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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Why do the Greeks not converge to the strike as the volatility tends to zero? [closed]
So, I was playing around with the Greeks in Python with some made up data for a European call option assuming the Black-Scholes model. I plotted the graphs to see what happens to the Greeks when ...
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High/Low range under GBM - Analytic solution?
Does anybody know of an analytical solution to the expected high / low range for an asset that follows a GBM process over sampling frequency dt? I have ran numerical simulations and find that the ...
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implied volatility for close to expiry ATM options vs VIX
All throughout my MFE I was told that implied volatility for close to expiry ATM options is a reasonable estimate for current volatility and tracks realised vol pretty well. Then why does VIX measure ...
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How to adjust an assets position to target volatility in a long-short portfolio?
I have a portfolio of weights $\mathbf{x}$ where some positions in $\mathbf{x}$ are short s.t. $\Sigma_i x_i=0$ (dollar neutral).
The standard way to estimate the volatility contribution per asset is ...
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Implied vs. Realized Vanna in Risk Reversal
I am trying to understand how to build an implied-to-realised Vanna trade using a risk reversal, as shown in the Hull's paper:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3968542
I have some ...
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Implied volatility greater than realized volatility at all strikes?
It is usually stated that the implied volatility is statistically generally --- not always --- greater than the realized volatility. It seems this statement is made with regard to the implied ...
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For each day I have volatility for country A and B. How to test if volatilities are different? [closed]
I have a dataset with 10Y benchmark government bond volatilities of two countries.
So, my data looks like this:
Date, Volatility5day_A, Volatility5day_B
The volatility measure itself is from Bloomberg ...
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0DTE volatility and greeks
When european stock options have very little time until expiration (less than 2-3 hours), they can exhibit extreme sensitivity to changes in the underlying asset's price. This behavior leads to ...
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What is the probability of an asset trending or ranging
Some assets are know(or at-least assumed)to trend more than others. Is the probability of an asset trending equal to the probability of that same asset ranging(i.e 50-50)?
Is there a mathematical ...
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How much can news events affect the volatility of a currency relative to another?
GBPUSD is usually more volatile than USDCAD. However during U.S related news releases like the NFP, is it possible for the USDCAD to experience significantly more volatility than the GBPUSD?
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Uncertainty on volatility prediction using GARCH(1,1)
I have daily returns data and I predict the variance for the next day using GARCH(1,1) as follows
...
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CBOE dispersion index formula
I came across the CBOE white paper Cboe S&P 500 Dispersion Index Methodology. The formula in Subsection Index Construction/Outline of the Dispersion Index Methodology on page 4 that defines the ...
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Calibration of Covariance Matrix for a Cumulative Period Return
I am trying to compute optimized weights (minimum-variance portfolio) for a cumulative return over a period (weekly or fortnightly). In a daily return setting, it is quite simple, I just compute a ...
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Python - yahoo finance options data - volatility smile plot
I have plotted the IV of TSLA options using yahoo options data, but the scatter plot doesn't look right, can anyone advise why the plot looks like this? I would expect to see a vol smile plotted.
EDIT ...
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what is the point of SABR model as an interpolation tool if we can already observe the whole vol cube from the market
on BBG and other data providers, it is common that you can find the whole vol surface/cubes. What is the point of the SABR model as an interpolation tool? why cannot people just linear interpolate the ...
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Calendar spreads through variance swaps
Please refer to this image from the famous paper JUST WHAT YOU NEED TO KNOW ABOUT VARIANCE SWAPS by Bossu et al. 2005 (page 6).
The underlined part, is there a typo?
"if the 2-year IV is above 20....
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Forecasting Realized Volatility with Machine Learning [closed]
How is the daily realized variance calculated for an intraday one minute data.
How can realized volatility be forecasted using machine learning techniques such as neural network and LSTM. Any detailed ...
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Vega, square root of time, and ATM straddles
Could someone intuitively explain why for say a 1y EURUSD option -
If you buy 100 (50/leg of straddle) of 1y at the money EUR vol, that = sq root of 12 x 100 = roughly 350k of EUR vol.
If you buy 100 ...
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What's wrong with calibrating implied volatilities with polynomials?
People use different parameterization schemes to fit the implied volatilities from the market, e.g., SVI. But often times they cannot always fit well, e.g., the "W"-shape before earnings, ...
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How to understand Short Gamma and Long Volatility for Leveraged ETFs?
In the book Leveraged Exchange-Traded Funds: Price Dynamics and Options Valuation, it describes a static delta-hedged long volatility position by simultaneously shorting regular/inverse leveraged ETFs ...
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spectral entropy as stock volatility
There are many way to capture to stock volatility and most common is Beta. But problem with beta this is difficult to select ...
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Value At Risk Modelling for electricity market with negative prices
I'm a bit at loss after trying to find papers regarding tail risk for electricity markets. There doesn't appear to be a whole lot of literature (or perhaps I haven't managed to find it) regarding ...
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How does implied volatility affect delta and gamma for different spreads? [duplicate]
Im looking at a call butterfly spread where i am long one ITM and OTM call option, and short two ATM call options. Also i have a time spread where i am long December put and short November put.
Now ...
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Assessing the value of risk reversal and the fly
This is important for traders.
What I'm really asking is how do we ascertain if vanna (or dvegadspot) is being valued correctly by the market?
and for the fly, fair fly value will be a combination of ...
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Volatility Mismatch in SABR Calibration
Problem Statement
Hi, I am trying to calibrate SABR on a new asset, which is not 'forward swap rate'. While using the vanillaSABR calibration, I find the parameter 'sigma' (one of model parameters, ...
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Calibration of Heston using implied vol as $v_0$
I am looking at the difference if you calibrated the heston from market data using objective function minimisation.
In scenario 1, I calibrate all the parameters from market data
In scenario 2, I ...
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Expectation of the realized volatility
I was reading Zhang and Wang 2023 and I have some doubts regarding it. The realized Stochastic Volatility Model is expressed as follows:
$$\begin{matrix}
y_t = \exp \big( \frac{h_t}{2} \big) \...
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What does it mean with regards to market conditions that the historical volatility is twice the implied volatility
I am trading the Indian market indices. I calculated the last three years historical volatility. Noted down 1 standard deviation of this value.
Then I took a weekly expiry of options on this index and ...
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What is the definition of aggregate volatility, and how to compute it?
I am quoting the following sentence from Andrew Ang's paper "The Cross-Section of Volatility and Expected Returns". Can someone explain how aggregate volatility is defined and how to compute ...
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Difference between statistical properties of log returns and simple returns
Given a time series of simple daily returns, how will mean and stddev of log returns and simple returns? I think, mean of simple returns will be higher due to volatility drain. But confused about ...
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what is the index to measure the credit volatility
Similar to VIX to measure the equity vol and Move for rates vol, is there a simple index to measure the credit vol
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Are ARMA-GARCH-type models suitable for monthly data?
I understand that ARMA-GARCH models and their variations are usually applied to daily time series. While I know that such models can be also estimated on monthly data, I have seen few applications in ...
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Calendar spreads under black scholes world
If IV skew is flat (all strikes with the same IV ss ATM) as in the black-scholes world for all maturities, would calendar spreads be considered as pure arbitrage?
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Forward Black Implied Volatility For Within Risk Neutral European Option Pricing
Going to preface this question with an acknowledgement with how silly the ask is, but alas that is the working world; if anyone can share any ideas I'm all ears.
We're pricing an exotic option in risk ...
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Uncertain Volatility Model - Option Pricing R code help
I am trying to price the following call option using the UVM method in R.
The code I wrote below keeps producing the same price for the min and max volatilities, which is wrong, however, I can't seem ...
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Calculating Volatility in the Avellaneda and Stoikov Model
I'm looking to understand the approach for calculating volatility (σ^2) within the context of the Avellaneda and Stoikov market-making model. I have a few specific questions on this topic:
Return Type:...
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How to calculate the variance of this coin flip?
I am reading the article “Shannon’s Demon & How Returns Can Be Created Out of Thin Air” by Richmond Quantitative Advisors (2021).
The main premise is a fair coin flip. If heads, you gain 50%. If ...
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Option Pricing for Illiquid case
I am currently studying crypto options trading and have observed that there is often a lack of liquidity for options (such as BTC Options) on various exchanges, including Binance. In many cases, there ...
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How is volatility surface re-calibrated with new inputs?
I'm a newby on this topic so please bear with me. My question is:
I've a strike by strike / listed products volatility surface, and I was asking how can I recalibrate my surface during the day ...
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Volatility Forecasting
I would like to clear a certain doubt about volatility forecasting: Are models like Parkinson, Rogers Satchell and Yang Zhang used for predicting future volatility?
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Best Method (Or Just a Good Method) of Predicting Intraday Volatility in Real Time?
I apologize if this is a stupid question, I'm a complete neophyte in academic finance but I am trying to learn.
I am trying to create an estimate of how likely indexes are to rise/fall by x% by the ...
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Expanding window with ugarchroll in rugarch in R
I was wondering whether my code is crafted correctly to satisfy this requirement:
use 1:1000 to predict 1001, then use 1:1001 to predict 1002, and so on
rOHLC has a length of 10079
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Clarifying Parkinson Python Code [closed]
I would appreciate opinions/reviews on whether my python code to calculate Parkinson Volatility index is correct. Thank you very much!
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Conventions and Modeling of CDS Options
I am curious about the current standard conventions and modeling techniques in the CDS options market. I would be glad if someone could elaborate on the following topics:
State of the art of index ...
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Rough Volatility and Change of Measure
When deriving the rough Bergomi model, Bayer et al in "Pricing Under Rough Volatility" (2015) perform a change of measure to ensure the price process is a martingale as shown in the ...
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Futures and Forward prices under the Heston model and their spread
This might seem like a very trivial question but I am really not so sure about it so I thought I post it here.
Assuming a Heston model of the form
\begin{eqnarray}
dS &=& (r-q)Sdt + \sqrt{v}...
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How to apply put-call parity in volatility surface construction?
How to make the volatility surface free of put-call parity arbitrage? If I bootstrapped the implied vol from a call price and plugged it into the BS model to have a put price, what if it violates the ...
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How does the inclusion of stochastic volatility in option pricing models impact the valuation of exotic options?
Been lurking this forum for quite some time and there’s this concept I can’t wrap my head around:
How does the inclusion of stochastic volatility in option pricing models impact the valuation of ...
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Why is the stochastic process of the volatility of a stock price square integrable?
I am taking a course in financial mathematics(Ito-Integrals, Black-Scholes,...) and there is something that is not immediately clear to me. When constructing our stock price model, the integral $\...
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Single outsized daily return value creates substantive discrepancy between annualized variance calculated from daily vs monthly returns
I am new here, and to the field. I hope my clunkiness in expressing myself can be forgiven.
My situation is as follows: I have around three years of daily return data for some financial asset. Out of ...
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