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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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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177 views

No arbitrage conditions for normal implied volatility

usually the term implied volatility refers to Black-Scholes implied volatility (also Log-Normal volatility): it is defined as a quantity which when plugged in the Black-Scholes formula returns the ...
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617 views

compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
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175 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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240 views

implied volatility and strike price

Assume for simplicity that the expiration time of an option is $1$ the initial stock price is $1$ and there is no dividend yield and the risk free return is $0$. How is it possible to show that the ...
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214 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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196 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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76 views

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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403 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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2k views

Implied volatility from American options using python

I am currently trying to construct volatility surface from american option prices (using Cox-Ross-Rubinstein tree) in Python 2.7. Below you can find the code I came up with. Any corrections would be ...
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231 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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Volatility of a stock basket

to determine the volatility of a basket of stocks, I often use the following formula: $\sigma_{basket}=\sum_{i}\sum_{j}w_i w_j \sigma_i \sigma_j \rho_{ij}$ where the $\sigma$ are the constituents' ...
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103 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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80 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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61 views

Equity Options - “How do I build a forward simulation model with regards to shocks in spot pricing and IV?”

I am trying to build a "What-If" Portfolio, consisting of a total of 20 options, across different tenors, strikes (delta), but on the same security. Simply put, the objective is for me to test the ...
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166 views

Relationship between Implied Volatility Curve Derivatives and the Underlying's Moments

Very probably this question has been posed before, so if someone can pose the link to the relevant question, it would be appreciated. What is the relationship between the implied volatility skew and ...
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1k views

What equation will convert implied yield volatility to implied price volatility?

I am trying to figure out how to turn implied yield volatility of a short-term interest rate into implied price volatility. Is there an equation to do this? I have come across the equation for a ...
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73 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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139 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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57 views

Fast implied volatility for american options

Peter Jäckel has developped a method to compute implied volatilites from option prices, called "by implication", see the papers : By Implication Let's be Rational on its website -- as well as a ...
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65 views

What are the main problems for calculating the implied volatility of in the money American put options?

As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
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42 views

GARCH(1,1) one-step ahead volatility forecast biased, higher than Parkinson's HL volatility

I am trying to create one-step ahead forecasts for the S&P500 using a GARCH(1,1) model. I am using the rugarch package in R. As you can see, the forecasted points are consistently higher than the ...
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123 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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93 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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37 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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58 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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79 views

Local variance derivation by Gatheral

I've bought Gatheral's book on Local Volatility and I have troubles with understanding a part where he shows that local variance is a conditional expectation of instantaneous variance. Why in the ...
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247 views

Implied Vol skew VS Local Vol skew (as presented by Derman 1995)

I am reading Derman's article/notes regarding local volatilty: http://www.emanuelderman.com/writing/entry/the-local-volatility-surface. I am examining the graph on page 13. The Implied volatility (...
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106 views

American options — doing better than Black's approximation when $r = 0$

I am trying to find the implied volatility smile for an American call option with a known dividend during the option tenor. For the sake of argument, let's say today is Jan 1, the dividend $D$ is paid ...
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128 views

Jim Gatheral's claim on the decay of the effect of jumps on the final return distribution

I got a full answer for my question on Jim Gatheral's book The Volatility Surface. I am going to try my luck again on another question on the same book. In Section The Decay of Skew Due to Jumps on ...
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353 views

American Vs European Options behavior with fixed strikes and varying expiration

Following is from page 10 of Fengler (2005), "The prices of American calls for the same strikes must be nondecreasing, Merton (1973), and in the absence of dividends, this property translates to ...
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195 views

CDO Implied correlation: what for?

Reading about CDOs and calibration to find the implied correlation, I came up with the following question. Suppose we are pricing a CDO over a pool of $N=125$ names, using the usual Gaussian copula ...
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130 views

from local volatility function to implied volatility for a given strike

Assuming we know the local volatility function σ(S,t) for all S and t, how can we recover the corresponding implied volatility for a given strike K (and the other necessary parameters, S, r, T, t...)? ...
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152 views

Implied Equity Volatility under Stochastic Interest Rate

I would like to draw some general conclusions for the effect of stochasticity of interest rate on the implied volatility of a European call of a stock. Below I show, trivially, the implied volatility ...
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80 views

Implied volatility

I have a question about calculating the implied vol. Assuming the implied vol that a option will expire in 1 day is $\sigma_1$, and the implied vol that the option will expire in 2 days is $\sigma_2$. ...
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98 views

Inverse Smile Volatility Ibex35

I was analysing ibex implied volatility and when I draw it I found it was reversed: X axis are the strikes and Y axis implied volatilities calculated by BS. The blue line is the spot price. Data (...
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345 views

Vol surface changes as underlying moves

We market make in highly liquid, near term options markets. I want to build a risk report that tells us how our portfolio's greeks will change as the underlying moves. This is for risk management in ...
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37 views

FX Implied Volatility for Longer Term Maturities

To my knowledge, FX implied volatility can only be obtained from the market for time horizons up to about 5 years due to liquidity limitations. So how would we obtain volatility estimates for longer ...
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99 views

Underlying changes impact on implied volatility

What are some valid techniques that can be used to simulate how changes in the underlying are most likely to impact implied volatility along with the skew of all strikes for options with the same ...
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298 views

Weighted average implied optionlet/swaptions volatility

Let an implied volatility curve/surface is made up by optionlets or swaptions Black's implied volatility. If you wanted to price, say, a FRN with cap and/or floor, a CMS et cetera you would input the ...
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997 views

Interpolate option volatility in delta space in R

I have a bunch of deltas and option implied vols at those deltas. I would like to interpolate them in R. Interpolating them in delta space seems difficult, since normally you would like the ATM calls ...
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79 views

Is there a method to interpolate the volatility smile?

I have a small question of interest. During my classes at the university I have learned about the Nelson-Siegel method to fit interest rate curves. With this method you are able to determine interest ...
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51 views

Why quote call options in terms of implied volatility of the Black-Scholes model?

I came across this seminal paper on SABR model where the value of the call option is computed (eq. A.52). After the dollar value of the option has been derived, a lot of effort is being put to ...
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49 views

Pricing forward start Cliquet option with implied volatility with Dupire

I have the following implied volatility matrix of a stock index downloaded the 15th February 2019, the value of the stock was 3188.44 at the time: ...
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39 views

Determinant of index implied vol

I find that unlike individual stocks, whose option trading and implied vol can be traced to the underlying liquidity and short-ability, the determinant of implied vol on index ETFs is quite confusing. ...
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77 views

Implied volatility as break-even delta hedge volatility

There have been some posts on this topic, but not what I am looking for, so a new post on an old topic.. I think some/most of us here are familiar with the following formula expressing implied ...
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28 views

Negative rates, what is assumed for short caplets to derive implied volatilities on long maturities

I have been looking at Black implied volatility data for caps with the Euribor 6M underlying. With negative rates many of the shorter maturity caps have no listed volatilities, and this I completely ...
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37 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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66 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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99 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 ...