Questions tagged [volatility]
A measure of the variation in price over time. Also a measure of the risk of a financial instrument.
1,470 questions
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On the correct definition of ex-post variables
I recently had an interview with a quant from a hedge fund and we were discussing about properly defining ex-post variables when backtesting the forecasting ability of certain market variables.
For ...
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Is GARCH assumption on constant drift wrong in log space?
GARCH assumes constant drift $\mu$ - this imply $E[e^r]$ won't be constant and jump wildly. And it contradicts the reality, for stock prices $E[S_{t}/S_{t-1}]=E[e^r]$ doesn't jump with each time step.
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Volatility of Hedging Error and Statistical Uncertainty of Estimates
In The Volatility Smile book by Derman & Miller at pag. 113, I don't understand the statistical uncertainty in the measurements of volatility and how to interpret the notation.
The authors state ...
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Computing Intraday Volatility using mid price
I’m working with an order book that contains the 10 best bid and 10 best ask levels. A common approach for estimating volatility is to use the mid-price, typically computed from the first best bid and ...
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Why is the forward measure needed for options on futures when the risk-neutral measure suffices?
I have been running around in circles with this attempting to make sense of this.
Universal pricing theorem
Given a numéraire asset $(N(t))_{t \geq 0}$ such that for all tradeable assets $(S(t))_{t \...
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Arbitrage-free interpolation
After constructing an arbitrage-free surface, when analyzing a slice of the surface, do practitioners use a slice generated from the calibrated surface, or would they re-calibrate along the slice that ...
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Question on Long Futures and Log Contract Replication in Variance Swaps
I’m currently reading a JP Morgan resource on Variance Swaps and have hit a snag in understanding a specific point in section 4.9: Replication and hedging in practice:
As demonstrated above, a ...
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How to evaluate whether academic research papers are practically useful or a waste of time? [closed]
Hi I'm currently an undergraduate student studying particularly derivatives pricing, volatility modeling and market microstructure.
I've been reading quite a few recent research articles and arXiv ...
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Expected vs Implied Volatility discussion - Gatheral chapter 3
On page 27-28 of Gatheral's book The Volatility Surface, the Black-Scholes forward implied variance is defined as
$$
\nu_{K,T} (t) = \dfrac{\mathbb{E} \left[\sigma_t^2 S_t^2 \Gamma_{BS}(S_t, \bar{\...
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Negative volatility and violated Feller condition in Heston model
EDIT: this question is about the Wikipedia page on april 14, 2025. This page has since been changed.
I think I am missing something, because the equations for the Heston model imply that the ...
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QuantLib interpreting parameters nu and alpha in SABR model
I would like to find out what represent "nu" and "alpha" parameters in QuantLib according to Wikipedia here:
https://en.wikipedia.org/wiki/SABR_volatility_model
Is nu from QuantLib ...
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What model(s) can be used to simulate the joint dynamics of the 2y forward curve and implied volatility surface?
I am trying to train a reinforcement learning model for dynamic hedging like Cao et al. 2023. Their model uses SABR to generate joint dynamics of implied volatility and underlying equity asset prices.
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How is the swaption vol grid clustered/seperated?
I understand that broadly you have gamma/vega and furthermore upper right/left and lower right/left. Can you break it up even more? I've heard "Belly Vega" thrown around.
The vega sectors ...
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Greeks of Forward Variance Swap
If I'm not mistaken, ignoring skew delta, the Greeks of forward variance swaps read
\begin{align}
\mbox{Dollar Gamma} &\approx 0\\
\mbox{Vega} &\approx 2K_t - \frac{t}{T_2 - T_1} (2K_{t,2} - ...
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What's the intuition behind "If I am long (short) a forward starting option, I am short (long) vol of vol?"
Traders keep telling me this (and sounds very trivial/straightforward), but I don't know why (intuition and mathematically). Could someone help?
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Volatility forecasting in presence of jumps
I have trained a GARCH(1,1) model that does a decent job of forecasting volatility (for real-world stock price time-series). For "known" events such as earnings announcements one can ignore ...
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Implied Volatility for illiquid FX currency
Can anyone help me by providing ideas and references for the following problem ?
I'm working on a certain currency pair USD/X where X is not a highly traded currency. I'm supposed to implement a model ...
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Metric for volatility time series similarity - European swaptions
I'm trying to estimate the volatility surface of illiquid swaptions (say CHF) given hourly data (atm vol, skew, for different strikes) of other liquid swaptions (EUR, USD, etc.). Having the underlying ...
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How to compute implied probability of Bitcoin price given noisy option data?
I am trying to calculate the implied probabilities of Bitcoin being within specific price ranges using option chains from Deribit. The challenge I am facing is dealing with bid-ask spreads, which are ...
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Articles on (asset-specific) covariance matrix estimation
As the title states, has there been any peer-reviewed articles or literature review on the empirical estimation of elements in the covariance matrix? I would prefer a paper showing some empirical ...
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Variable-length lookback variance
Assume a universe of n assets of the same asset class, each with an unknown mean return and stdev, with some assets having a longer time from inception than others (so, stock-marketish). These assets ...
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Python implementation of the BNS (Barndorff-Nielsen & Shephard) jump test
Is there a reliable implementation in python of the BNS jump test available?
Barndorff-Nielsen & Shephard (2006) "Econometrics of Testing for Jumps in Financial Economics Using Bipower ...
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Calculating the minimum variance portfolio given a desired expected return as a constraint
I'm replicating the equations in Cochrane 2005 using all the stocks in the S&P 500. I am questioning my results - I get that the daily volatility of a portfolio with a return of 10% (annualised) ...
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Why does IV smile imply a more "peaked" distribution than lognormal?
Below, Hull claims that a U-shaped volatility smile suggests that "both small and large movements in the [underlying] are more likely than with the lognormal distribution, and intermediate ...
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How to derive the volatility of options PL (hedged) as a function of implied volatility and measured realized volatility
This is my first time asking a questions. Apologies in advance if I mess something up. If this happens, please let me know if I do and I'll try to fix it.
My question is regarding the equation Euan ...
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