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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What are state-of-the-art methods for forecasting of rates and volatilities?

Usually forecasting is based on a model for the evolution of a value $x(t)$ based on some parameters ${\beta}$ that can then be estimated using various statistical means. For yield curves and ...
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Libor Market Model

I try to simulate forward rates with the Libor Market Model (LMM). Unfortunately, I just have data for normal vols instead of lognormal vols which are assumed in the LMM. Is there a way I can adjust ...
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Why do unleveraged VIX ETPs have large beta relative to VX futures, with much faster decay?

I hope the title explains it fairly adequately. To add a little more detail, it's my understanding that VIX ETPs such as VXX and VIXY hold VX Futures as their underlying assets. I believe that this is ...
109 views

Master Thesis about Heston vs. Duan option pricing model

I would like to write my master's thesis on volatility in option pricing. My idea was to compare the stochastic volatility model of Heston 1993 with the GARCH option pricing model of Duan 1995. For ...
1 vote
128 views

How to calculate the spot variance from the TSRV (Two-Scale Realized variance)

If the TSRV is given by: $$TSRV = \frac{1}{K} \sum_{i=K}^{n} (S_i - S_{i-K})^2 - \frac{\bar{n}}{n}\sum_{i=1}^n (S_i - S_{i-1})^2$$ where $\bar{n} = \frac{n - K + 1}{K}$, with $n$ is the number of ...
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Forward Rate Volatility Calculation - Caps

I am trying to calculate the forward rate volatilities from cap volatilities using Rebonato`s volatility model. Unfortunately, my approach always results in unrealistic forward rate vols. Furthermore, ...
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1 vote
128 views

Standard deviation of large equal-weighted portfolios

Say I've got a portfolio of shares with the following parameters: Let $n$ be the number of shares in the portfolio, let $\bar\sigma$ be the average standard deviation (volatility/risk) for each share, ...
1 vote
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Distribution of Geometric Brownian with time-dependant volatility

The process $S(t) =\exp\left(\mu.t + \int_0^t\sigma(s) \text{d}W(s) - \int_0^t \frac{1}{2}\sigma^2(s)\text{d}s\right)$ where $\sigma(s) = 0.03s$ is log-normally distributed, but i'm not sure about the ...
125 views

Optimal Price Metric for High-Frequency Volatility: Executed Price, Mid Price, or Weighted Mid Price?

In the context of high frequency trading, I'm exploring the application of the mean absolute deviation estimate for high-frequency volatility calculation. What would be the optimal choice for this ...
161 views

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 ...
1 vote
120 views

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 ...
1 vote
378 views

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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1 vote
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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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1 vote
643 views

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 ...
38 views

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?
169 views

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 ...
1 vote
274 views

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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1 vote
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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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1 vote
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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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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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1 vote
149 views

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 ...
1 vote
486 views

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 ...
1 vote
126 views

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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