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Interpolation of term structure of implied volatility

I have a dataset of options traded at each day, including the time to maturity, delta, strike price etc. Now I want to get the implied volatility of an option with time to maturity 30 days through ...
Masmar's user avatar
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Volatility surface for futures options

When looking at futures options such as CME's Gold options or many equity index futures options, the underlying is not the index but to be precise the closest to delivery futures contract. That means, ...
not_sure95's user avatar
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Functional From to Approximate Volatility Surface

I have a finite difference pricing model and would like to factor in a volatility surface for each underlying equity. However, I have limited data. Essentially I'm just pulling a few implied ...
Charles0349's user avatar
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What are some effective and easily implementable volatility smile/skew smoothing models?

Inspired by another post on Bakshi et al. (1997), the paper talks about the feasibility of option pricing models, particularly the SVSI-J variant. I would like to ask the Quant community if there are ...
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QuantLib error: `RuntimeError: negative local vol^2 at... the black vol surface is not smooth enough` for calibrating the SLV model

I am trying to generate the SLV process using QuantLib on real SPX data. The issue that I am having is that calendar arbitrage is being violated. I put my data in a list in my code, and am using $r\...
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Are there standardized measures to characterize the volatility skew?

Might be too simple a question, but I saw in Gatheral & Jacquier (2014) that commonly used features to match volatility skews are (and then I subsequently ChatGPTed some commonly used industry ...
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Estimating dynamics of volatility surface?

I have a daily time series of volatility smiles for an option contract. How can i calculate whether the smile is sticky strike, sticky delta or something in-between!
David's user avatar
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What is the informational content of the volatility skew?

The option-implied volatility is well-known as a measure for the risk-neutral future expected risk for the underlying asset. However, the market prices of options (across different strikes) imply ...
KaiSqDist's user avatar
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Seeking Advice on Normalizing Implied Volatility Change for Options Modeling

I'm working with a substantial dataset spanning five years of weekly options data, with records down to the second. My goal is to develop a model that can accurately predict the probability mass ...
Manish Arora's user avatar
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In the Stochastic-Local Volatility (SLV/LSV) calibration procedure, which surface is used when calibrating the Leverage function

Before we match the leverage function $L(S_t,t)$ to the implied volatility surface generated from the market, we are supposed to calibrate the pure Heston parameters, $(\theta, \kappa, v_0, \rho, \xi)$...
Xerium's user avatar
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filtering implied Vol surface for butterfly arbitrage

Suppose I have a volatility surface (matrix in time and strike) but it might have butterfly arbitrage in it. I want to remove nodes from the surface so that the Vol surface is butterfly arbitrage free....
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Arbitrage-Free implied/local volatility surface with Cubic Spline Interpolation

I am trying to create a local volatility surface using a cubic spline interpolated implied volatility surface. In other words, I have a function $\sigma(T,K)$, that is arbitrage-free $\forall T,K$ (...
THATS MY QUANT MY QUANTITATIVE's user avatar
2 votes
2 answers
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Delta on x-axis in Volatility smile

I want to ask a perhaps simple question: Why do we use delta on the x-axis instead of the strike price when discussing volatility smile or volatility surface? In the book I'm currently reading, it is ...
Miroslav Holub's user avatar
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1 answer
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Creating Implied Volatility surface using log moneyness [closed]

When creating the implied volatility surface using $\left(T,log\left(\frac{K}{S_0}\right)\right)$ as $(x,y)$ axis, do the inputs for the implied vol calculation need to be logged too? In other words, ...
ayamathss1's user avatar
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287 views

Creating the local volatility surface from the IV surface

I have been using the dupire equation: $$ \sigma_{LV} (K,T) = \frac{\sigma_{i m p}^2+2 \sigma_{i m p} T\left(\frac{\partial \sigma_{i m p}}{\partial T}+(r-q) K \frac{\partial \sigma_{i m p}}{\partial ...
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week-over-week impacts on IV of of options with close to before/after EOY expirations

Tomorrow is the last trading day of 2023. Compared to last week, I noticed that $SPY ATM or close-to ATM options for the end of month/quarter (Dec-29) exp experienced a spike in IV since yesterday, ...
VolatiCity's user avatar
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Calibrating an FX Vol surface via Global Optimiser

My objective is to determine an FX volatility surface calibrated by interbank market prices. Suppose that a vol surface, $\Sigma(t,k)$, returns a volatility for time to expiry and strike. The surface ...
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When getting the local vol surface from the implied vol surface, do we interpolate the strikes?

Using the dupire method: $$\sigma(T, K)=\sqrt{\frac{\sigma_{\mathrm{imp}}^2+2 \sigma_{\mathrm{imp}} T\left(\frac{\partial \sigma_{\mathrm{imp}}}{\partial T}+(r-q) K \frac{\partial \sigma_{\mathrm{imp}}...
Xerium's user avatar
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volatility surface interpolation across expiry

In the usual adjusted Black Scholes world where BS vol varies with strike and with time to expiry as extracted from a market snapshot at moment 0, assuming a certain of interpolation method across ...
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Intuition behind the benefits of Stochastic Local Volatility (SLV) models [duplicate]

There have been various posts on this topic, but they don't really discuss the intuition behind the benefits of the stochastic local volatility (SLV) models over normal stochastic volatility (SV) ...
THATS MY QUANT MY QUANTITATIVE's user avatar
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Fitting volatility using SABR

I have been working on generating a volatility surface for options on SOFR futures with the help of the SABR model. I am running into some trouble for low strikes in particular, in that I cannot seem ...
Zac Likes Vol's user avatar
2 votes
2 answers
258 views

Extending/Subclassing QuantLib Classes in Python?

I'm using quantlib via the quantlib-python or open-source-risk-engine both on pypi. The question relates whether it's possible to extend QuantLib term structure base classes in python rather than C++....
Phil's user avatar
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How to trade forward volatility?

What would be the best way to trade forward volatility or term structure? One way, I think of is through gamma neutral calendar spreads. The problem with this approach is "change of ATM" and ...
smg_08's user avatar
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What's wrong with calibrating implied volatilities with polynomials?

People use different parameterization schemes to fit the implied volatilities from the market, e.g., SVI. But often times they cannot always fit well, e.g., the "W"-shape before earnings, ...
Michael's user avatar
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Effect on Forward Swap Rate from a parallel shift in forward curve

Can anything be said on how a parallel shift in the forward curve affects the forward swap curve? To be more concise, say we have a model estimate of the implied vol for the 2Y-10Y point (2Y ...
J Muscat's user avatar
3 votes
0 answers
487 views

Best practices for building an FX volatility surface with Quantlib in Python

Generally my question is: what are best practices for building FX volatility surfaces with Quantlib? In FX options, I would like to price structures such as risk reversals, strangles and butterflies. ...
Wynn's user avatar
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Empirical Evidence for Support/Resistance Levels in Martingale Price Processes and Its Impact on Option Volatility Surfaces

In financial mathematics, the martingale property often serves as an essential foundation for the stochastic processes that underlie securities pricing models. According to martingale theory, the most ...
GotTheTrumpCard's user avatar
2 votes
1 answer
2k views

Option Pricing for Illiquid case

I am currently studying crypto options trading and have observed that there is often a lack of liquidity for options (such as BTC Options) on various exchanges, including Binance. In many cases, there ...
Starlord22's user avatar
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Local Volatility Derivation

In Jim Gatheral's book (The Volatility Surface), in the first chapter, it says below while deriving Dupire Equation for Local Volatility. I do not understand how the drift term got removed. Can ...
Pranav's user avatar
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What does volatility process mean and how is it different from volatility?

I have been reading the paper "Bridging P-Q Modeling Divide with Factor HJM Modeling Framework" by Lyashenko and Goncharov (2022). On Equation 5 of page 4 of the paper, I came across the ...
Dishay Mehta's user avatar
3 votes
2 answers
425 views

Strike of a Variance Swap in a Sticky Strike World

Imagine there exists a typical negative skew for some underlying I want to price a variance swap on. Critically, let’s say we are in a sticky strike world (the vols of each strike will not change with ...
Saul5813's user avatar
3 votes
1 answer
108 views

Drift of stochastic variance as slope of the short end of the forward variance curve

I was re-reading Chapter 6 of Stochastic Volatility Modeling by Lorenzo Bergomi. On page 203, he considers a forward variance of the following form: $$ d\xi_t^T=\lambda_t^T dZ_t^T, $$ where $Z_t^T$ ...
fwd_T's user avatar
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3 votes
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Is negative forward variance an arbitrage?

I believe that having a negative forward variance on a ATMF implied volatility curve of a volatility surface could imply the existence of a static arbitrage (for example, a calendar arbitrage). ...
fwd_T's user avatar
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4 votes
1 answer
122 views

BS price as the first term of option price expansion

I recently saw someone write, on a generally non-technical platform, that the Black-Merton-Scholes vanilla option price is the first term of an expansion of the price of a vanilla option. I get that ...
Frido's user avatar
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1 vote
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Questions on limitations of local volatility model

I am currently studying local volatility for equity models and I am trying to understand some limitations of the model: 1. under local volatility, the forward smile gets flatter and higher. Lorenzo ...
StochasticMan's user avatar
3 votes
0 answers
99 views

Which expiry interpolation method for caplet/floorlet surfaces?

I want to bootstrap an (implied volatility) caplet/floorlet surface from quoted cap/floor volatilities on a fixed strike grid. I'm thinking about either using a left-continuous or a linear ...
BerndSchmitz's user avatar
5 votes
1 answer
2k views

How to structure a trade using vanilla equity options to get vega exposure to forward volatility?

I have been thinking about structuring a trade to get exposure to the forward volatility. For example, let's say SPY ATM 1 month IV is 20 vol and SPY ATM 2 month volatility is 30 vol. Then the forward ...
kwantify's user avatar
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0 answers
48 views

Pricing and Risk Management of Exotic Options with a Volatility Surface [duplicate]

Bit of a newbie question; but I see this pop up from time to time. If we have a volatility surface (e.g. for the S&P500) built from market options what more can we do with it, but price other ...
Sinbad The Sailor's user avatar
3 votes
0 answers
144 views

Joint SPX and VIX calibration - volatility surfaces construction

I am currently researching the joint calibration problem of SPX options and VIX options. A question that comes to mind is the construction of each assets respective volatility surface. In the articles ...
Sinbad The Sailor's user avatar
1 vote
0 answers
93 views

what does correlation $\rho$ means in surface SVI?

Why does everyone say $\rho$ is correlation in Surface SVI? $w = \frac{\theta_t}{2}(1+\rho\psi(\theta_t)k + \sqrt{(\psi(\theta_t)k+\rho)^2+1-\rho^2})$, with $\rho \in [-1,1]$ This paper says it is ...
StupidMan's user avatar
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2 votes
0 answers
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Barrier on realized volatility

I am trying to understand the risk exposures of vanilla options that also have a European barrier on realized volatility. For example, the option could knock out if the realized volatility over the ...
fwd_T's user avatar
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3 votes
0 answers
153 views

Popular treasury futures bond options volatility surface model/s

I am looking for volatility surface parametrisation model used for treasury futures bond options. I know that most popular for options on equities its SVI, on FX its Vanna-Volga, on rates its SABR. ...
sle's user avatar
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2 votes
1 answer
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Volatility swaps hedging

I have heard that traders use a straddle to hedge volatility swaps (in the FX context), although I could not figure out the specifics. Is this type of hedge used in practice? And if yes, how does it ...
fwd_T's user avatar
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3 votes
2 answers
2k views

SABR model - beta

In the SABR model, the parameter beta largely controls the back-bond behaviour of the model. How do people estimate beta? One approach is to regress atm vol vs forward, i.e. $$\ln(\textrm{atm vol}) = \...
JohnRoper's user avatar
1 vote
0 answers
92 views

How can I derive the price of american options given the european options prices? [closed]

I have the european volatility surface of a given asset. What is the correct procedure to compute the price of the options with american exercise type?
Rodrigo's user avatar
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0 answers
152 views

Quantlib Monte Carlo using regular Volatility Surface, not Local Volatility surface

I am trying to run a Quantlib Python Monte Carlo simulation using either the ql.BlackScholesMertonProcess or the ql.GeneralizedBlackScholesProcess. I have a vol surface that I have generated using ql....
vman's user avatar
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1 vote
0 answers
655 views

Implied volatility to local volatility via Dupire

I am doing some self study on stochastic local volatility modelling and am having a hard time replicating some results from the paper "FX Option Pricing with Stochastic-Local Volatility Model&...
APMATH24's user avatar
3 votes
1 answer
496 views

Quantlib vol surface issue 'the black vol surface is not smooth enough'

I create a vol surface from the market and do smoothing(interpolation and extrapolation), and explicitly correct for any total variance decreasing on a given strike as we increase maturity. I create a ...
vman's user avatar
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6 votes
2 answers
3k views

Is it possible to have only one volatility surface for american options (that fits both calls and puts)?

Put-Call Parity does not hold for american options. Hence, I don't see how it would be possible to have one surface that would encompass both calls and puts. For example: Let pick a call lying in the ...
Rodrigo's user avatar
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2 votes
1 answer
190 views

Does the CME Option on 1M SOFR keep trading in the compounding period

I am working with implied vol surfaces for money market options and trying to understand the dynamics of the CME's options on one-month SOFR futures. I want to establish whether trading ceases before ...
Andrew Kirk's user avatar