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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29
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4answers
21k views

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: ...
35
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5answers
67k views

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, ...
10
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1answer
1k views

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 ...
28
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5answers
14k 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. ...
4
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1answer
2k views

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 ...
8
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2answers
2k views

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 ...
5
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3answers
5k views

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 ...
9
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0answers
285 views

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 ...
26
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5answers
18k views

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?
6
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2answers
2k 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"...
18
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1answer
2k views

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 ...
14
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2answers
5k 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 ...
10
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4answers
1k 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 ...
10
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3answers
5k views

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 ...
10
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2answers
2k views

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 ...
2
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2answers
1k 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 ...
5
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1answer
1k views

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 $...
2
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3answers
215 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, ...
6
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2answers
1k 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 ...
14
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3answers
9k views

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 ...
10
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1answer
3k views

Delta Hedging with fixed Implied Volatility or floating Implied Volatility?

When delta hedging an option until expiry at implied volatility, is it better to rehedge using the fixed implied volatility given by the option price upon its purchase (or sale), or to rehedge using ...
9
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4answers
1k views

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 ...
9
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1answer
1k views

For pricing, what types of Exotic Options are suitable using Local Volatility Model or a Stochastic Volatility Model?

I understand that stochastic volatility models should be used when the exotic option payoff is volatility dependent (such as variance swaps and volatility swaps). Stochastic volailtiy models should ...
7
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3answers
2k views

Forward implied volatility

Can one price accurately by only using vanilla options a derivative that is exposed/sensitive mainly to the forward volatility ? If it is impossible, why do we hear sometimes "being long a long ...
19
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8answers
11k views

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 ...
15
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5answers
9k views

What is a regime switch?

I've come across the term regime switch in volatilities when reading about the modelling of interest rates but could not find a definition for a regime switch and what a regime is. Can somebody give ...
11
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3answers
18k views

Does implied vol vary for calls vs puts?

Volatility skew tells us that options with the same maturity at different strikes can have different implied vol. However, can a corresponding call and put for the same strike and maturity have ...
9
votes
1answer
769 views

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 ...
7
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2answers
2k views

Constructing an approximation of the S&P 500 volatility smile with publicly available data

Besides of the VIX there is another vol datum publicly available for the S&P 500: the SKEW. Do you know a procedure with which one can extrapolate other implied vols of the S&P 500 smile with ...
3
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2answers
1k views

Delta Hedging with fixed Implied Volatility to get rid of vega?

I'm wondering if i should use a floating IV or a fixed IV to delta hedge my options every day. I've read this post but would like different information : Delta Hedging with fixed Implied Volatility ...
5
votes
2answers
846 views

SKEW and VIX relations?

My question is about the CBOE published index VIX and SKEW. To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston model....
3
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1answer
2k views

Implied Volatility Surface - log forward moneyness

I'm reading this paper by Fengler (2005) and have came across the below snippet. context: Implied volatiltiy surface plot has 3 dimensions IV, Strike, Time to Maturity. Author replaced Strike with ...
8
votes
1answer
275 views

Jim Gatheral's assertion on ATM implied volatility vs. square root variance

In Jim Gatheral's book The Volatility Surface Section Dependence on Skew and Curvature on page 138, he asserts that We know that the implied volatility of an at-the-money forward option in the ...
8
votes
3answers
2k views

Concave volatility smile

Under what circumstances can implied volatility smile be concave (ATM implied volatility higher than OTM put and call)? I know that a slight concavity is not prohibited by no-arbitrage... What are ...
8
votes
5answers
1k views

Does an implied volatility always exist for a binary option?

I'm trying to compute the implied volatility of a binary option but I cannot get some of the strikes to reach a convergent solution using either a Monte Carlo pricing model or an analytical Black ...
8
votes
1answer
1k views

How to approximate the time to mean reversion for implied volatility

Given an option and its implied volatility, and also the mean value of the implied volatility over the last 30 days, if we find that the current IV is significantly (> 1 std dev.) away from the mean, ...
6
votes
3answers
2k views

Which volatilities should I use for Quanto Options?

Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate. How can I read the "right" volatilies ...
4
votes
2answers
9k views

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 ...
2
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1answer
1k views

Log-normal Volatility Approximation

In a comment to this question, it is mentioned that, under the log-normal distribution, \begin{align*} vol(k) \approx vol(atm) \times \sqrt{\frac{atm}{k}}. \end{align*} Here, $k$ is the strike, $atm$ ...
8
votes
3answers
891 views

How to calculate Implied Volatility for out-of-the-money options?

I'm trying to calculate the implied volatility for out-of-the-money options, and to a lesser extent, in-the-money options. Most of the literature estimations I could find for implied volatility were ...
5
votes
0answers
445 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 ...
2
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1answer
140 views

Why isn't this IV calc correct?

I'm trying to calculate implied volatility for the following put option: Stock price = 185.55 Strike = 180 Option price = 3.00 Days to expire = 63 I've run the ...
1
vote
1answer
209 views

What is market standard model in equity, FX and interest rates exotics?

Is there any industry consensus about the model to use for pricing exotics in equity, FX and interest rates? I assume that for vanilla options they all use Black model, but how about exotics? Also, ...
1
vote
1answer
474 views

Why is the VIX computed that way?

The VIX as a clear definition as defined in this paper I am interested to know why they came up with this formula. I smell some reasonably complicated explanation here so any pointer to a paper ...
7
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1answer
4k views

SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
6
votes
1answer
484 views

How is implied volatility derived?

How to compute Implied Volatility Calculation? The above link shows that there multiple ways to calculate implied volatility. My question is that for most of the common data sources like Bloomberg, ...
6
votes
1answer
202 views

Derivation of the Stochastic Vol PDE

I'm trying to follow the derivation of the stochastic vol pde for an option price - as given in Gatheral (The vol surface), Wilmott on Quant Finance and many other places. As usual one starts off with ...
5
votes
0answers
203 views

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 ...
4
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4answers
11k views

Why is short term implied volatility typically higher?

Why do short term implieds move more than long term?
3
votes
3answers
419 views

Implied volatility of a complex options position

Assume I have a "complex" options position like a straddle, strangle, or iron condor. In other words, several options traded together as a single position against one underlying asset (not a basket ...