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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589 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 ...
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2answers
188 views

Is there a better way to price options than with historical volatility?

I know that annualized historical volatility calculated with closing prices is a much rougher estimate than implied volatility for the correct "volatility" parameter in options pricing models. ...
4
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2answers
356 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 ...
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4answers
3k views

How to calculate the implied volatility using the binomial options pricing model

I want to calculate IV for american options with dividends. So far I have found algorithms to calculate the option price given a volatility. Please can you point me to paper or implementation (R, ...
4
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2answers
136 views

Bloomberg implied volatility smile for equities

I was wondering if someone knows how Bloomberg does their computations for the implied volatility smile for equities. As far as I understand, they use a lognormal mixture to model the stock prices. ...
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2answers
177 views

Indexes/stocks with flat implied volatilities

After the 1987 crash, the S&P500 index implied volatility changed from nearly flat to negatively sloped. According to Rubinstein the Black-Scholes model was not so wrong when applied to the ...
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1answer
60 views

Determining the implied volatility for options with bid/ask prices below the intrinsic value

I need some help in understanding the Black-Scholes option pricing model. In my data there are several deep itm European index put options that have an ask price below the intrinsic value. ...
4
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2answers
79 views

Implied volatility and nonconstant volatility

John Hull states in his text that "AS the maturity of the option is increases the percentage impact of nonconstant volatility on (option) prices becomes more pronounced, but its percentage impact on ...
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3answers
902 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 ...
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1answer
499 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 ...
4
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1answer
150 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 ...
4
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1answer
368 views

Volatility Return Distribution/Garch Modeling

For simplicity sake, if stock returns are normally distrusted, would that imply that second moment, variance/volatility, is chi-squared distrusted? If so wouldn't that imply the statistics(employed to ...
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2answers
635 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 ...
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1answer
4k views

When the Inverse Correlation between the SPX and VIX breaks down

As we all know the S&P and its implied vol, the VIX, generally move in opposite direction. To a large extent, the correlations makes sense. IV is one of the main drivers of the price of options, ...
4
votes
3answers
317 views

self-consistent parametric form for equity implied volatility

I recall reading a paper, but can't remember where I found it. In short, there was a parametric form for volatility smile/skew that fit both index and single stock vol slices and had intuitive ...
4
votes
2answers
122 views

Relation between IV and SD

In option pricing, volatility naturally appeared through the Black-Scholes (BS) model where it was a coefficient for the linear diffusion term $\sigma S\,\mathrm dW_t$, and as such represented the ...
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1answer
100 views

Extrapolating SVI

In his paper Gatheral presents the following parametrization of the implied total variance $w(k,T) = \sigma_{BS}(k,T)^2T$ $$ w(k) = a + b\{\rho (k-m) + \sqrt{(k-m)^2 + \sigma^2} \}.$$ Assuming that ...
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4answers
5k views

Why is short term implied volatility typically higher?

Why do short term implieds move more than long term?
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2answers
58 views

Difference in implied volatility calculation

I've been using vollib to calculate IV, but my answers have been different by tenths from other sources like NASDAQ and Yahoo. The answers range +- 0.5, sometimes even more. The inputs are: $S$ ...
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1answer
124 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 ...
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3answers
123 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 ...
3
votes
1answer
81 views

How to get Correlation using Options data?

I can calculate the "Implied Beta" using implied volatility for the option stock, and implied volatility for the market (VIX). Is there any way to calculate also the correlation without performing a ...
3
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1answer
164 views

Different Exercise Style Options on Same Underlying

Some equities on European markets have options traded in two different exercise styles: American and European. Examples: ABB and ABB (european) on Eurex Banco Santander on MEFF Consider ...
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1answer
503 views

Interpreting QuantLlib implied volatility numbers

I am using QuantLib to calculate implied volatilities. I am trying to understand the calculated figures (especially, when compared to historical volatility). The calculated implied volatility numbers ...
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2answers
1k views

How to calculate COMPOSITE underlying implied volatility from ATM (near month) option prices?

I am trying to calculate the implied volatility of an underlying given observed prices of call and puts. There are two scenarios: The ATM strike is pinned by the market (i.e. underlying level == ...
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votes
1answer
201 views

Is it possible to estimate the correlation between an equity and its IV, purely from its IV skew?

If we know the options Implied Volatility (IV) skew for an equity, is it possible to calculate the probability of the equity moving, given a move in the IV? We can define IV skew as the difference ...
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1answer
33 views

Valuation of option on amortized IR swap

I'm currently valuing swaptions using an implied volatility surface and Black's formula. This formula is given by $$A (S\Phi(d_+) - K \Phi(d_-))$$ where $$ d_{\pm} = \frac{\log\left(S/K\right) \pm ...
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1answer
210 views

Why is the volatility smile important

One thing I can't understand clearly is why there is so much focus on the volatility smile. Given my knowledge of the Black and Scholes model, this is what I get: People use the volatility smile as a ...
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votes
1answer
170 views

Why future (forward) volatility smile is important to path dependent option?

I was wondering why future volatility smile is important to path dependent option and American type option such as Bermudan swaption. It would be best if someone could provide a reference article as ...
3
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1answer
829 views

Implied Volatility for Asian option

I am new to the topic of Asian options. Assume I want to price an Asian put (fixed strike, discrete average) in the Black Scholes world. I know implementations to calculate the value but what is the ...
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votes
1answer
527 views

Why does Skew measure remain more-or-less constant for Listed Expiries?

I have looked at the Variance Swap Papers published by GS-VarSwap and JPM-VarSWap where they talk about approximation to VarSwap strike using ATMF vol and Skew (slope of the volatility skew for 90-110 ...
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votes
1answer
85 views

Constructing a minute-by-minute volatility curve

For market making in front month vanilla commodity options we need a volatility curve that updates every second or so as the underlying and the options change prices. If all the strikes have a good ...
3
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1answer
129 views

Hedging - calculating option prices using implied volatility surface

To hedge a strategy is it accurate "enough" to price an option using an implied vol curve vs moneyness (strike/spot) assuming sticky delta? The moneyness can be read off the chart, its corresponding ...
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0answers
66 views

Discount of Asian vs European vols

I understand the discount for Asian vs. European vol depends on time to expiry and length of averaging period. This makes sense intuitively; a short averaging period far away blurs into a single ...
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0answers
130 views

What is the relation between return volatility and return rank volatility, and how can I control the latter?

I have no experience in finance, but I've been playing around with a virtual portfolio. I'm trying to control the "rank volatility" distribution - that is, the volatility of a stock's daily rank in ...
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0answers
147 views

Could the Implied Volatility distribution change again? [closed]

It is well documented that following the stock market crash in 1987 the prices of options started to demonstrate skew and smile in the distribution of implied volatilities. This feature has been ...
3
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0answers
193 views

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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votes
2answers
245 views

Is implied volatility flawed?

Was going through how Implied Volatility is used by option traders and in delta hedging. Correct me if I am wrong, doesn't IV consider a standard deviation of the stock price over say the past 1 year? ...
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votes
2answers
482 views

Black-Scholes: Why the focus on volatility?

We know Black-Scholes is an imperfect model for options pricing. Why is so much of the analysis of its defects focused on implied volatility? The fact that IV varies for the same stock at the same ...
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votes
2answers
416 views

VSTOXX Implied Volatility Calculation

What is the industry consensus (if it exists) about implied volatility calculation for options on VSTOXX (OVS)? I've experimented with the following approach: Standard Black-Scholes VSTOXX futures ...
2
votes
1answer
214 views

Why is IV different between put and call of same strike

In his book 'Dynamic Hedging' Nassim Taleb says that the volatility of an OTM put should be exactly equal to that of a corresponding in the money call of same strike. But in option chains, the ...
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2answers
382 views

Is there a good closed-form approximation for Black-Scholes implied volatility?

While the solution for IV can certainly be reached using numerical search methods, I wonder if a high precision closed-form approximation exists. For example, there is a very robust (precise within ...
2
votes
2answers
2k views

Delta Neutral / Gamma Neutral Positions

I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ...
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2answers
238 views

How to interpret Realized Volatility and TSRV using R

I am looking at some high frequency data and I would like to know how to interpret and compare Realized volatility (RV) and Two Scale Realized Volatility (TSRV). References below. Given X is the log ...
2
votes
1answer
115 views

Effect of vol smile on risk neutral probability of ITM

I was asked in an interview about how the vol smile affect the price of a binary option, which is essentially the Prob(ITM) under risk neutral measure. My thought is that the implied vol at spot ...
2
votes
1answer
85 views

If an option went down in value, how much is due to theta decay and how much due to fall in IV

Let us say that there was a stock trading at 100 and the 105 call was trading at 3 $. with 1 month to go Now stock went up to 104 after 15 days, and the call dropped to 2.80 $, to the call buyer's ...
2
votes
1answer
226 views

Some questions about implied volatilities and how to generate theoretical prices when market prices are not available

I am building a little Excel file that take some option prices in input and plots the volatility smile/surface. I have a script that reads market prices from the option chain for 3 different ...
2
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1answer
329 views

Commonly used vol surface calibration model in the industry

I have 2 questions: What is the most commonly used equity option pricing model? I learned jump diffusion at school, read about Hensen and a few other models online. I am actually only calibrating ...
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1answer
613 views

How does Volatility Pairs Trading work?

I've read some material related to pairs trading for equities and I understand the process of finding non-stationary pairs price series that can be cointegrated to form a stationary series. The basic ...
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1answer
543 views

European Swaptions: does implied volatility of swap rates decreases both with start and tenor?

Does implied volatility of swap rates decreases both with start and tenor? Given a Swaption price and a discount curve I calculate the swap_rate from the curve, then I define implied volatility as ...