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Questions tagged [implied-volatility]

The volatility of the price of the underlying security that is implied by the market price of an option based on an option pricing model.

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Expected daily range (SPX) and daily realized range

I'm new in quant math, I'm self-studying it. I have two question in exp. daily range topic. How can we make the possibly most accurate estimation for expected daily ranges? My idea was to take data ...
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How do linear wings reconcile with volatility frowns

I was recently looking at a paper that brought up that under certain market conditions the risk neutral density can exhibit thin tails, yielding a volatility frown as opposed to the more usual ...
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Why would you take a Loan when trying to Illustrate a Riskless Hedge?

I'm reading an article trying to derive option pricing with a simple approach, but I got stuck. In the second paragraph of this article (Name – Options Pricing: A Simplified Approach), which takes ...
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Why do we use OTM options to extract implied vol?

It is often common practice to calculate implied volatility using puts for low strikes and calls for high strikes, so to always employ out-of-the-money options. Why is this often preferred to using ...
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What are common parametric forms for VIX smiles?

It is common in SPX markets to fit smiles using Stochastic volatility-inspired and Surface stochastic volatility-inspired parametric forms introduced by Gatheral and Jacquier (2014). In VIX markets ...
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yang zhang vol daily return [closed]

can i get SPX daily returns by yang zhang only using ohlc datas? i read somewhere when SPX on 3th of january 2022 was open 4778.14; high 4796.64; low 4796.17 and close 4796.56 (previous close was at ...
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How to calculate overnight implied volatility?

I am trying to workout how to calculate the implied volatility of the overnight movement from market close to open. That is, the volatility of the from the closing price $S_t$ to the opening price $S_{...
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Negative Dupire Variance

I want to compute Dupire Local volatility using the identity that links Dupire local variance to BS implied total variance. I calibrated an SVI on options data to get the implied total variance ...
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Arbitrage-Free, Breeden-Litzenberger and Risk-Neutral Measure

Let $\sigma_{\text{BS}}(K, T)$ a given IV slice at $T$, which is implied by a price slice $C(K, T)$. From this price slice, we can infer the Risk Neutral density of the price distribution at $T$ using ...
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Describing the volatility skew with a set of options

Say you have a set of options data, and you filter the dataset based on certain criteria such as the bid-ask spread, open volume etc. and you end up with a set of liquid options based on said criteria....
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Interpolation of IV based on delta

I have a dataset with options, all the same date and time to maturity but different IV and delta. Now, I want to find the IV for certain delta values (e.g 0.5) through interpolation. Do you think that ...
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Can a Call and a Put with same strike price and expiration date and underlying asset have different implied volatility?

Furthermore, assume that the current price of the underlying asset equals the strike price of the options. If volatility measures variance without a direction, it doesn't make sense to me that the ...
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Summarizing the Volatility Skew as a Single Number

Related questions to this topic/subject: Expressing Volatility Smile as One Number Volatility skew and how to capture it? In both posts, the authors/respondents recommend using the second derivative ...
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Interpolation of term structure of implied volatility

I have a dataset of options traded at each day, including the time to maturity, delta, strike price etc. Now I want to get the implied volatility of an option with time to maturity 30 days through ...
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Heston model calibration to option prices and implied volatility

I hope that you are having a great day, I am trying to write a research paper on the Heston model deep calibration. I noticed during my literature review that the most common approach is to calibrate ...
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Volatility surface for futures options

When looking at futures options such as CME's Gold options or many equity index futures options, the underlying is not the index but to be precise the closest to delivery futures contract. That means, ...
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Functional From to Approximate Volatility Surface

I have a finite difference pricing model and would like to factor in a volatility surface for each underlying equity. However, I have limited data. Essentially I'm just pulling a few implied ...
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What are some effective and easily implementable volatility smile/skew smoothing models?

Inspired by another post on Bakshi et al. (1997), the paper talks about the feasibility of option pricing models, particularly the SVSI-J variant. I would like to ask the Quant community if there are ...
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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 ...
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Deep calibration in the Heston Model

I am doing my master thesis on deep calibration in the Heston Model, and after reading a few academic paper (eg. Horvath et al. 2019) on the subject I understand pretty well the procedure and the ...
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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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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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What is the informational content of the volatility skew?

The option-implied volatility is well-known as a measure for the risk-neutral future expected risk for the underlying asset. However, the market prices of options (across different strikes) imply ...
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How is option pricing related to the correlation between implied volatlity and the underlying?

The correlation between the index returns (e.g SPX) and its changes in option-impled volatility (e.g. VIX), is strong, stable and negative (the implied volatility feedback effect). To me at least, it ...
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Seeking Advice on Normalizing Implied Volatility Change for Options Modeling

I'm working with a substantial dataset spanning five years of weekly options data, with records down to the second. My goal is to develop a model that can accurately predict the probability mass ...
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Infer implied volatility skew/smile from implied distribution

My question is closely related to the answer of @LocalVolatility and his blogpost. I am trying to reproduce his first figure and I am struggling with the implied volatility. With the help of $$ f(S) = ...
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Future Implied Price from Option Implied Distribution

Been reading on option implied distributions and understand that this can be transformed into a confidence interval/fan chart showing the implied future price. Was wondering how I could go about doing ...
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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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Expected underlying daily move from implied volatility

Suppose I have 3 ATM call options on an underlying with time to maturity 1, 2, and 3 months, respectively, priced at implied volatility level $\sigma_1$, $\sigma_2$, $\sigma_3$. Given that there will ...
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Python Quantlib for the calibration of interest rate caps

I am trying to calibrate the G2++ model to interest rate caps using the Quantlib library in Python. I have the problem that my optimization always stops with the starting values. So probably either my ...
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filtering implied Vol surface for butterfly arbitrage

Suppose I have a volatility surface (matrix in time and strike) but it might have butterfly arbitrage in it. I want to remove nodes from the surface so that the Vol surface is butterfly arbitrage free....
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Determing "fair" implied volatilities for SPX options

I'm trying to come up with a method to calculate fair IVs for SPX options based on historical data. I can't find much information on this so here's how I've thought to do it: Determine a metric for ...
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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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Does Gatheral formula for local volatility translate to a constraint on implied volatility

In Gatheral's "The Volatility Surface : A Practitioner's Guide", Equation (1.10) page 13, the following relation linking squared local volatility and squared implied volatility is expressed :...
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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 ...
Miroslav Holub's user avatar
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Derivation in Jaeckel's "By Implication" paper

In this paper by Jaeckel (2006), he derives the asymptotics for the option price $b$ as: \begin{align*} \lim_{\sigma \to \infty}b= e^{\theta x/2} - \frac{4}{\sigma}\cdot \phi(\sigma/2) \tag{2.7}\\ \...
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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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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 ...
Mark's user avatar
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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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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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week-over-week impacts on IV of of options with close to before/after EOY expirations

Tomorrow is the last trading day of 2023. Compared to last week, I noticed that $SPY ATM or close-to ATM options for the end of month/quarter (Dec-29) exp experienced a spike in IV since yesterday, ...
VolatiCity's user avatar
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smile dynamics IV appendix 4

I am having difficulty in recovering some result in smile dynamics of Bergomi https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1520443, the paper gives $(1-3\alpha x +(6\alpha^2 - \frac{5}{2}\beta)...
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Price Option B Knowing The Price of a Similar Option A

How do we find the implied volatility from the price in a call option and apply it to another option without a calculator? Or is there actually a better way? For example, given a 25-strike 1.0-expiry ...
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When getting the local vol surface from the implied vol surface, do we interpolate the strikes?

Using the dupire method: $$\sigma(T, K)=\sqrt{\frac{\sigma_{\mathrm{imp}}^2+2 \sigma_{\mathrm{imp}} T\left(\frac{\partial \sigma_{\mathrm{imp}}}{\partial T}+(r-q) K \frac{\partial \sigma_{\mathrm{imp}}...
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Moneyness, implied volatility and option greeks

I know that the more an option is ITM, the more is the implied volatility. I would like to deep dive into the concept, what is the logic that drives this statement? Also comparing an option with a ...
Maurizio Marinaro's user avatar
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152 views

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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Approximating implied price vol from implied yield vol?

I am wondering if there are any approximations that exist to convert yield vol to price vol? I am dealing options on SOFR futures, which can be quoted in yield and price (i.e. 3% put and $97 call are ...
Zac Likes Vol's user avatar
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Fitting volatility using SABR

I have been working on generating a volatility surface for options on SOFR futures with the help of the SABR model. I am running into some trouble for low strikes in particular, in that I cannot seem ...
Zac Likes Vol's user avatar
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340 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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Lognormal-mixture dynamics and calibration to market volatility smiles

Can someone assist me in replicating the code and results from page 11, Figure 3 of the paper 'Lognormal-mixture dynamics and calibration to market volatility smiles' by Damiano Brigo, Fabio Mercurio, ...
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