# 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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### Variance swap volatility - ATMF vol, Skew and Curvature

In a pure diffusion setting, it is a well known result that the volatility $\sigma_T$ of a fresh-start variance swap of maturity $T$ as seen of $t=0$ verifies \begin{align} \sigma_T^2 &= \Bbb{E}_0^...
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### Jim Gatheral's ansatz

In the Ansatz section of Jim Gatheral's book Volatility Surface (page 32), he assumes $$\mathbb E[x_s|x_T]=x_T\frac{\hat w_s}{\hat w_T}$$ where $\hat w_t:=\int_0^t \hat v_s ds$ is the expected total ...
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### compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
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### Arbitrage free smoothing of volatility smile - cubic spline - implementation procedure

I am studying the paper Arbitrage-Free Smoothing of the Implied Volatility Surface, from Matthias R. Fengler (https://core.ac.uk/download/pdf/6978470.pdf). The problem I want to solve is much simpler ...
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### Measuring implied move priced into an event

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
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### Autocallable option Delta

There have been numerous exotic trading desk blow ups lately, related to various reasons. However, in particular, one bank had some issues where they were pricing autocallable notes with Local ...
679 views

### (C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas

I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
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### implied volatility and strike price

Assume for simplicity that the expiration time of an option is $1$ the initial stock price is $1$ and there is no dividend yield and the risk free return is $0$. How is it possible to show that the ...
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### How companies choose earnings release dates, & effect on Implied Volatility

A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
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### How are VIX futures being priced when the VIX itself is not being calculated because of circuit breakers

I see that CBOE has halted trading all SPX options, which means the VIX cannot be calculated. Yet VIX futures are still trading and we are very close to the last trade date for the March contract. I ...
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### Black-Scholes: Volatility Smile "sharpens" with time to expiry

I have tried to calculate IV and log-moneyness (=log(S/K)) for different times to expiry (M = less than 1 month, Q = less than 1 quarter, S = less than 1/2 of an year, Y = less than 1 year, Y (+) = ...
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### asymptotic behavior of the pdf constraints due to Roger Lee

In a beautiful paper, http://math.uchicago.edu/~rl/moment.pdf, Roger Lee (2004) shows that implied variance is bounded above by a function linear in the log-strike k. Does anybody know how it ...
836 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 (...
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### Anyone know if this daily report discontinue to publish? Goldman Sachs - "Global Index Volatility and Correlation Monitor"

I used to receive this daily report in my workplace from Goldman Sachs mailing list but the mailing list discontinued in May 2019 without any notice. The report is an pdf attachment which send from "...
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### Quantitative approaches to measuring the effectiveness of a Stock Option Pricing Model?

My question contains many parts, but I will try to keep it somewhat focused. I am primarily looking for a framework to evaluate the accuracy of a stock-focused Options Pricing Model. One of the ...
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### Bates Model on Quantlib

I am actively trying to price an option using bates model on Quantlib.However,when I input my volatility I find the same Black Prices with the basic Heston Model.I wanted to know if my code was right. ...
153 views

### How does VIX interpolate implied volatilities?

In the CBOE VIX white paper (direct link to PDF), it is explained that once the implied volatility of the near and next-term options $\sigma_1^2$, $\sigma_2^2$ are found, the constant-maturity 30-day ...
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### R: How do i finish the tails in the risk neutral density, obtained from option prices

Im currently working on constructing the risk neutral probability distribution of a stock, based on the option prices. In doing so, i calculate the implied volatilities from the option prices, and ...
218 views

### The error term of Hagan's approximation of Black's vol in SABR

Hagans approximation of Black's implied vol in SABR is very! difficult to understand fully. But I want to ask in here if anyone can tell me more about the error term. Consider the paper: http://web....
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### Volatility of a stock basket

to determine the volatility of a basket of stocks, I often use the following formula: $\sigma_{basket}=\sum_{i}\sum_{j}w_i w_j \sigma_i \sigma_j \rho_{ij}$ where the $\sigma$ are the constituents' ...
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### Alternative Method for Determining Option-Implied pdf

As I am refining a pricing model to incorporate skew, and not just ATM volatilities, I need to create random realizations of the underlying consistent with the skew-implied pdf. When searching, one ...
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### Implied volatility from American options using python

I am currently trying to construct volatility surface from american option prices (using Cox-Ross-Rubinstein tree) in Python 2.7. Below you can find the code I came up with. Any corrections would be ...
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### What is the longest number of consecutive days that options implied volatility has stayed "extremely high" for any particular underlying?

Curious as to whether or not there is any sort of all time record. Any index, future, or stock will do. Volatility must be well above the average 1 year volatility for all periods.
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### How to shock the IV surface w.r.t VIX and keep AOA

I have to compute the sensitivity of a set of option prices on a single sotck (range of tenor is over the whole surface) to an increase of 100% in the VIX.. and I am trying to get to the most ...
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### Does convexity in the IV space means convexity in the price space?

Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND). As the RND is the second derivative of the price of the option with respect to the strike, we would expect ...
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### Fast implied volatility for american options

Peter Jäckel has developped a method to compute implied volatilites from option prices, called "by implication", see the papers : By Implication Let's be Rational on its website -- as well as a ...
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### What are the main problems for calculating the implied volatility of in the money American put options?

As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
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### Volatility surface fitting, interpolation and extension from sparse data

There are some nice papers about constrained spline fitting essentially giving you a smoothing and arb free surface. I am focusing on the oil market here: The market is essentially split in a very ...
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### Is implied volatility really all that usefull?

I take implied volatility as the positive floating point number which lets the BS formula match an observed option price (assuming we have some useful interest rate, some underlying, etc). How useful ...
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### Understanding the BAML MOVE index

Hello quant community. I am looking for more information about a very interesting index: BAML-ICE MOVE index. There is very little literature online that details how the index levels are calculated ...
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### Implied Gamma VS Implied Volatility

Reading this paper, I'm struggling to understand what the author is saying with paragraphs below (see pages 39-42): We define Implied Gamma ($\Gamma_{\operatorname{implied}}$) as the value of the ...
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### 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 ...
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### Dispersion Trading with a 2 component index

I have a dispersion question I need help with...An index SPY has only 2 components - AAPL and AMZN. We are given the implied volatility of SPY and AAPL as well as the correlation between the 2 assets. ...
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### Implied volatility surface modelling in filtered historical simulation

What is the best way to model implied volatility surface in filtered historical simulation (other than keeping it constant)? Is it appropriate to apply GARCH-like model to every point on the surface? ...
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### Intraday and Intra-Week Pattern of Implied Volatility in FX market

Q1. How does implied vol changes from market opening time to market close time? I have read that it decreases during the day i.e. it opens high and closes low. what is intuitive and mathematical ...