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

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9 views

Interpreting and scaling of Realized Variance with sample data

I have some question about realized variance(RV) and I have some sample prices below to work with. You can run the R code below to build a vector of log returns. Three are 78 5-minute buckets in a ...
3
votes
1answer
111 views

How to get around flat likelihood function when calibrating GBM parameters

(Hope this is the correct place for this question - I posted it first on stackoverflow:) I want to calibrate jointly the drift mu and volatility sigma of a geometric brownian motion, ...
3
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1answer
216 views

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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0answers
39 views

Estimate volatility in forecast

I have a model with a rolling forecast. In each time step $t$, I predict the price for the next periods, e.g. $\hat{p}(t, t+1)$ and $\hat{p}(t, t+2)$. If I start in $t=0$ and arrive at $t=2$, I ...
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1answer
53 views

Garch models and assumption of stationarity ?

I found big inconsistency in the GARCH models and their underlying assumption of stationarity. GARCH models require that data must be stationary, where stationary means both mean and variance are ...
8
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2answers
310 views

GARCH model, expectation of volatility?

Consider a time series $\{r_t\}$ following a standard GARCH(1,1) model, i.e., $$ r_t = \sigma_t \epsilon_t,$$ where $\epsilon_t \sim N(0,1)$ and are i.i.d, and $$\sigma_t^2 = \omega + \alpha_1 ...
4
votes
3answers
204 views

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 ...
2
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2answers
102 views

How to interpret Realized Volatility and TSRV using R

I am looking at some high frequency data and I would like to know how to interpret and compare Realized volatility (RV) and Two Scale Realized Volatility (TSRV). References below. Given X is the log ...
2
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3answers
125 views

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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2answers
38 views

Approximating the IV of an underlying from Individual Options IV

Is it possible to get a calculation of IV from the volatility on components of the options chain? EG I have this data: ...
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0answers
61 views

Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
1
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1answer
117 views

How to adapt a Moving Average period to market conditions?

I would like to know if there is some way to adapt the period of a moving average to market conditions like for instance the stop loss can be adapted to market conditions using the average true range. ...
4
votes
1answer
271 views

Moving window forecasting in Python

I am looking to create some code that will out-of-sample forecast the HAR-RV model. The model itself is formulated as the following, and the betas are estimated through HAC-OLS or Newey-West. ...
0
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1answer
86 views

Calculate the realised volatility from a time series

Does anybody know how to calculate the realised volatility from a series for a certain time frame? For example, I am looking at 5 days, 21 days, 63 days, 126 days and 253 days. thanks
4
votes
1answer
1k views

Historical volatility from close prices (Haug pg 166)

I have implemented a function for calculating historical volatility using close the close method as described by Haug on page 166. When I implemented the formula given by Haug, it resulted in some ...
3
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2answers
47 views

Implied volatility and nonconstant volatility

John Hull states in his text that "AS the maturity of the option is increases the percentage impact of nonconstant volatility on (option) prices becomes more pronounced, but its percentage impact on ...
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votes
1answer
62 views

Constant decreasing volatility, GARCH forecasting

I am trying to forecast the volatility using GARCH modelling in R. I fit an ARMA(1,1)-GARCH(1,1) model, but my sigma predictions are constantly decreasing. Anybody know why? ...
4
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1answer
66 views

volatility factor

I am trying to add a volatility factor to Fama-French factor model. Does anybody know of a source where I can get data for "volatility mimicking factor" or suggest a simple methodology for ...
12
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5answers
3k views

Why is the VIX futures market usually in a state of contango?

I'm a VIX newbie and I'm trying to understand why the VIX futures market is usually in a state of contango. All I can figure is that the sellers of VIX futures contracts demand high "prices" (because ...
2
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1answer
69 views

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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0answers
133 views

Reference request about stochastic volatility model

I'm fiddling with estimation of stochastic volatility models and have build up a somewhat flexible framework using indirect inference. I would like to try and throw a lot of different continuous ...
19
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2answers
1k views

Have Goldman Sachs Quantitative Strategies Research Notes been published as a book or a comprehensive collection?

Back in the 90's, Goldman Sachs (publicly?) released a series called "Quantitative Strategies Research Notes" — mostly technical papers on topic. Emanuel Derman co-authored almost all of them. Some ...
2
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1answer
106 views

How to use calibrated Standard Stochastic Volatility?

I'm considering the standard stochastic volatility model: $$x_t = \rho x_{t-1} + \sigma \epsilon_x$$ $$y_t = \beta \exp\left[ \frac{x_t}{2} \right] \epsilon_y$$ where $y_t$ is the log-returns and ...
2
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2answers
63 views

Measuring Volatility from Execution Prices

I was told of a way of measuring the volatility of a stock by looking at the reported execution prices (from Level III or Level II data.) I'm well aware of how to measure volatility by looking at the ...
6
votes
3answers
230 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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2answers
83 views

Uses of Volatility models

I'm reading about volatility analysis here http://vlab.stern.nyu.edu/doc?topic=mdls. There are many variations of GARCH. My question is: rather than trial-and-error approach, is there any systematic ...
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1answer
56 views

FX Portfolio Volatility Targeting

If I have 3 different currency trades (ex short EURSEK, short NZDUSD, long USDJPY), how do I size each trade if I wish to allocate risk equally in order to target a 12% portfolio volatility (allowing ...
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1answer
70 views

Looking for a definition of financial entropy

In Science, Entropy is generally considered to be the irreversibility of stuff. Google defines entropy as: lack of order or predictability; gradual decline into disorder The 'gradual decline in ...
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0answers
26 views

Return volatility or Price Volatility [duplicate]

Which is a better method to calculate volatility - Price variance or return variace or is it subjective to the use of volatility figure?
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0answers
39 views

Realized Volatility: errors correlation

When using Realized Volatility (sum of squared intraday returns) to estimate volatility, following the model: $$r_t = \sigma_t \epsilon_t $$ where $\sigma^2_t$ is the volatility at time $t$ and ...
2
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0answers
49 views

How to compute/find the volatility of an index like the S&P 500 to be used to control risk exposure? [closed]

I've asked two related questions. First this one on the money stack exchange and this one on the math stack exchange. But have not yet found a complete answer. Given an index such as the S&P ...
2
votes
1answer
66 views
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0answers
29 views

Relation between Parkinson number and historical volatility

In his book 'Dynamic Hedging', Nassim Taleb gives the relation: P = 1.67*historical volatility, where P is the Parkinson number. What is the basis of this relationship. Does this hold under special ...
3
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0answers
83 views

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 ...
5
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1answer
146 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 ...
1
vote
1answer
118 views

Mean reversion time estimation

I am new to mean reversion trading, and I would like to get some good references about how to estimate the time it takes to a mean reverting process to cross its long term mean.
0
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1answer
52 views

Portfolio volatility

Problem True or fale? The stock of a firm has an expected return of 10%, and a volatility of 10%. The weight of the stock in a portfolio is 5%, and the correlation of the stock’s return with the ...
5
votes
5answers
519 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.
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6answers
12k 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 ...
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0answers
72 views

High frequency price forecast model ARMA GARCH or another?

Can you reccomend model for high frequency data (1 second and less) (returns and volatility forecasting)? Most papers use ARMA, GARCH etc in 1 minute and lower time frame. PROBLEM ARMA does not know ...
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2answers
104 views

A good way to calculate the realised daily volatility

Currently, I am confused about the calculation of realised daily volatility. Assume I have daily returns, for example, FTSE, then I need to estimate the daily realised volatility. I read some ...
0
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1answer
67 views

Volume or Volatility?

I've recently been given a project which came with some documentation. In this documentation is a bullet point that reads: Liquidity Risk in Equity, Credit and Vol I'm unsure as to whether vol is ...
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0answers
61 views

Cointegration and variance of time series

Given that $X_t , Y_t$ are two cointegrated random processes, what can we say about the relationship between variance of the two increments $var(X_{t+h}-X_t)$ , $var(Y_{t+h}-Y_t)$ for a given ...
0
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2answers
64 views

Short Volatility [closed]

Being net short options is an obvious case of being short volatility. But what other investments are "functionally" short volatility? Is long equities long or short volatility? Is short Apple long or ...
1
vote
3answers
125 views

Direct use of implied volatility

I am not sure to understand exactly the direct use of implied volatility. Let's take an example: if an instrument has a daily volatility of $\sigma$, there is a 68% probability that its value will be ...
7
votes
1answer
930 views

Correctly applying GARCH in Python

Problem: Correct usage of GARCH(1,1) Aim of research: Forecasting volatility/variance. Tools used: Python Instrument: SPX (specifically adjusted close prices) Reference material: On Estimation of ...
2
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1answer
56 views

Solving a Non-Linear PDE using a Finite Difference Scheme

I have the following non-linear PDE and I have no idea how to go about solving it using a finite difference scheme in Python. Can someone get me started and/or point me to an algorithm for doing this? ...
0
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0answers
57 views

variance ratio for pair-trading

I am using the variance ratio test to check whether my sequence is mean reverting in that test there is a parameter n, How in general I choose this n? or what is the meaning of this parameter? ...
4
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2answers
666 views

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, ...
7
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1answer
455 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 ...