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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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Black-Scholes volatility implied by stock prices only

I was solving Problem 2.47 from T.F. Crack's "Heard on the Street". I think that the answer given in the book is not correct and I would be thankful if you tell me, where I am mistaken. Question 2....
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34 views

Temporal aggregation of daily implied volatilities

Suppose I have a time series of daily implied volatility values for a given month and I am interested in calculating the monthly implied volatility for that month. What would be the most theoretically-...
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77 views

Is there a simple, intuitive derivation (using Taylor series) of the following approximation to Vega-weighted Implied Volatility?

The approximation is: $$\sigma \approx \frac{\sum V_j\sigma_j}{\sum V_j}$$ Background information from the first answer to this post: "Say that you have a portfolio of options with prices $P_j$. ...
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30 views

Alternatives to implied or historical volatility for calculating implied correlation

For my thesis, I'm trying to calculate implied correlation values from bivariate options. I train my model on 10 years of returns data, price the options, and then invert Stulz's Formula (basically ...
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91 views

Implied volatility in Monte Carlo models

Suppose I want to get the implied volatility for a given option, whose process does not generate a closed-form formula. In that framework, how is the IV calculated, given the fact that bisection ...
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58 views

Can implied volatility be 0?

I am calculating IV for intraday options and sometimes I am getting the value as "0"? Is that possible? For example: Strike = 26700 PE Fut = 26962.55 Spot = 26902.55, TimeToExpiry = 797340sec. Price ...
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40 views

Reasonable Minimum Value for Volatility?

I am looking at an implementation of Bjerksund and Stensland (2006), and notice that it doesn't work well for very small volatilities. What is a reasonable minimum volatility to use in an algorithm ...
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79 views

Strategy for implied volatility

I encountered this question: "A trader observed that the implied vol of OTM calls and puts are higher than that of ATM option, what is the best strategy among: Calendar Spread, Bull Spread, Bear ...
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1answer
83 views

Short time to maturity behaviour of implied volatility

There are several perturbative expansions in derivatives literature on the short-time to maturity behaviour of implied volatility. When it comes to implied volatility in (local) stochastic volatility ...
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77 views

Why historical volatility is calculated as N-days annualized?

Annualized historical volatility is always calculate with 10-, 20- days time window. I don't quite understand. Compare with annualized historical return, annualized historical return is never ...
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0answers
85 views

Fitting Gatheral's SVI model

I was considering using Gatheral's formula for fitting option skew. In the specific (commodity) market that I am concerned with, the underlying is ca. at 50, and typically 5 integer strikes left and ...
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3answers
158 views

What does Volatility Smile tell? [closed]

Could you please share your opinions about Volatility Smile? What does it tell us when it gets more convex or when its level changes over time or any other change on it. Any paper/work/blog ...
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108 views

python scipy optimize minimize arguments for Implied Volatility

I am having some trouble getting the 'correct' solution to a function where I am trying to utilize scipy.optimize.minimize. In the code below, I create a function <...
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70 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) ...
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1answer
150 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, ...
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1answer
71 views

Volatility surface tenors

I don't think this has been asked before, but are the tenors on a volatility surface out of spot date for the currency pair or out of value T+0?
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28 views

The Free Boundary SABR: Natural Extension to Negative Rates

In the paper by Antonov, Konikov and Spector An alternative approximation for the SABR model is presented. I'm interested to implement the formula for the ATM swaptions implied volatilities in the ...
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2answers
325 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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385 views

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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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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52 views

Term structure of the ATM implied volatility of short term weekly options

It's an empirical fact that the implied volatility of short term weekly options are significantly higher than options that expire in a few weeks, and the volatility of the near term options get even ...
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1answer
202 views

Vanilla Option Prices from Local Vol Surface (using neither MC nor PDE)

There are numerous papers that describe the derivation of the Local-Vol equation using available market prices of options. For example: Dupire's formula (see e.g. OpenGamma (2013)) gives us LV in ...
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1answer
178 views

What is forward moneyness and how to calculate it?

I'm now studying the concept "implied volatility", and my teacher gave us a figure about the implied volatility with respect to the moneyness which is expressed by ...
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2answers
211 views

What is the Brownian motion in the model for the return of a stock price trying to capture?

I have read that in the derivation of the Black-Scholes PDE, we assume that the return of a stock $S$ is given by $$\frac{dS}{S}=\mu dt+\sigma dB$$ where $\mu$ is the average growth of $S$, $\sigma$ ...
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38 views

What volatility to use to estimate BDT?

I am attempting to estimate the value of a bond with prepayment option (callable bond). In order to do so, I am fitting a lattice to the Libor Swap curve using a BDT model. The measurement date is ...
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66 views

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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40 views

Smoothing of Implied Volatilty

I'm using ATM 30D implied volatility in a model I'm building, but need to smooth out the data. Is the best way just to use exponential smoothing or are there any better alternatives?
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2answers
185 views

How is volatility different from variance?

I always thought volatility was just variance ^ (1/2). Now I'm reading this book and it's saying that the two are different concepts. Excerpts include: Partly due to its use in Black-Scholes, ...
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1answer
135 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 ...
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1answer
62 views

implied volatility indice and implied volatility [closed]

Can anybody explain to me Why should we calculate implied volatility if there is already an implied volatility index where implied volatility is already calculated??? I can't understand the difference
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30 views

Data request: Option prices for a liquid index/stock

Currently doing a course project on option pricing as a part of my undergraduate studies. However I cannot find a free dataset $D=[d_1,d_2,...,d_N]$, which would represent a time-serie of daily option ...
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1answer
48 views

Filter options used in the construction of implied volatility surface

Currently trying to model the IV Surface using the APPL options, to compare how different models of the underlying move the IV Surface. However, after getting the data, I've seen that some option ...
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1answer
77 views

VXX Put pricing

Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
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Basic questions on options, implied volatility and SPY

I am a bit confused about the impact of implied volatility on options, SPY options especially. I know that option's price decays with time and that is positively correlated with implied volatility but ...
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92 views

Black Scholes on Eurodollar Options

I am trying to replicate the Black Scholes results of CME option calculator for options on Eurodollar Options. (link) I am trying to replicate the implied volatility result by unaltering the spot and ...
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1answer
121 views

Why are implied volatility and the volatility required for an option to be profitable two different things?

SPY currently trades at $278, a put option expiring in 7 days against SPY, at this strike price, quotes \$2.40. This means one person (the option buyer) is betting SPY will quote below $280.40 (278 + ...
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51 views

Black-Scholes IV from Characteristic Function

I'm trying to follow Gatheral 2006 on his derivation of the BSIV from a characteristic function. The most relevant formula is (5.7) page 60. $$\int_0^\infty\frac{du}{u^2+(1/4)}\Re[e^{-iuk}\left(\...
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1answer
72 views

For equity options, does the implied vol change if the price of the underlying does?

For example, consider S&P options. My reasoning is rooted in the fact that VIX returns and S&P returns have a negative relationship, since VIX is a measure of S&P options' implied vol. ...
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1answer
277 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, ...
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1answer
263 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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105 views

Calibration of parameters of implied vol smile

Here is the book Foreign Exchange Option Pricing: A Practitioner’s Guide, p.56 by Clark (2015). The context is a little bit long. I summery my understanding as follow: We first assume the form of ...
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48 views

Wrong understanding of implied vol cannot be linear interpolated

There is a well known conclusion that implied vol cannot be linear interpolated. But I am not sure this interpolation is for ...
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1answer
140 views

Linear interpolation of local vol no arbitrage

We already know the equivalence between local vol, implied vol and option price and there ...
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1answer
94 views

Implied volatility for American options- time to expiration?

I am trying to compute the implied volatility of the OBM contract (on Euronext), using R, and I was wondering if, for the time to maturity, I should put the time until the contract expires or the time ...
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74 views

Expected VIX at different levels of SPX

I'm looking for a model that computes the expected VIX based on SPX price moves. For instance, SPX is currently at around 2650, and VIX is at 24. If SPX jumps to 2600, at what level would the VIX be? ...
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145 views

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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1answer
132 views

Suggestions of papers for computing market implied probability distribution function

I need suggestions of papers that propose simple and fast methods (not heavily dependent on simulations, nut can depend on simulation) to derive the market implicit probability distribution function ...
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1answer
114 views

Of what use is this implied volatility formula?

From a paper I am reading, it is written These equations do not make any sense. If $s = k$, i.e. if we are pricing ATM options, then this volatility is identically zero, hence useless. How am I to ...
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1answer
147 views

Interpretation of IV and its use in stock movement prediction

I would like to validate my understanding of IV as a prediction tool. Black-Scholes model is based on the assumption that rate of return of a stock is a Wiener process: $$ \frac{dS_t}{S_t} =\mu \,...
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suggestion for NDX volatility index prior to 2000

NDX index is available since 1984 in Bloomberg. There's VXN index that represents the implied volatility of NDX, which is available since 2001. I need some index or series that represents implied ...