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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How is a LIBOR Market Model volatility skew determined?
LIBOR based interest rates are derived from the prices (supply / demand) of swaptions, caps and floors.
These prices are generally quoted in yield vols. Their prices are given by the Black formula.
...
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32 views
Temporal aggregation of daily implied volatilities
Suppose I have a time series of daily implied volatility values for a given month and I am interested in calculating the monthly implied volatility for that month. What would be the most theoretically-...
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1 day VaR vs 10 day VaR
Even while using historical simulation VaR, 1 day VaR is converted into 10 day VaR by multiplying 1 day VaR by Sqrt(10) for regulatory reporting purposes.
What are the underlying assumptions for ...
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Proof of no arb condition after shifting SABR’s rho
Does anyone know of any paper or research where they shift SABR’s skew and rebuild the surface?
In particular, I would like to prove theoretically whether the no arbitrage condition hold for the ...
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1answer
75 views
VaR equivalent volatility meaning
I have a hard time with interpreting VeV. I mean - I see its just standard deviation derived from Cornish-Fischer VaR, but I don't really know how to interpret it. The formula for VeV is:
...
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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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37 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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1answer
64 views
Volatility surface for Swaptions
I understand the volatility surface for swaption is built using implied vols of ATM swaptions. I had a question on the instruments that are used.
Should the instruments used change depending on the ...
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76 views
Why historical volatility is calculated as N-days annualized?
Annualized historical volatility is always calculate with 10-, 20- days time window. I don't quite understand.
Compare with annualized historical return, annualized historical return is never ...
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1answer
78 views
Inherent volatility of selling longterm options and buying short term options
A two-month option has an implied vol of 60%, the corresponding 2-year option has an implied vol of 34%. You buy the short terms and sell the long terms. What is the inherent volatility of the total ...
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3answers
156 views
What does Volatility Smile tell? [closed]
Could you please share your opinions about Volatility Smile? What does it tell us when it gets more convex or when its level changes over time or any other change on it. Any paper/work/blog ...
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Break-even volatility for delta hedge portfolio
After simulating practical and theoretical PnL of a delta hedged portfolio on some data from the SPX500 under 0.15 management Vol I want to find the Vol which gives me an accumulated PnL of 0.
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54 views
Multivariate Markov Regime switching GARCH
I have a regression with 4 independent variables and a dependent variable. I want to implement a Regime switching GARCH model but have been unable to find a package in R,Python or Matlab.
MSGARCH ...
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68 views
What is 'conditional variance' in a GARCH model?
How can a single observation possess variance (by definition it is 0)? For example, we read notation such as sigma(t) as the conditional variance at time t? Yet GARCH's generate conditional variances ...
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31 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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1answer
63 views
Are extended SABR models useful for options with non-negative underlying
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2731359
http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf
In the two articles listed above we see several ways to extend the original ...
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1answer
150 views
Derivation of VIX Formula
I've read a lot of derivations about VIX formula. I can say it is -adjusted- fair strike of variance swap. But I can't see how it goes from variance swap rate to VIX formula. In particular I can't see ...
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2answers
75 views
Option value with different spot prices [closed]
I found this post online which is plotting different results for option value and greeks depending on spot price.
Why would someone want to do calculate the value of the option with different spot ...
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Mixed local-stochastic volatility model in Quantlib
At a conference the speaker mentioned that it is a standard approach today to use a mix of local and stochastic volatility model in equity, FX and interest rates.
Can you please suggest the most ...
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2answers
74 views
Finding Lead-Lag Relationship [duplicate]
Given two series of data, volatility and returns, is there a way (Excel) of finding which one is the leading factor and lagging factor?
Thank you for your help.
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2answers
40 views
Threshold to consider the daily change of a bond price unusual?
In the context of compliance and market abuse monitoring, what relative change threshold would you choose to decide if transactions should be looked into?
For example, if a bond price had a relative ...
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1answer
379 views
Variance swap volatility - ATMF vol, Skew and Curvature
In a pure diffusion setting, it is a well known result that the volatility $\sigma_T$ of a fresh-start variance swap of maturity $T$ as seen of $t=0$ verifies
\begin{align}
\sigma_T^2 &= \Bbb{E}_0^...
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What are the different indicators to measure historical volatility for stocks on individual basis?
Google search shows there are three indicators to measure volatility: 1. Average True Range 2. Standard Deviation / Variance 3. Bollinger Bands.
What are the indicator(s) that you use to identify ...
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Whats the big deal between volatility and the risk free rate?
I am trying to understand asset price volatility.
Many of the news articles I read link how stock market volatility is linked to asset price volatility?
To give an example, in Mike Mackenzie's (...
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1answer
99 views
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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32 views
Volatiliy in a at-the-time call option [duplicate]
I understand that the vega of the Black-Scholes equation is a positive function, which means the value of the option is an INCREASING function of the volatility, since vega is the derivative of the ...
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Does your Parkinson volatility ratio work as Taleb explained?
According to Dynamic Hedging: Managing Vanilla and Exotic Options (Taleb, 1997), the Parkison volatility estimator has several meaningful properties. It is defined
$$P=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\...
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1answer
201 views
Vanilla Option Prices from Local Vol Surface (using neither MC nor PDE)
There are numerous papers that describe the derivation of the Local-Vol equation using available market prices of options. For example:
Dupire's formula (see e.g. OpenGamma (2013)) gives us LV in ...
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69 views
Rolling forecast using GARCH model
EDIT
This is not a duplicate of my original question linked, since I have since overcome that problem and have posted an answer. Since solving the previous problem, I have run into the problem ...
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50 views
Intuitive description of the Spillover Index by Diebold and Yilmaz
I am struggling to grasp the steps outlined in the 2009 paper by Diebold & Yilmaz, which introduces the framework for a spillover index.
The final expression for a spillover index for a two ...
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0answers
47 views
Estimating an GARCH(1,1) model? Long hand method
I am really trying to invest some time to estimate a GARCH(1,1) method, I know there is many statistical packages that will do this for me (Eviews, MATLAB, R), but I am trying to do this by hand, so ...
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1answer
110 views
Is this the correct way to forecast stock price volatility using GARCH
I am attempting to make a forecast of a stock's volatility some time into the future (say 90 days). It seems that GARCH is a traditionally used model for this.
I have implemented this below using ...
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2answers
63 views
Difference between volatility measures of a basket of assets
I am trying to understand intuitively the difference between two different measures of realized variance of a basket of assets.
The first measure I am aware of is when you take the realized variance ...
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1answer
59 views
In search of nice (approx) function forms of the volatility of cumulative simple returns
Let's consider a period $t\in[0,T]$, and let the simple return over year $t$ ($1\le t\le T$) be $r_t$. Assume $r_t$ are iid normal. The cumualative simple return over the whole period $[0,T]$ is
$$R_T=...
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2answers
185 views
How is volatility different from variance?
I always thought volatility was just variance ^ (1/2). Now I'm reading this book and it's saying that the two are different concepts. Excerpts include:
Partly due to its use in Black-Scholes, ...
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1answer
98 views
Good references on Heston Model?
I am looking for good bibliographic references on Heston Model and Stochastic volatility models in general.
Does anyone know any good introductory/intermediate references on this topic?
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How rapidly should estimated volatility and volume change for estimating market impact in small markets?
The cost of market impact is usually modeled as:
$$
\Delta{P} = \delta \sigma (\frac{Q}{V})^{1/2}
$$
Where:
$ \Delta{P} $ is the change in price of the asset caused by the transaction size $Q$
$\...
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101 views
Poor results forecasting stock price volatility using Python's GARCH model
As far as I understand, forecasting stock price volatility should be more achievable than forecasting absolute prices or returns. It seems as though GARCH models are the traditional and most widely ...
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How to reasonably aggregate returns across both different assets and different time-horizons?
This might be a somewhat open question, so any suggestion of improvement is welcome.
Suppose at time $t=0$, we have $N$ different assets whose weights are $w_1,\cdots,w_n$ ($\sum w_i = 1$), and they ...
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1answer
135 views
Splitting theta from vol carry
What is the best way to splitting theta and vol carry on say a long calendar trade?
Basically trying to split the "good" carry component of a trade from the "bad" carry (theta) which could be earned ...
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1answer
73 views
How to calculate number of round trips given volatility?
Suppose we know stock price volatility is normally distributed with mean = 0 and annual volatility say 20%. Let's assume markets never close and we can trade at 1 second intervals. Let's assume stock ...
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1answer
77 views
VXX Put pricing
Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
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41 views
What is the use of undiscounted Futures/Option Prices
Reading the great book of Gatheral on Vol Surfaces (link) I can't help but notice that throughout he uses undiscounted option prices (though he obviously never assumed rates to be zero).
See e.g. ...
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3answers
306 views
arbitrage free volatility surface
Why is calendar spread arbitrage equivalent to $\partial_t \omega(k,t) \geq 0, \forall k \in \Bbb{R}$ where $\omega(k,t) = \sigma^2(k,t) t$ and $\sigma(k,t)$ represents the Black-Scholes implied ...
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1answer
105 views
implementing Volatility Managed Portfolios
How to I calculate the value of c in the vol-managed equation specified by Moreira & Muir Volatilty Managed Portfolios (2016) Equation 1?
Portfolio return in month t+1 =$$\frac{c}{RV_t^2}f_{t+1}$$...
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63 views
What is, here, the relationship between “compound” and “arithmetic return” and “volatility”?
I'm trying to find the exact (ie, not an approximate) relation between the "Compound Return", "Arithmetic Return", and the "Annualised Volatility" as given the assumptions below, and from there the ...
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1answer
50 views
Variance Swap : dividends and rates
In a simplified world you can assume that the var swap is replicated by a continuous set of calls and puts and interest rates are equal to zero. So your PNL is only sensitive to the volatility.
But in ...
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1answer
221 views
Fractionally Integrated GARCH
I am currently working on a project to compare different GARCH(1,1) models on a financial data set. I use the rugarch package in R, and everthing seemed fine at first. However, now that I have started ...
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1answer
81 views
Relationship between asset volatility and debt and equity value
So how I understand it, higher asset volatility implies a higher call option price. The Merton Model holds that the value of equity is a call option. This therefore implies that the equity value must ...
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1answer
124 views
Options on realized volatility / variance
If I'd like to price options on variance/volatility in the Heston model. Is MC simulation and/or finite difference the only way to do it? Or is there an analytical expression for the probability ...
