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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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FX Options price vs implied vol

From the screenshot below, what is the difference between the option price by strike in the table versus the implied volatilities by delta in the chart at the bottom? https://www.investing.com/...
Student's user avatar
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35 votes
4 answers
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How to derive the implied probability distribution from B-S volatilities?

The general problem I have is visualization of the implied distribution of returns of a currency pair. I usually use QQplots for historical returns, so for example versus the normal distribution: ...
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6 answers
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A simple formula for calculating implied volatility?

We all know if you back out of the Black Scholes option pricing model you can derive what the option is "implying" about the underlyings future expected volatility. Is there a simple, closed form, ...
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Effect of Implied volatility on option delta

I am currently hedging a short put option where strike is 6027 and expiry is 30th Mar 2023. As per my understanding when option is ITM increase in volatility will decrease the delta and decrease in ...
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Variance replication using options

I would like to understand the intuition behind the following question: Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying? A variance swap ...
Escachator's user avatar
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Is it possible to have only one volatility surface for american options (that fits both calls and puts)?

Put-Call Parity does not hold for american options. Hence, I don't see how it would be possible to have one surface that would encompass both calls and puts. For example: Let pick a call lying in the ...
Rodrigo's user avatar
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Option Pricing for Illiquid case

I am currently studying crypto options trading and have observed that there is often a lack of liquidity for options (such as BTC Options) on various exchanges, including Binance. In many cases, there ...
Starlord22's user avatar
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1 answer
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Continuous delta hedge formula

When we buy a call and continuously delta hedge using some implied volatility $\sigma_i$, what is the formula for our aggregate profit given that the actual realized volatility is $\sigma_r$? Say $...
deriv's user avatar
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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 ...
Philipp's user avatar
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Arbitrage Free Volatility Smile

When ATM implied volatility is higher than OTM put and call I believe that the volatility smile is no longer arbitrage free? Why is that? On the other hand, when ATM implied volatility is lower than ...
chengcj's user avatar
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What does implied volatility say about the underlying?

Here's a question that's been on my mind on-and-off for some time now. It's well known that Black-Scholes is an unsuitable model for pricing in the current (post 80s) market as it fails to capture the ...
OJK's user avatar
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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 ...
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Where can I find caplet implied volatility data?

I am looking for caplet implied volatility data for Libor-EUR. Is there any online data base etc. available to get such data? Does ...
Brian Smith's user avatar
38 votes
5 answers
22k views

How should I calculate the implied volatility of an American option in a real-time production environment?

There are many models available for calculating the implied volatility of an American option. The most popular method, employed by OptionMetrics and others, is probably the Cox-Ross-Rubinstein model. ...
Tal Fishman's user avatar
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Calendar Arbitrage in a Vol Surface

I am trying to determine the condition such that my implied vol surface doesn't have calendar arbitrage. I have done research and found that one such condition is that total variance should increase ...
Jim's user avatar
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Why does implied volatility show an inverse relation with strike price when examining option chains?

When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts. As a current ...
Joseph Tanenbaum's user avatar
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3 answers
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How to exploit calendar arbitrage?

Say we are looking at European Call options in a toy environment with zero deterministic interest rates, a stock paying no dividends, no repo rates etc... Let $C(T,K)$ be the price of a call with ...
Alexander Chertov's user avatar
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0 answers
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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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7 votes
3 answers
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What is an efficient method to find implied volatility?

I have a code that finds the implied volatility using the Newton-Raphson method. I set the number of trial to 1000 but sometimes it fails to converge and doesn't find the result. Is there a better ...
opt's user avatar
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6 votes
2 answers
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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 ...
Van Tom's user avatar
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how to do interpolation in the term structure of volatility surface?

everyone~ I am a newbee in the quantitative finance and I meet a problem in working out an equity option volatility surface. We use the reasonable market data to derive the implied volatility, then ...
Tim's user avatar
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Bartlett's delta gives wrong signs for calls and puts

There is a paper by Bruce Bartlett introducing a modified delta for SABR model which accounts for the correlation between forward and volatility processes. The main result of the paper is that if $dF$ ...
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Realized Variance (realized volatility)

I'm confused about realized variance. I roughly know the theory around Ito Calculus and quadratic variation and integrated volatility so I understand what realized variance measures (even though as ...
s5s's user avatar
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3 votes
3 answers
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Normal vs Log normal implied volatility

I am referring to an earlier discussion at How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)? For the short rate case, is there any ...
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Valuation of Corridor Variance Swaps

Given that the payout of the Corridor Variance Swap (CVS) is $V \left(\frac{\sum_{n=0}^{N}I}{T_2 - T_0} (\sigma^2 - K^2) \right)$, where $\sigma^2$ is the realized variance within the pre-specified ...
AK88's user avatar
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6 answers
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How do you explain the volatility smile in the Black-Scholes framework?

Does anyone have an explanation for the currently naturally forming volatility smile (and the variations) in the market?
user avatar
20 votes
2 answers
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Gamma Pnl vs Vega Pnl

Why does Gamma Pnl have exposure to realised volatility, but Vega Pnl only has exposure to implied volatility? I am confused as to why gamma pnl is affected (more) by IV and why vega pnl isnt affected ...
Trajan's user avatar
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18 votes
4 answers
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Why is realized volatility typically lower than implied volatility?

A number of quantitative finance textbooks mention something along the following lines, without further explanation: A typical feature of implied volatility from stock index options is that it is ...
arni's user avatar
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18 votes
1 answer
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So many volatility models. Any comparisons of them?

Are there any papers that make an explicit contrast/comparison of the following (or other) vol models in terms of the suitability for addressing some empirical problem? Wavelet multiresolution ...
Jase's user avatar
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17 votes
2 answers
7k views

How to extrapolate implied volatility for out of the money options?

Estimation of model-free implied volatility is highly dependent upon the extrapolation procedure for non-traded options at extreme out-of-the-money points. Jiang and Tian (2007) propose that the ...
Tal Fishman's user avatar
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16 votes
7 answers
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Why does the volatility smile flatten as maturities increase?

First, I can't find a purely "financial" explanation for this. Also the only mathematical explanation I've found so far was using the large deviations theory, which is quite complex. Is there a ...
Dark's user avatar
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3 answers
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Volatility arbitrage - how is the profit extracted?

Is there any paper that describes in detail how the profit is extracted in directional volatility bet (vol arb)? I mean in the case that I bet the realized volatility will be lower than currently ...
Paya's user avatar
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12 votes
5 answers
2k views

Why use implied volatility

First I'll describe the way I understood things so far from the literature, feel free to correct me here, and then I formulate some questions. I'd search through QSE, but haven't found so far similar ...
SBF's user avatar
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11 votes
1 answer
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Transition Between Volatility Regimes

Emanuel Derman wrote a great paper in 1999 about volatility regimes and the adjustments the market makes during these periods (sticky strike, sticky implied tree, sticky delta, etc). Has any ...
Jared's user avatar
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10 votes
2 answers
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How to calculate the most realistic historical option prices with additional publicly available parameters

This is a follow up question of this one. My aim is to create the most realistic historical option prices possible with publicly available data. I want to do this for backtesting purposes. The ...
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9 votes
2 answers
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Is there anywhere I can read the paper, "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves"

Hello there was a paper published by: M. Arslan, G. Eid, J. El Khoury and J. Roth titled "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves" (2009). I believe they ...
user avatar
8 votes
2 answers
6k views

Local vol, stochastic vol, implied vol

I've been studying volatility modelling over past the few days; in particular, the connections between local vol, stochastic vol, implied vol. I've been reading Gatheral's book "The volatility surface"...
Ryan J. Shrott's user avatar
7 votes
2 answers
983 views

What's the connection between implied vol curve of SPX and SPY?

I think there should be an obvious connection of the two implied vol curves from the SPX and SPY markets since the underlying of SPX is SP500, while the underlying of SPY is a ETF which tracks sp500 ...
DeepRed's user avatar
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7 votes
1 answer
1k views

What is the connection between the risk neutral implied density and the real world density?

I understand that we can use option prices to imply volatilities and ultimately to imply a risk neutral density. I also understand that this implied density is not the same as the "real world density"....
roz's user avatar
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6 votes
2 answers
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How can I calculate the strike price or implied volatility from a given delta?

I have calculated the implied volatility for all strikes of a certain product (options on futures) and approximated the ATM volatility. My question is how can I figure out the implied volatility for a ...
Stu's user avatar
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6 votes
2 answers
3k views

Lower bound of ITM Calls when computing Implied Volatility

Assuming the Black Scholes model and pricing formula of a European call option. Then, if the call is ITM, i.e. if $ln(\frac{S}{K})>0$, the $d_1$-term will go towards infinity as $\sigma$ goes to ...
Good Guy Mike's user avatar
6 votes
1 answer
4k views

When to use a Local Vol model vs Stochastic Vol Model?

I'm new to volatility modeling, I'm struggling to understand when to use a Local Vol model and when to use Stochastic Vol Model, Also now we use a hybrid model combining the two models ? Can someone ...
Gogo78's user avatar
  • 636
5 votes
3 answers
4k views

Implied Vol vs. Calibrated Vol

Consider the Black-Scholes model, in which the log stock return over a time period $\Delta t$ is given by $$ \log(S_{i+1}/S_i) = (\mu - \sigma^2/2)\Delta t + \sigma \sqrt{\Delta t} Z_i, \qquad Z_i \...
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4 votes
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How is Emanuel Derman's implied tree model implied volatility skew derived?

I am reading Emanuel Derman's paper Patterns of Volatility Change. The section, Implied Volatility In The Sticky Implied Tree Model has the linear skew approximation near the old underlying $S_0$ $$\...
Hans's user avatar
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3 votes
1 answer
266 views

Compare equity option volatility under SOFR vs LIBOR

We know that after the big bang from LIBOR to SOFR, LIBOR will eventually disappear. This brings up one question that I do not have a clue to answer: How to evaluate derivative in a consistent manner ...
user avatar
2 votes
2 answers
2k views

How should I convert FX Volatility Surface from one base currency to another?

This might be a very simple question but I wanted to understand how to convert FX volatility surface points which are quoted in one base currency to another currency? Eg I have fx vol quoted in EUR ...
InfoLearner's user avatar
2 votes
2 answers
3k views

SABR Implied Volatility and Option Prices

I am trying to understand the SABR model. Specifically, I am having difficulty to understand how to calibrate the model parameters, that is, initial variance, volatility of variance, exponent for ...
user1131338's user avatar
2 votes
3 answers
445 views

Why is $dS/S$ an estimate of realized volatility?

For one period, $dS/S$ is an estimate of realized volatility, which we can annualize by dividing with $\sqrt{\Delta t}$. But.... why? How is $dS/S$ an estimate of volatility? Volatility is, to me, ...
Jaood's user avatar
  • 285
1 vote
2 answers
562 views

Converting implied volatilities into digital option prices

I have Black and Scholes (1973) implied volatilities computed and I would like to convert these IVs to digital option prices using a Black and Scholes type of formula, I can't find a formula to do ...
pyCthon's user avatar
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26 votes
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What does the VIX formula measure and how does it work?

I have read the CBOE's white paper on the VIX and a lot of other things, but I need to honestly say, I don't really get it, or I am missing something important. In semi-layman's terms, is the VIX ...
CQM's user avatar
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