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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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1 answer
36 views

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 ...
0 votes
1 answer
57 views

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 ...
4 votes
6 answers
11k views

Value of Call Option as Volatility goes to Infinity

Why would the value of a call option go infinity as volatility goes to infinity? I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
1 vote
3 answers
334 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 ...
0 votes
1 answer
78 views

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, ...
2 votes
3 answers
166 views

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_{...
-3 votes
0 answers
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ESSVI not calibrating [closed]

The parameters rho and psi are not updating for each time slice. Here is my code import numpy as np import scipy.optimize as sp epsilon = 10**(-5) xi = 0 i = 1 r = 100 def e_SSVI(rho, psi, logmf_array)...
1 vote
2 answers
174 views

Practical approach to get average option IV

Is there a practical method to calculate some sort of average IV for each level of moneyness of equity options? I'm thinking of an algorithm to find mispriced options and do to so, we need to figure ...
2 votes
2 answers
327 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 ...
0 votes
2 answers
84 views

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....
2 votes
0 answers
41 views

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 ...
7 votes
1 answer
772 views

How to interpolate on an implied volatility surface based on forward moneyness?

Should be a simple matter, but perhaps I'm misunderstanding something fundamentally. Look first at the below image of the BVOL surface from Bloomberg, to my understanding from looking at the white ...
0 votes
1 answer
61 views

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 ...
0 votes
1 answer
99 views

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 ...
1 vote
0 answers
58 views

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 ...
0 votes
0 answers
36 views

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 ...
0 votes
2 answers
250 views

Converting Historical Volatility to Implied Move

I am trying to calculate an implied one-day move value for an instrument given its historical volatility. While I am familiar with this formula for implied volatility to implied move: and intuition ...
6 votes
2 answers
2k views

Option Price vs. Implied Volatility

I was doing an exercise on investigating the relationship between European Call option price and its volatility. I was asked to compute $\frac{\partial^2C}{\partial \sigma^2}$ and find out the domain ...
6 votes
0 answers
628 views

Caplet stripping in the bwd-looking RFR world with/without maturity adjustment

Since the beginning of this year, LIBOR rates have ceased in some markets like GBP, CHF, and JPY and rates pricing has moved into the RFR space, using compounded overnight rates as the underlying for ...
1 vote
2 answers
411 views

Calendar arbitrage in implied vol grid with discrete and proportional dividends

I have an implied vol discrete grid, obtained from market data. To obtain prices from these implied vols, a dividend model with discrete and proportional dividends is used. How can I verify if there ...
0 votes
1 answer
175 views

Covariance Matrix of Correlated Random Variable

Suppose I know or have estimated the covariance matrix for one random variable (for example an asset) and have: $$ \begin{bmatrix} <\text{spot, spot}> & <\text{atmv, spot}> \\ <\...
1 vote
0 answers
91 views

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 ...
3 votes
0 answers
56 views

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 ...
1 vote
1 answer
465 views

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 ...
1 vote
1 answer
87 views

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 ...
1 vote
0 answers
62 views

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 ...
1 vote
1 answer
93 views

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 ...
1 vote
1 answer
100 views

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 ...
1 vote
0 answers
72 views

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 ...
1 vote
2 answers
317 views

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) = ...
1 vote
0 answers
101 views

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 ...
0 votes
1 answer
432 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%...
0 votes
1 answer
244 views

Trading term structure of skew

Is there a way to trade IV skew between two maturities? For example, bull put in near maturity and bear put in far maturity.
3 votes
2 answers
387 views

Local variance derivation by Gatheral

I've bought Gatheral's book on Local Volatility and I have troubles with understanding a part where he shows that local variance is a conditional expectation of instantaneous variance. Why in the ...
6 votes
1 answer
1k views

Procedure/methodology for building equity volatility surface

EDIT: I update while making progress: I am trying to build (model implied) volatility surfaces for individual equities. I will use these surfaces to calibrate models to price different derivatives (...
4 votes
0 answers
95 views

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 ...
3 votes
1 answer
113 views

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}\\ \...
1 vote
1 answer
1k views

Delta Volatility Surface Usage to value the option

I always find myself in the unknown charted territory when it comes to non-Linear Instruments. I come across the scenario, How to value the option using Delta Vol surface? Example I have CME traded ...
15 votes
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 ...
0 votes
0 answers
36 views

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 ...
1 vote
1 answer
259 views

Issues with calculating IV with options bar data

I am currently working with some options OHLC data (30 minute bars) from IBKR for a range of strike prices, maturities and for both calls/puts. For each bar, I am trying to back out the IV (crudely ...
4 votes
2 answers
3k views

Which models do Bloomberg/Reuters use to derive implied volatility for interest rate derivatives with negative forward rates?

can anybody tell me which models Bloomberg and Reuters ares using to derive implied volatility for interest derivatives with negative forward rates? I know that Black-76 is the standard model, and ...
1 vote
0 answers
85 views

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 ...
0 votes
0 answers
80 views

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 ...
2 votes
1 answer
262 views

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 ...
5 votes
2 answers
351 views

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 ...
1 vote
0 answers
336 views

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 ...
0 votes
1 answer
179 views

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....
0 votes
0 answers
47 views

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 ...
7 votes
1 answer
948 views

compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...

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