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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11
votes
1answer
504 views

“Extract” the density of the underlying, given the implied volatility “surface”

Suppose given implied volatility quotations $\widehat{\sigma}(T_i,K_j)$ of call options on an underlying $S$ for various expiries $T_i$'s and strikes $K_j$'s. I am interested in the following problem :...
10
votes
1answer
593 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^...
9
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0answers
289 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 ...
9
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0answers
208 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 ...
8
votes
1answer
533 views

Transforming 3M volatilities into 6M volatilities in EUR forecast curves

I have implemented a stripping algorithm to extract forward volatilities from cap/floor flat volatilities for different currencies. I am however struggling a bit when implementing a method to convert ...
8
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0answers
632 views

compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
7
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0answers
231 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 ...
6
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0answers
248 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 ...
6
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0answers
215 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, ...
5
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0answers
455 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 ...
5
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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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0answers
81 views

Anyone know if this daily report discontinue to publish? Goldman Sachs - “Global Index Volatility and Correlation Monitor”

I used to receive this daily report in my workplace from Goldman Sachs mailing list but the mailing list discontinued in May 2019 without any notice. The report is an pdf attachment which send from "...
4
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0answers
50 views

Measuring implied move priced into an event

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
4
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0answers
78 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 ...
4
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0answers
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 ...
4
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0answers
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.
3
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0answers
34 views

Does convexity in the IV space means convexity in the price space?

Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND). As the RND is the second derivative of the price of the option with respect to the strike, we would expect ...
3
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0answers
162 views

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' ...
3
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0answers
127 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 ...
3
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0answers
82 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? ...
3
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0answers
63 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 ...
3
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0answers
168 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 ...
3
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0answers
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 ...
3
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0answers
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 ...
2
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0answers
35 views

Vol surface fitting to options on commodity futures

Trying to fit variants of SVI (Zeliade method, SSVI etc) to options on futures price data. One of the core ideas of the SVI parameterization is the absence of calendar spread arbitrage. I think the ...
2
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0answers
22 views

How to derive the half slope rule from asymptotic relation between implied and local volatility?

In their paper(https://www.sciencedirect.com/science/article/pii/S0764444200017493) BERESTYCKI, BUSCA, and FLORENT proved an asymptotical relation(for short maturity) between implied and local ...
2
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0answers
72 views

Procedure/methodology for building equity volatility surface

EDIT: I update while making progress: I am trying to build (model implied) volatility surfaces for individual equities. I will use these surfaces to calibrate models to price different derivatives (...
2
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0answers
30 views

Dimension reduction for worst of basket on $min(S_1, S_2)$

Suppose we want to price an exotic equity which is a function of $min(S_1, S_2)$. To do this, I'm trying to compute an implied volatility surface for $min(S_1, S_2)$ and then price the option using ...
2
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0answers
67 views

Why do coefficients flip after the including a lag in the optimisation? implied volatility/skewness/ivspreads

I'm hoping some of you guys can help me out. I am applying the paramametric portfolio optimisation of Brandt, Michael W., Pedro Santa-Clara, and Rossen Valkanov. in which the weights on specific ...
2
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0answers
61 views

Finding Jump Probability For Time Series Data

I'm relatively new here, so if it seems like I'm asking a bad question, go easy on me. So I was looking at the Merton Jump Diffusion Stochastic Model on Turing Finance's article. Instead of creating ...
2
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0answers
81 views

Is it possible to compute implied returns from volatility?

If we assume that, broadly speaking: Assets in liquid markets are fairly priced to its value Volatility is predictable (volatility clustering, GARCH, etc) Investors are rewarded and earn a return for ...
2
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0answers
68 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 ...
2
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0answers
78 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 ...
2
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0answers
63 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 ...
2
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0answers
174 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 ...
2
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0answers
133 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) ...
2
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0answers
53 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 ...
2
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0answers
61 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(\...
2
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0answers
91 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 ...
2
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0answers
271 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 (...
2
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0answers
116 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 ...
2
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0answers
134 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 ...
2
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0answers
379 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 ...
2
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0answers
215 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 ...
2
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0answers
140 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...)? ...
2
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0answers
165 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 ...
2
votes
0answers
81 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 $\sigma_2$. ...
2
votes
0answers
102 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 (...
2
votes
0answers
370 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 ...
2
votes
0answers
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 ...