatility for higher frequency data

I'm doing some academic work on volatility forecasting. I've got 1-minute bar data. It is not clear to me what model is best suited for forecasting volatility when higher frequency data is available. ...
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61 views

How do we compute FX volatility for any given FX strike and time to maturity?

I want to implement a function which is passed two inputs: a strike and a time to maturity (which can be arbitrary within a specified range) and returns an FX volatility for this strike and maturity ...