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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Binomial Options u, volatility, and Taylor Series Expansion [closed]
Within binomial option price modelling, I am trying to derive the result that
$u=e^{\sigma \sqrt {Δ t}}$
from
$e^{r \Delta t}(u+d)-ud-e^{2r \Delta t}= \sigma^2 \Delta t$
there are a few similar ...
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Are there consistent trading ranges and how does that affect volatility? [closed]
The Euro/Dollar often have a varying daily trading range within same week just like almost every other currency. It could be 84 pips on Monday, on Tuesday 52 pips, Wednesday 112 pips, Thursday 95 pips ...
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Simple Black-Scholes alternatives
I work at an accountancy firm and we use Black-Scholes to value equity in private companies that has option like features. The equity we typically value is akin to deeply out of the money European ...
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Student-t measure of return volatility and time scaling
I have a series of price returns of an asset (4 days worth of data). They are relatively high-frequency.
My ultimate goal is to calculate realized volatility, but using a student's t-distribution.
I ...
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How does autocorrelation bias annualizing variance?
I read somewhere that autocorrelation prevents someone from annualizing variance. But how does it bias it? Let's say you have daily returns. If autocorrelation is high, should that overstate or ...
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Volatility Modelling negative GJR-GARCH-X coefficient
I have estimated GARCH and GJR-GARCH with several exogenous variables. Some of the exogenous variables have negative coefficients that are statistically significant. For instance, I can write my GJR-...
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How do I estimate volatility for MPR historical data
How can I estimate volatility with historical data for Monetary Policy Rate (MPR) to use in a short rate model?
I could use regular techniques like simple standard deviation or max likelihood, but the ...
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Daily vs Monthly vs. other return for volatility calculation?
I thought I read/heard somewhere that annualized volatility, using monthly returns vs daily returns is usually lower. With that said, I can't seem to find any papers on this.
Does anyone have any ...
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Different volatilities in Reiner Rubinstein barrier option model
Wanted to ask if a single or different volatilities should be used in Reiner-Rubinstein's option barrier pricing formulas given the following:
An Up-and-out call (Cuo) with strike K and barrier H is ...
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Basket variance with correlation 1
I'm reading the famous nuclear phynance primer on dispersion trading and finding difficulty in understanding the author's simplification for the variance of a basket with correlation 1. See below:
I ...
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What does it mean to "sell skew to buy vol"? [closed]
A bit confused here. Skew can mean so many different things. It can mean the different IVs along the strike axis (sometimes called vertical skew), can mean the IVs along term structure (sometimes ...
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Ito's lemma in stochastic volatility models [closed]
I couldn't help but notice that in all stochastic volatility models articles I consulted, whenever Ito lema is applied with a process of the sort
$$\frac{d S_t}{S_t} = \sigma_t d W_t $$
With $(\...
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How to forecast volatility using gamma exposure index?
Brainstorming this afternoon.
GEX is the gamma exposure index (https://squeezemetrics.com/monitor/static/guide.pdf). It's the sum of gamma exposure for call and put.
Using IV, strike and BDS you can ...
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hedging out of cross-ccy vol risk using direct ccy options [closed]
Lets suppose a G10 FX vol market-maker starts out with a flat book. During the day, the market-maker bought a EURUSD 1 week ATM straddle from one client while sold USDJPY 1 week ATM straddle from ...
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Binomial tree with time dependent volatility
In the Cox approach for binomial trees, the up move $u$ and down move $d$ are given by: $u = e^{\sigma \sqrt{dt}}$ and $d = e^{-\sigma \sqrt{dt}}$. In this approach the volatility $\sigma$ is assumed ...
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Why does a long gamma trader sit on the bid and offer?
I have read in Bennett - Trading Volatility the following quote.
As shown above, a long gamma (long volatility) position has to buy shares if they fall, and
sell them if they rise. Buying low and ...
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Contradictory arguments for ATM/ITM/OTM option demand
I am trying to understand which of the options have the most demand, and found this discussion here. The arguments presented are as follows:
ATM is more liquidly traded than ITM/OTM because they are ...
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Model based PnL explain for FX Options
In FX options the vol surface for a given maturity is usually described by three or five points, I.e. Atm, 25 delta risk reversal and butterfly and 10 delta risk reversal and butterfly. Then models ...
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Very close local volatility and implied volatility using Dupire's equation
I used Dupire's equation to calculate the local volatility as in https://www.frouah.com/finance%20notes/Dupire%20Local%20Volatility.pdf and Numerical example of how to calculate local vol surface from ...
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BLOOMBERG Strike vs Straddle Volatility
In Bloomberg's VCUB, what is the difference between the "strike" volatility and changing this option to "straddle"? It seems like the "straddle" vol should be the same as ...
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Volatility formulas in Sinclair's "Volatility Trading" book differs from TTR
In "Volatility Trading" Euan Sinclair defines Yang-Zhang volatility estimator as
$$ \sigma = \sqrt{\sigma^2_o + k\sigma^2_c + (1-k)\sigma^2_{rs}} $$
where
$$
\sigma^2_o \propto Variance\...
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Convert implied probability into real probability
In this article I have read that:
A risk-neutral world is one where all investors are indifferent to risk and don’t require any extra risk premium for the risk they bear. In this world, all assets (...
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Volatility forecast for 5-minute frequency data
I have high frequency data for financial stocks (5-minute periodicity) and I want to forecast volatility.
I'm familiarized with the usual ARCH/GARCH models and their variants for daily data but after ...
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When calculating VIX, how to deal with the problem of asymmetry of put and call data?
I'm trying to calculate the VIX index according to the methodology of CBOE. I am looking at commodity options. I found that at some time, like at this minute, there are 13 call options out of the ...
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How to calculate the local volatility from implied volatility in practice
The local volatility can be derived from the implied volatility. But in practice how we deal with the first-order and second-order derivatives?
I have seen this formula
$$
\sigma_{\mathrm{Dup}}(T, K)^{...
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Quantifying volatility: a step by step approach?
I am a former electronics engineer and I'm fairly new to financial time series analysis. I'm currently working on a thesis on copper determinants and what factors influence its price from an economic ...
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Delta hedging when volatility is stochastic
From my understanding in a BSM world you can make a bet on volatility using options and delta hedging with the underlying.
If you think realized volatility of the underlying will be higher than the ...
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What are the advantages and disadvantages of converting standard deviation of higher-frequency returns to a lower sampling frequency?
I have a minute-by-minute price series of a stock. I would like to calculate the daily volatility or standard deviation of the stock's returns.
One way to do so is to get the end-of-day prices (i.e. ...
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Best way to extrapolate on implied volatility
I am doing some standard svd calibration to mark market implied vols in difference to a previous volatility surface.
For longer term maturities where there is no market data, I am extrapolating ATM ...
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simple volatility surface interpolation
I'm trying to build an implied vol surface from some listed options. In particular I have data for calls and puts for different strikes and expiries. I'm not looking to price on the interpolated vols ...
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black Scholes model hedging without constant volatility
I have started to look deeply in the hedging and I have created some simulations to simulate delta hedging strategies. I use BS model to calculate delta. The only issue was, which Volatility should I ...
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A lower bound for variance swap strike
There is a famous formula for the variance swap strike that reads
$$
K_{var}^2 = \int_{-\infty}^\infty dz\, n(z) I^2(z)
$$
where $I(z)$ is the Black-Scholes implied volatility function,
$$
n(z) = \...
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When / how do I vol-scale portfolio weights when optimizing the portfolio?
I have a set of portfolio weights $w$. I'm using cvxpy to optimise the portfolio sharpe, subject to a set of constraints.
$$
\text{maximize} \hspace{10mm} \mu^Tw - ...
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If $\Delta \log(V_{t})$ behaves like the increments of fractional Brownian motion, why do we model the rough volatility as follows
From Gatheral's paper, Volatility is rough and empirical evidence, it is clear that $\big\{\log(V_{t+1})-\log(V_{t})\big\}_{t}$ behaves like the increments of fractional Brownian motion $B^{H}$ with ...
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Pricing FX options on pegged currencies
I'm wondering what's the standard (if any) for practitioners to trade volatility on pegged currencies. Is there any specific convention? I'm thinking situations like EURCHF before the unpeg, how were ...
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Why can't the curve find the least squares parameters when I used it in SABR model? (SABR Calibration)
Follow is the SABR function part of my code in python：
...
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Dupire's tradable realized volatility estimators
It seems to have vanished off the web but a few years back Dupire published two tradable realized volatility estimators in 2015, I even asked a question around it here. What makes a realized vol ...
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Introductory material for getting started with local and stochastic volatility modelling
Are you able to provide some suggestions for resources to get started with non-flat volatility modelling? The models I am interested in are the likes of CEV, Heston, SABR etc.
I have tried looking ...
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The use of the trading time variance/volatility curve
In trading, how is the trading time variance/volatility curve and spread curve such as depicted and parameterized on p. 277 of Jim Gatheral and Roel C.A. Oomen, Zero-intelligence realized variance ...
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Can one estimate rather than forecast volatility using the GARCH model?
Can one use the GARCH model to estimate the realized variance/volatility, such as done in this paper, rather than forecast the volatility, from (high frequency) price/tick data?
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Daily realized volatility and true daily volatility
Can someone help if I am thinking correctly?
If $R(t,i)$ is the i'th log-return for $i = 1\ldots,M$ of day $t$ for $t = 1\ldots,T$.
Can I assume that the daily realized volatility (denoted $RV(t)$) is ...
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Integrated volatility and realized volatility
Since integrated variance can be estimated via the sum of squared returns (which connects closly to the realized volatility, can I also asusme that "the integrated volatility is an estimator of ...
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Estimating Intraday Volatility with OHLC Data [duplicate]
I'm trying to estimate intraday volatility for some ETFs, but don't have the intraday data to actually calculate it. I do, however, have historical daily OHLC data for the ETFs. I thought I saw ...
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Fitting model between security price and intraday volatility
I'm trying to construct a model which shows how much the closing price of a security ($P_t$) differs from the VWAP of that security on that day ($VWAP_t$). I'm calling this measure the "VWAP ...
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mean return and volatility with transaction cost
What means that 5 bps per half-turn for transaction cost?
How can I implement mean return and volatility with this transaction cost in formula or python code?
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Annualized rolling volatility? [closed]
I have 600 days of closing prices of a stock. I want to calculate the annualized volatility for 6 day window. How do i do that?
If I calculate the std dev of the first 6 days, i get, say 1%. This is ...
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What is the consensus interpretation of index future dealer gamma?
I'm trying to confirm that I'm understanding this concept correctly: dealer gamma exposure. I can make sense of dealers / gamma in isolation:
Dealers: make markets for certain securities, notching ...
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Estimating historical volatility from inconsistent time intervals
Given historical asset prices at consistent time intervals, one can estimate annual volatility as:
SampleStDev(log(Si/Si-1)) / sqrt(interval)
What's the correct way to do this when the time intervals ...
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How to optimize two highly correlated risky assets?
Suppose you have two highly correlated risky assets.
Correlation coefficient: 0.9
Volatility:
Asset 1 price varies 2.5% /day
Asset 2 price varies 5% / day
What can be done to do reduce the risk and ...
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Which is more valuable: a basket of optimal stopping problems or an optimal stopping problem on a basket?
Fidelity now offers direct indexing for individuals for 40 bps per year, as well as zero-fee total market index funds. Which one should I dollar cost average (I.e., invest $x every n-th month) in? ...
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