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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1answer
391 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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218 views

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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2answers
378 views

Does higher vega imply higher IV and vice versa

If an option A has higher vega than option B, does that also mean that A has a higher IV than B? I understand that by definition, a higher vega means that A's price is more sensitive to its IV than B. ...
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2answers
297 views

How to derive this approximation of the risk-neutral expectation of the variance?

On the paper Bollerslev, Tauchen and Zhou (2009 RFS) the authors say about equation (15): The corresponding model implied risk-neutral conditional expectation $$E^Q_t(\sigma^2_{r,t+1})=E_t(\sigma^...
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1answer
618 views

SSR definition in Bergomi in relation to sticky strike and sticky delta

In Bergomi [Stochastic Vol Modelling] (Sec. 2.5.2), in the section on surface dynamics, the following definition of the "Skew Stickiness Ratio" (SSR) is made: $$ SSR = \dfrac{1}{\mathcal{S}_T}\frac{d\...
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 ...
5
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2answers
194 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 S&...
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 $...
5
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1answer
167 views

Why do we fit volatility surfaces implied from a option pricing model to the empirical data?

As far as I understand volatility surface. It is made of 2 components, the volatility skew/smile and the volatility term structure. Together they form something like Implied volatility is ...
5
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3answers
463 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 ...
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1answer
149 views

Nested volatility

The introduction VIX options makes the concept of "volatility of volatility" a real life concept. The idea of "nested volatility" seems interesting, and I am wondering if there are any academic ...
5
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1answer
279 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 ...
5
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1answer
482 views

Comparing historical to implied volatility

As title states, I am trying to compare historical to implied volatility of a stock. I approximate the single implied volatility (30 days forward) of the stock by first finding 2 series that ...
5
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1answer
145 views

Why is the implied volatility on Bank of Tokyo-Mitsubishi UFJ trending so high?

For the last few weeks, the 12-month ATM call implied volatility of MUFG (TSE 8306) has been trending around 30-35% (according to Bloomberg). This is by far the highest of the major Japanese banks by ...
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496 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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205 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 ...
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2answers
3k views

Why an option has sometimes and implied volatility greater than 100%?

Sometimes, in an option chain, the implied volatility of an option is greater than 100% . How is this possible? I mean, it is possible for 100$ stock to increase more than 100%, but not decrease more ...
4
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4answers
2k views

How to select the initial guess for implied volatility?

When we calculate the implied volatility, we would need to give the solver a range to start with. For example, QuantLib uses [0,4.0] for the range, which is another way of saying try all possible ...
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2answers
5k 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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4answers
980 views

Trading spot volatility

I am reading a paper that very briefly talks about some volatility arbitrage strategies. It's so brief that I do not exactly understand how it works. It says one of the strategy is based on "short ...
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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?
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2answers
2k views

Sticky Strike or Sticky Delta

Given market tick data for a single tenor for a futures and a set of options on the futures, how can I say if the IVs in the market at this point is sticky strike or sticky delta? I was trying to ...
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2answers
168 views

Deriving implied volatility programmatically

I'm working on a project to calculate the value of options using Python. I'm using the Black-Scholes model, and I can get accurate results by plugging in a given ...
4
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1answer
279 views

Options Market Making Used Implied Volatility Surface

Suppose you are a market maker with a model that is producing an implied volatility surface for you. Suppose you quote bid/ask prices (vols) around the prices given by your implied vol surface. In ...
4
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2answers
850 views

Is the Implied Volatility Curve different under the Black-Scholes and Bachelier models?

Say we plot the implied volatility against strike price and moneyness for some options. As the implied volatility depends on the option pricing model it is reasonable to expect some differences here. ...
4
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1answer
3k 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 ...
4
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2answers
270 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
688 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 ...
4
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2answers
103 views

What are popular metrics for Option Skew?

What are popular metrics to track skew? Would it be the difference between OTM option and ATM option IV? Would it be a percentage difference in IV? Also, if both are valid, would a % change be ...
4
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1answer
658 views

Proof of arbitrage-free implied volatility surface in relation to local volatility surfaces

I'm looking for proof of the following statement: "The existence of an arbitrage-free implied volatility surface is equivalent to the existence of a well-defined local volatility surface."
4
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1answer
198 views

Implied vol vs Realised vol on Event Days

How implied vol varies vis-a-vis realised vol on an event days?
4
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1answer
541 views

Realized volatility forecast vs Implied volatility

I have forecasts of realized volatility, as well as implied volatility for individual traded options of the S&P500. I want to simulate a simple trading strategy; that is, buy signal=1 if ...
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2answers
2k views

Autocallable pricing under stochastic vs. local volatility

I am interest in the reason why an Autocallable (structured product) is cheaper under local volatility compared to stochastic volatility. I thought this was due to the following: when thinking in ...
4
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2answers
337 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 ...
4
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3answers
815 views

Why can't you arb skew by buying options with low implied vol and selling high implied vol in the same month and dynamically hedging?

there's something I've been trying to understand for a while now and I just can't quite understand with regards to skew. In the same month, why can't you buy a option that have low implied vol on the ...
4
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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 ...
4
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1answer
582 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 ...
4
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1answer
753 views

Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
4
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1answer
565 views

Volatility Surface Constituents, do's and dont's

Recently I have been working a lot with implied volatility and volatility surfaces. The basic idea is easy to follow: 1) Gather market prices of options at different (Strike,Expiry) 2) Calculate ...
4
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1answer
2k 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 ...
4
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1answer
322 views

Local Volatility with Monte Carlo Simulation

I am trying to implement a Monte Carlo Simulation using Local Volatility Model (Dupire’s Equation). I’m pretty sure I can build a very good LV surface, however, I do not know how to use it in the MC ...
4
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1answer
153 views

Effect of Vol-of-Vol on VIX

What is the effect of vol-of-vol of an underlying on the VIX Index? The VIX is computed as hedging portfolio of log contracts to isolate pure volatility exposure without specifying an underlying ...
4
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1answer
238 views

Using SVI model for IV surface

I am using well-known paper of J. Gatheral & A. Jacquier Arbitrage-free SVI volatility surface to explore SVI model. on the page 6 in the bottom is statet that The SVI-Jump-Wings (SVI-JW) ...
4
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1answer
298 views

Splitting theta from vol carry

What is the best way to splitting theta and vol carry on say a long calendar trade? Basically trying to split the "good" carry component of a trade from the "bad" carry (theta) which could be earned ...
4
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1answer
595 views

Modern market conventions for interpreting interest rate swaptions quotations in a negative interest rate environment

I have broker data and I see three sets of swaption vol data: Lognormal (Black) Shifted Lognormal (Black with displaced diffusion) Normal (Bachelier) The quotes are given by the following key (Date, ...
4
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1answer
595 views

MTM Hedging Performance of Vanna-Volga

I was wondering how well Vanna-Volga (VV) Implied Vols "perform". So I experimented with the following option parameters $$S_0=100,\ K=92,\ r=0.03,\ q=0.01,\ T=2$$ and VV parameters $$K_1,K_2,K_3=...
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1answer
3k views

Where can I find open swaption implied volatility data?

Anyone have a good place to find interest rate swaption implied volatility data? Does Bloomberg's python API allow access?
4
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2answers
198 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 ...
4
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1answer
574 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 ...
4
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1answer
181 views

Dependence of implied volatility on spot-vol correlation

I have the following general SV model: $$ dS = \sigma S dW_S $$ $$ d\sigma = a(\sigma,t) dt + b (\sigma, t) dW_\sigma $$ $$ dW_S dW_\sigma = \rho dt $$ where $a , b$ are deterministic functions of $\...