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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Calibrating Hull White volatility on swap rate volatility

I'm strugling with the Hull-White 1F model. I'am trying to calibrate the volatility with the swap rate volatility. Here is the model I'am curently working on : $$ \begin{align} dr_t = a(b-r_t)dt + \...
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1 answer
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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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221 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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1 answer
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Question about marginal risk contribution / portfolio volatility decomposition

I am trying to understand the rule where you add a new asset to a portfolio if its Sharpe ratio is greater than the product of the portfolio sharpe ratio and the correlation between the portfolio and ...
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Multivariate Markov Regime switching GARCH in R

I am looking for R package handling Multivariate Markov Regime switching GARCH models, but MSGARCH package only work for univariate time series. Any suggestion would be welcomed, thanks!
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How to calculate historical returns and variance for a non-BAH trading strategy?

Suppose i have a strategy that is not buy-and-hold type of strategy. It can have unique entry timing and unique exit timing for a single asset and both long and short positions will be allowed, and ...
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1 answer
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GARCH before and after a shock. How to test if volatilities are different?

I have an intraday dataset with minute returns for a bond. At a specific point in time, say 10:30, there is an external shock (in my case an auction where that bond is traded). I want to know whether ...
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Implied forward volatility definition

What is the rigourous definition of the 'implied forward volatility' and how is it calculated? I couldn't find a rigorous definition as would be the case for 'implied volatility'. Also, could anyone ...
2 votes
1 answer
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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 ...
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1 answer
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How should I go about computing the 30-day model free implied volatility (MFIV) daily?

As the title suggests, how can I calculate the MFIV daily (for a market index)? My MFIV follows the procedure described in DeMiguel et al. (2013) Improving Portfolio Selection Using Option-Implied ...
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1 answer
372 views

Interpretation conditional volatility plot

I have plotten the log differences of exchange rates and in the same plot, I show the conditional volatility $\sigma_t^2$. The conditional volatility follows approximately the same path, but is much ...
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Are there standardized measures to characterize the volatility skew?

Might be too simple a question, but I saw in Gatheral & Jacquier (2014) that commonly used features to match volatility skews are (and then I subsequently ChatGPTed some commonly used industry ...
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4 answers
9k views

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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Cross corridor var swap

How should I think about replicating a cross corridor variance swap like breaking into strips of calls and puts and an over hedge that I can rebalance at some frequency? Given the earnings move, I can ...
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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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1 answer
427 views

Eurodollar futures volatility

Considering each point is 2500, how can I get the volatility of the jun 24 contract? On tastyworks I'm seeing a 0.7% iv for the contract, how can I translate it to standard deviation? Ex:sp500 15%...
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1 answer
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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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337 views

Volatility surface

When fitting/calibrating a option model like heston to option data, what are some useful data handling to do? The basic thing is to remove all options with no trade/volume, but how many maturities ...
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2 answers
181 views

How do options traders capture volatility?

Let's say I'm an options trader, and I want to go long volatility on a particular underlying. How do I capture this volatility mispricing? How do I convert my forecast into a bet with a cash payoff. ...
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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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1 answer
151 views

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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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 ...
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1 answer
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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, ...
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1 answer
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Deriving eq. 5 in Carr & Madan 1998

I don't understand this derivation from Carr & Madan (1998), specifically the derivation of the third term on the left (left-most term on the bottom line). My attempt Let $h(t, F_t) := V(F_t, t; \...
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2 answers
13k views

Long Gamma vs Vega

What is the difference between being long gamma and being long Vega? I understand that gamma is the vol of delta and that vega is the vol of the underlying. However, I have also found that being long ...
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2 answers
354 views

You are long a hedged ATM SPX Call and the market moves down. Do you gain or lose in volatility terms?

The shape of the volatility curve in index options trading typically shows that the 'just' OTM Calls (ITM Puts) options have the lowest implied volatility. If you are long an ATM Call and the market ...
3 votes
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158 views

Spread vol for interest rate spread options in normal environment

Suppose I am long spread option with underlying : rate A - rate B. The vega on the option would be positive. But if I want to compute the option vega with respect to individual rates, can I use the ...
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Vol Smile Call/Put Wing calibration

Is call/put wing volatility smile calibration approach used in practice? To calibrate an index (SPY) using only more liquid OTM calls/puts, to kind of use an "if" condition on K to S0 to ...
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1 answer
277 views

Annualization of discrete returns

There is a well known approach to annualize volatility of log-returns for a given frequency. Let $P(t)$ a price process and define a log return $r_l(t)$ as $$r_l(t) = \ln \left( \frac{P(t)}{P(t-1)} \...
5 votes
2 answers
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When calculating VIX, how to deal with the problem of asymmetry of put and call data?

I'm trying to calculate the VIX index according to the methodology of CBOE. I am looking at commodity options. I found that at some time, like at this minute, there are 13 call options out of the ...
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Volatility of a stochastic Process given by an SDE

I am currently working on this thesis: http://arks.princeton.edu/ark:/88435/dsp01vd66w212h and i am stuck on page 199. There we have a portfolio $P=\alpha F+\beta G $ with $\alpha +\beta =1$ and ...
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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 ...
2 votes
1 answer
377 views

In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
3 votes
1 answer
940 views

Dupire (Local Vol with Imp Vol)

I am trying to implement a local volatility pricer using Monte Carlo and Dupire's equation in function of implied volatilities and I was told that first of all I have to check Dupire is well ...
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1 answer
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the pre-averaging function in Jacod et al

In the paper of jacod et al the authors used the pre-averaging function to deal with microstructure noise. They suggest the easiest function which is $$\bar{Z_i} = \frac{1}{kn} \left( \sum_{j=kn/2}^{...
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3 answers
299 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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Vol-Vol Breakeven (MC Estimation)

I am currently reading the paper Computation of Break-Even for LV and LSV Models. This paper defines the vol-vol breakeven \begin{align*}\tag{1} B_t(T,K,T',K') &\ :=\ d\langle \ln \sigma^{T,K}...
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Arbitrage-Free implied/local volatility surface with Cubic Spline Interpolation

I am trying to create a local volatility surface using a cubic spline interpolated implied volatility surface. In other words, I have a function $\sigma(T,K)$, that is arbitrage-free $\forall T,K$ (...
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Modeling mean-reversion for different volatility regimes

Motivation: Half-life (HL) period shows how long it takes for a mean-reverting process to return halfway to its mean after a deviation. Most commonly, an Ornstein–Uhlenbeck (OU) process is applied to ...
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2 answers
137 views

Delta on x-axis in Volatility smile

I want to ask a perhaps simple question: Why do we use delta on the x-axis instead of the strike price when discussing volatility smile or volatility surface? In the book I'm currently reading, it is ...
2 votes
2 answers
291 views

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 ...
1 vote
1 answer
286 views

Binomial tree with time dependent volatility

In the Cox approach for binomial trees, the up move $u$ and down move $d$ are given by: $u = e^{\sigma \sqrt{dt}}$ and $d = e^{-\sigma \sqrt{dt}}$. In this approach the volatility $\sigma$ is assumed ...
2 votes
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Measure of the behavior of Swaption surface

I'm looking to find a different measure than average shift move to explain the behavior of the IR VOL products say Swaption. I know it's a very open question not only touching upon IR VOL scope. Let ...
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1 answer
283 views

Is a volatility forecast essentially a delta forecast in vanilla European options?

As the title suggests. I want to understand why delta hedging is done. I'd like to illustrate with an example: Say you have 7 dte option chain with 15.8% IV ATM straddle on an underlying of spot 100. ...
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We can forecast the direction of (constant maturity) implied vol of various indices well. Is that useful?

We've been financial building ML models for years, and have multiple portfolios live - but we're new to the volatility space, none of us are options traders. How could we effectively use implied vol ...
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Instrument volatility scaling as a function of sample rate

Question: I did some experimentation today to see if volatility changes as a function of the sample frequency. Prior to starting this experiment, I believed that volatility was a function of sample ...
3 votes
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Do options/prop trading firms put any effort into predicting (the direction of (implied)) volatility?

What are the "best practice" models that quant firm that trades options would use to "predict" (let's say SP500) implied vol, that they integrate into their decision making? Do ...
4 votes
1 answer
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Option price calculation using Local Volatility and Monte Carlo

The below formula is used to convert the implied vol into the local volatility, my question is, once I have converted it into the LV ( and have built the full surface), what models do I use to ...
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1 answer
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Creating Implied Volatility surface using log moneyness [closed]

When creating the implied volatility surface using $\left(T,log\left(\frac{K}{S_0}\right)\right)$ as $(x,y)$ axis, do the inputs for the implied vol calculation need to be logged too? In other words, ...
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1 answer
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Shortcut for cutting portfolio volatility

When calculating the portfolio's historical volatility, do I need to factor the volatility of each asset individually and then do a covariance calculation or can I get away by measuring the volatility ...

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