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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Dispersion Trading with a 2 component index

I have a dispersion question I need help with...An index SPY has only 2 components - AAPL and AMZN. We are given the implied volatility of SPY and AAPL as well as the correlation between the 2 assets. ...
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Historical volatility - Black Scholes

How do you best incorporate the weekends in the calculation of the Black Scholes historical volatility? (Of course historical volatility serves as approximation, if the market price of the options is ...
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Why my delta position is increasing with increase in spot?

I am trying to take position in future as per the delta position of short put. My strike is 13794 for short put option, spot 10305.3 and volatility is 20.153 then I am getting 5890 position to buy and ...
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Implied volatility of hypothetical options market

I am attempting to create a volatility surface for a US electricity market that has a liquid futures market but nearly non-existent options market (<5 trades per month across all strikes and ...
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Value Option with Forward Volatilities

That is probably a rather simple question but I got confused and would be very thankful for help. Imagine we are in 2015 and have an option that expires in either 2016, 2017, 2018, 2019, 2020 or 2021. ...
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Historical VIX term structure data

I see that there is a CBOE page for collecting individual moments of term structure data, however, I'm wondering if anyone knows how to access historical data in bulk. Here's the CBOE page: http://...
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annualised returns and volatility for 3 month data

I have a portofolio with 30 indexes and I want to calculate the annulised returns and volatility because I want to compare it with another portofolio with different number of indexes (but same time ...
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Ratios or combinations of risk measures

In finance, alternative risk measures such as value-at-risk (VaR) and GARCH are introduced as replacements to standard deviation volatility. Is there any application or value where several risk ...
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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 ...
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Implied Volatility, annualized quantity ? And Total Implied volatility

so Implied Volatility is computed by equalizing the value of the call option given by the black and scholes model with the one observed. Then, by inversing $C_{BS}$, one gets "$\sigma_{IMP}$"...
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Implication of forward-rate dynamics when the short-rate follows a normal process

In the section 3.2.3 of the second edition of "Interest Rate Models - Theory and Practice" by Brigo and Mercurio, the forward-rate dynamics implied by the CIR model is derived as follow: The ...
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Annualized Volatility with simple returns

I am aware of the way to annualize a volatility using log returns (stdev(daily log returns) * sqrt(252)). But how can I do the same if I have a time series of simple returns (price_t - price _t-1) / ...
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How to obtain one-step ahead forecast in Python based on GARCH?

I am trying to produce one-step ahead forecast using GARCH in Python using a fixed windows method. I ultimately want to put the code below in a for loop, but this code snippet does not perform as I ...
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What is the difference between parametric and non-parametric models?

I'm reading about volatility modelling and I came across the concept of parametric and non-parametric models. For example, GARCH is a parametric model and Realized Volatility is a non-parametric model....
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Literature on realized volatility and sampling frequency?

I was looking for some papers that explicitly show how realized volatility changes as we change the sampling frequency. For example, comparing the annualized volatility estimated from daily data is ...
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GARCH(1,1) forecast plot in R with training data

I've fit a GARCH(1,1) model in R and would like to create a plot similar to the one in this question: Is this the correct way to forecast stock price volatility using GARCH Could someone direct me to ...
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Where can I find a Python module for Stock volatility estimators using Yang Zhang method?

Does anyone know of a Python library that includes the calculation of historical stock volatility using the Yang Zhang estimator? I have tried and failed to find one but would expect this to have been ...
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Stochastic Volatility Models - are they complete markets?

I'm reading about stochastic volatility models - the ones which resulted after Wiggins proposed in 1986/7 that $\sigma$ in Black-Scholes should be a stochastic process rather than a constant. In ...
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Do I have to annualize daily volatility? [closed]

I computed daily returns via $\ln(P_t)-\ln(P_{t-1})$ in order to get the volatility. But I do not want to present my results over a certain period of time (whether it's a week, a month or a year). I ...
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How to evaluate embedded floor option in inflation linked bonds if interbank inflation floor instruments cannot be used or do not exist

Suppose we consider simple case that only par is protected against base price index, so it is with zero coupon floor feature. How do we value this option given that there is no inflation floor ...
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Can simple risk management outperform portfolio optimization like this, or is there most likely an error?

I am using a simulation approach to compare the performances achievable by simple risk management and portfolio optimization for portfolio selection. My problem is that my results indicate that simple ...
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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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How to predict realised variance?

I am trying to predict the realised daily close to close variance of an equity index. I checked the literature on volatility forecasting and tried a bunch of things on a dataset for the S&P 500....
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Call/Put Open interest difference on similar underlying

High open interest for a given option contract is an indicator for interest in that option. For that reason I wanted to take a look at how the open interest of options on volatility have evolved in ...
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realized correlation estimation

I'm trying to implement the Hayashi - Yoshida estimator for correlation (T. Hayashi, N. Yoshida: On covariance estimation of non-synchronously observed diffusion processes, 2005) and there's something ...
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Is Hodges-Tompkins adjustment applicable for all volatility estimators?

Can the Hodges-Tompkins adjustment (S. Hodges, R. Tompkins, The Sampling Properties of Volatility Cones 2000,2002 JoD) be used to de-bias any estimator computed from overlapping observations? It ...
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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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vol swap and vol of vol

why people say vol swap is short vol of vol? Say we consider a simple vol swap with 3% strike with two days maturity here: scenario1: realized vol is 2% on day1 and 4% on day2 scenario2: realized vol ...
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Realized Volatility of Volatility versus VVIX Index

Hello people of the internet I am doing a little experiment where I want to examine how well the VIX predicts the realized volatility, and how well the VVIX (Volatility of VIX Index) predicts the ...
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Variance risk premium: When is realized vol higher than implied vol in practice?

I’m doing some work around the variance risk premium currently, and I’m interested in understanding the situations when realized volatility is > implied volatility in practice. I know in generally ...
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What does it mean for something to become more gaussian?

I was reading something in which the author said: "the longer the maturity, the more and more gaussian the gamma of your option is". What exactly is the author trying to say in non-math terms and what ...
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Investment & Trading — Tracking Error

I think i am having a problem annualising my tracking error because im getting an oddly big number especially its bps. So my values are taken from Market-class where we get our returns yearly, which ...
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Vega of binary option

I'm calculating the greeks for a hypothetical binary option, and I'm getting a symmetrical parabola for the vega's of both put and call options that are OTM, ATM, and ITM. Both of them dip into ...
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Intraday volatility measures in comparison to end of day measurement

I'm experimenting with Parkinson's Number and the Garman-Klass estimator I'm wondering what the appropriate number of days to sample over, is the number over 1-day useful at all, or should one take it ...
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Why do surprises in macroeconomic variables average out to zero?

In the book Investments (Bodie, Kane, Marcus), in chapter 8, the authors discuss index models (page 247) and, in its context, systematic risk. The authors state, without explanation, that the market ...
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difficulty pricing options using stochastic volatility

can someone kindly explain why it was difficult to obtain an explicit formula for pricing options under stochastic volatility. Thanks alot.
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How accurate is the square root of time rule for VaR for a portfolio containing several different types of instruments

Assuming that your value at risk model is based on normality assumptions, e.g. using a Delta-Gamma normal model does the approximation hold perfectly for a portfolio of stocks and options? What about ...
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Expected Delta hedging frequency as function of implied (and realized) volatility

I'm looking for a proxy (or some rule of thumb) that can create a link between the implied volatility, the realized volatility and the frequency of Delta hedging required to keep the Delta as close as ...
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Looking for a math description of upside/downside implied vols - does Dupire help?

This is in continuation of this post which explained the meaning of the vols in the vol smile as follows: Suppose you have a downsloping vol smile. Then, the fact that the vol is higher on the ...
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Are statistical arb and relative value arb strategies implicitly short volatility?

I obviously don't want to generalise here, but my initial impression of stat arb and relative value arb is that these strategies earn stable pennies during bull markets when volatility is depressed ...
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Hedging vega risk with varswaps

I have encountered a statement that in summary reads like this: Varswaps became popular after the LTCM meltdown due to high levels of implied volatility the market was seeing at the time. Hedge funds ...
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Is there anywhere I can read the paper, “The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves”

Hello there was a paper published by: M. Arslan, G. Eid, J. El Khoury and J. Roth titled "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves" (2009). I believe they ...
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calculating sharpe-ratio and annualized returns

Im trying to get the sharpe ratio to be calculated daily but I can only calculate it annually, this is also happening for my annualized returns, can somebody help me please? ...
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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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118 views

Forecasting volatility with machine learning: Performance comparison

ARIMA and GARCH are old news for predicting volatility time series of asset returns. How does the performances of machine learning algorithms compare (such as random forest, support vector ...
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Most profitable PUT strike price in these times of high volatility?

At close 3/13/20 SPY was at 270.2, by close 3/16 it dropped to 239.41 ~ 8.8% drop... I'm looking at how to capitalize on these big swings with options. I'm backtesting option strategies and plotted ...
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What are some heurestics you could use to judge if skew is cheap or expensive? If any?

Are there rules of thumbs/models that you could use to develop intuition for when skew is cheap or expensive? From what I gather, volatility is a number that is backed out of price in a sense, "the ...
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VIX and Realised Volatility Scaling

I have calculated the VIX implied volatility according to the CBOE Whitepaper: \begin{equation*} \sigma^2 = \frac{2}{T} \left(\sum_i \frac{\Delta K_i}{K_i^2} Q(K_i) e^{rT} \right) - \frac{1}{T} \...
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I would like to fit a CARR model using the 'rugarch' package in R - what should I include in the specification?

I know I have to specify a GARCH model for the square root of range without a constant term in the mean equation - just unsure how to apply this in the rugarch function.
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Hedge performance in times of volatility: Beta changes impacting PnL during market rebound

I hedge a portfolio of Global Equities (200 stocks within MSCI World universe) by shorting futures on MSCI World Net Total Return. The hedge is calculated using Beta. Beta is calculated using a risk ...

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