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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32 views

How to deal with blank entries in computing log growth

I am conducting a study to discover which variables best explain stock volatility during COVID. I am currently completing linear regressions before implementing GARCH, however I have come across a ...
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82 views

What is the difference between log volatility and simple volatility in a GBM? [closed]

What difference do they make? Why do many people seem to find more accurate simulations with log volatility? standard volatility in GBM is defined as $\sigma = \frac{1}{N}\sum_{i=1}^N(x_i-\mu)$ where $...
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First Principal Component Large Volatility

I am conducting PCA on several return series of funds and am finding that when I look at the first principal component the values are huge and this the volatility is also enormous relative to the ...
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111 views

How much does a rise in volatility in a short-term option affect a longer-term option

How would a rise in implied volatility on a short-term option affect the implied volatility of another short-term option with the same strike, but with slightly-longer expiry? Assuming that the short-...
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Comparison of results given by volatility estimators: Garman-Klass Vs Garch(1,1)

I am pretty new with volatility estimators and I am trying to see if Garman-Klass estimator and Garch(1,1)estimator are closed. So I implemented a python code for the two estimators (an also for the ...
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71 views

Implied volatility model-free

I know that $\operatorname{IV-model \space free}=2 \int_{0}^{+\infty}\frac{c_0(T,Ke^{r(T-t)})-c_0(t,Ke^{r(T-t)})}{K^2}\operatorname{d}K$ is calculated using an iterative procedure, i.e. setting a ...
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PRIIP Stressed Volca Calculation

Hello dear Finance mates, i have a question regarding the calculation of the stressed volatility for the stress scenario. I hope I actually typed the right formula for calculating the scenarios for ...
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40 views

Constructing Idiosyncratic Risk Factor

I am studying idiosyncratic volatility. After applying the Fama Frech 3 Factor model with its Marktet, SMB and HML factors I want to build a factor based on idiosyncratic volatility. Can I just build ...
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81 views

What is the market standard for measuring historical volatility?

Hope to get some help with the following questions: Can someone explain what is the industry standard to calculate stock options historical volatility? I am using this estimator https://portfolioslab....
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Relationship between time decay and gamma

In a paper titled Investing in Volatility published in 1998 by Emanuel Derman, Michael Kamal, Iraj Kani, John McClure, Cyrus Pirasteh, and Joseph Z. Zou, I found the following assertion (on page 9) ...
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50 views

Calculating Daily Realized Variance with Non-Constant Sampling

I was able to obtain some tick data on a particular asset and I wanted to calculate the daily realized variance of the asset. After browsing through a few threads here, it seems the formula to ...
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Do you need multi-period ahead covariance forecast, in order to construct portfolios with weekly/monthly rebalancing?

Suppose I want to rebalance my portfolio each week. Do I then need weekly covariance forecasts, from some multivariate volatility model to do this? Ie. Insert the weekly covariance forecast $\Sigma_{t+...
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Implied Gamma VS Implied Volatility

Reading this paper, I'm struggling to understand what the author is saying with paragraphs below (see pages 39-42): We define Implied Gamma ($\Gamma_{\operatorname{implied}}$) as the value of the ...
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10-day VaR for a portfolio

So, Bank ANZ owns a portfolio of options on the USD/GBP exchange rate. The delta equivalent position of the portfolio is GBP 56.00. The current exchange rate is 1.5, with a daily volatility of 0.7 ...
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62 views

Looking for a good introduction to modelling ARCH-type models

I am starting to think about my dissertation topic for my undergraduate degree. I am interested in comparing volatility of stock indices during COVID-19 to the years leading up to the pandemic. I have ...
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Squared Residuals equal Variance of Dependent Variable (ARMA-GARCH)

My understanding of ARMA-GARCH models for a variable $X$ is as follows: I estimate a conditional mean of a variable $X$ by use of the ARMA part of the model. I estimate the conditional variance of ...
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GARCH model with exogenous events

GARCH models capture positive serial correlation in volatility. Sometimes events occur "out of the blue", causing volatility that a GARCH model cannot be expected to predict. One example is ...
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EGARCH and GARCH effects with White Noise squared residuals

I'm asked to model a series which it's returns are white noise and after adjusting a regression like $r_t=c$ and looking it's squared residuals (white noise too) I'm asked to adjust a GARCH and EGARCH ...
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49 views

Volatility of a function of an asset

Suppose that $ G $ is a function of the underlying asset $ S $, which follows a geometric Brownian motion. Suppose that $ \sigma_{S} $ and $ \sigma_{G} $ are the volatilities of $ S $ and $ G $, ...
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Performance metric that integrates market volatility?

Is there a performance metric like Sharpe that takes into account the volatility of the current market instead of only the volatility of the fund? I believe investors may have different degrees of ...
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63 views

European call option on constant volatility or drawn from a volatility distribution

Which is more expensive: A European call option on constant volatility of 30% or or drawn from a random distribution of mean 30%? The answer in A Practical Guide To Quantitative Finance Interviews, ...
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57 views

The shape of the volatility smile for bimodal outcome

Let's say that we have a biotech company that awaits FDA approval. In the case of approval the company gets a cash injection and in the case of denial it is pretty much bankrupt. Clearly, this is a ...
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149 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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Is there a Dupire's Formula for put options?

Generally, Dupire's formula is taking derivatives on the call option prices. Here it only uses information of the call options. If now we have the data including both call and put options, is there a ...
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Arbitrage Free Interpolation of Implied Volatility on Time Dimension

I’m working on a project to build a local volatility model out of implied volatility data and I’m currently testing the no-arbitrage version of SVI model as described in this paper Section 5.1 [...
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Bergomi: Skew arbitrage

In his paper "Smile Dynamics IV" (https://www.fields.utoronto.ca/programs/scientific/09-10/finance/derivatives/bergomi.pdf) as well as in his book "Stochastic Volatility Modeling" (...
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143 views

Question About SVI and SSVI Tradeoff between Fitness and No-Arbitrage

I’m currently working on a project to build a local volatility model out of implied volatility data and am struggling in the selection of an appropriate method to interpolate the volatility surface. I ...
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101 views

Annualizing intraday volatility

I've been experimenting with end-of-day volatility-based stock trading strategies and I'm looking to see if it's possible to use similar strategies over shorter time frames. Given that market ...
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180 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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36 views

Entropy-implied volatility requires itself to be calculated?

\begin{align} H &= \frac{1}{2} \ln (2\pi\sigma^2) + \frac{1}{2}\\ &= \frac{1}{2} \ln (2\pi e \sigma^2) \end{align} is the analytical solution for the entropy of a Gaussian random variable, ...
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123 views

Probability of an Option maturing In-the-money vs. Volatility

How will the probability of an option ending up in the money change if the volatility of the underlying stock increases? Intuitively, I think the answer to this is that if volatility goes up the ...
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59 views

How does volatility affect an option payoff diagram? [closed]

I am a beginner to financial mathematics, and my lecturer asked me to ponder about how volatility may affect the value of an option (as a function of spot price). For example, if an option had a (...
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53 views

Close Volatility - Open-Close Volatility

Could anyone please give the detailed expression of either the close-close or open-close volatility ? Thanks
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141 views

Can we model Implied volatility using GARCH?

Can I use Implied volatility as a dependent variable in a GARCH model? I believe my IV data shows ARCH effects and hence can I use it to model volatility of the volatility? I know literature has used ...
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Availability of historical data on variance swaps [duplicate]

I want to do research on variance swaps. Where can I get/buy historical data (other than Markit)?
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Is there a relation between the so-called volatility drag and the sigma term in Black-Scholes' model? [duplicate]

The closed-form solution of Black Scholes Dynamics $dS_t=S_t(\mu dt +\sigma dW_t$) is $$S_t=S_0 e^{(\mu -\sigma ^2/2) t+\sigma dW_t}.$$ The $-\sigma^2/2$ term is quite similar to the volatility drag ...
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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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Estimating constant and local volatility based on passage times

Consider a Brownian motion B_t with constant instantaneous volatility σ and zero drift where ...
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103 views

Angular bracket notation (physics)

In a few papers I have seen the following notation: $$ \langle X_t \rangle $$ Also, in Bergomi's book, at page 8, we have the following equality: $$ \biggr\langle \int_0^T e^{-rt}s^2 \frac{d^2P_{\hat{\...
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Why approximating dSigma/dS with dSigma/dK changes the ATM volatility at twice the rate?

I'm referring to the paper "Delta Hedging With a Smile", Sami Vahamaa (2004). It mentions: By approximating ∂σ/∂S with ∂σ/∂K, it is assumed that as S changes by one unit, there is a ...
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56 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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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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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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15-min, 30-min and 60-min volatility forecasts

I have high-frequency market data (irregularly spaced nanosecond timestamps) and would like to compute the volatility forecasts of the next 15, 30 and 60 minutes. Most of the literature I looked up ...
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Is there Cornish-Fisher volatility, given that there is Cornish-Fisher Value-at-Risk?

The Cornish-Fisher expansion is used to approximate the quantile $q_\alpha$ of a return distribution in order to extend the traditional Value-at-Risk (VaR) measure $$VaR = \mu(X) + \sigma(X) q_\alpha $...
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Option Price vs. Implied Volatility

I was doing an exercise on investigating the relationship between European Call option price and its volatility. I was asked to compute $\frac{\partial^2C}{\partial \sigma^2}$ and find out the domain ...
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171 views

Implied volatility quote vs. Price quote

After reading this and this, I still don't understand the reason for why options are quoted in terms of implied volatilities. My question is: can somebody give an example that shows the value/...
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101 views

Expected Forward Volatility vs. Different Strikes

While theoretical options prices are derived from models, such as Black-Scholes, IV and IV skew reminds us that options prices are ultimately based on supply and demand. My question is the following: ...
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Should diverging valuation multiples affect beta estimate?

Suppose we experience a significant equity market crash. All equities are affected, but the drawdown disproportionately affects equities in a specific sector - for example, say the broad equity market ...
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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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