Questions tagged [volatility-surface]

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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 ...
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Different volatility surface ( Local vol, Stochastic vol etc.)

Despite many questions about local and stochastic volatility available on this forum, i still have a few doubts left. Essentially I am seeking validation whether I am interpreting things correctly. ...
Ussu's user avatar
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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 answers
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What does it mean to "calibrate vols"

As a beginner, it can sometimes be hard to discern what different terms and phrases mean in QF. I've heard multiple people such as academics and market-makers say things like "calibrate vols" or "...
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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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5 votes
2 answers
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Interpolation of FX Vol Surface from non-uniform strike vs tenor grid

TL;DR I'm trying to fit a vol surface to market FX options quotes in order to build a local vol model to price with. Unlike listed options that typically have a nice rectangular grid of strikes and ...
StackG's user avatar
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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
5 votes
1 answer
1k 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."
pyCthon's user avatar
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5 votes
1 answer
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How to interpolate on an implied volatility surface based on forward moneyness?

Should be a simple matter, but perhaps I'm misunderstanding something fundamentally. Look first at the below image of the BVOL surface from Bloomberg, to my understanding from looking at the white ...
Oscar's user avatar
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Hedging : effect of not matching the term structure of skew

Let us assume that we construct a pure stochastic volatility model calibrated to the implied volatility surface, but that the model does not replicate accurately the observed term structure of the ...
fwd_T's user avatar
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Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
Archetupon's user avatar
4 votes
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Why use moneyness as an axis on a volatility surface

A simple volatility surface might have X axis = strike, Y axis = expiry and Z axis = implied volatility. But in many papers I see them use moneyness instead of strike. I have two questions. Why do ...
brownie74's user avatar
4 votes
1 answer
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Intuition for the Effect of Vol of Vol in Heston Model on Volatility Surface

I was hoping someone could describe the economic/mathematical intuition behind the effect that the vol of vol parameter has on the volatility surface, in particular the slope to maturity. Take for ...
Archetupon's user avatar
4 votes
1 answer
2k views

What interpretation can I derive from an inverted volatility surface?

While pulling some reports from Bloomberg today I came across the volatility surface for NYSE: ONDK, set for an earnings call next Monday. From what I've seen before (not much, 1 month on the job and ...
Brothernature's user avatar
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Spot and Vol Correlation in Idealised Regimes of the Volatility Surface

From http://www.globalvolatilitysummit.com/wp-content/uploads/2015/10/Santander-Volatility-Trading-Primer-Part-II.pdf it states that there are the four idealised regimes of volatility surface. 1) ...
Trajan's user avatar
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4 votes
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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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SSVI parametrization motivation , SSVI implementation

I've read the following paper of Gatheral and Jacquier https://arxiv.org/pdf/1204.0646.pdf about volatility surfaces. I'm thinking about the SSVI surface. Is there any motivation why they choose ...
P.G.'s user avatar
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$\frac{\partial C_{BS}}{\partial T}$ in local volatility derivation in terms of implied volatility

In Gatheral's book, in the derivation of local volatility in terms of implied volatility, we use the regular Dupire formula $$ \frac{\partial C}{\partial T} = \frac{1}{2} \sigma^{2}K^{2}\frac{\partial^...
Ruse's user avatar
  • 109
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
3 votes
1 answer
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Implied Volatility Surface - log forward moneyness

I'm reading this paper by Fengler (2005) and have came across the below snippet. context: Implied volatiltiy surface plot has 3 dimensions IV, Strike, Time to Maturity. Author replaced Strike with ...
quantfin_enthusiast's user avatar
3 votes
1 answer
374 views

Question about volatility surfaces

As a learner, I'm curious to know the answer to 2 questions regarding volatility surfaces 1) It's stated that volatility surface should be flat accdording to Black-Scholes model. Why is that? Time (...
techie11's user avatar
  • 213
3 votes
1 answer
355 views

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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3 votes
1 answer
230 views

Warrant volatility surface differs for each issuer

I have written a rudimentary program for fitting volatility surfaces for warrants of call and put options for the purpose of some basic scenario analysis. In my country, trading options privately in a ...
JMC's user avatar
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1 answer
717 views

How to get the local volatility from IV surface?

I have to work on Dupire's model. If I understand Fengler's paper well enough we can get the local volatility from implied volatility smoothed surface because if not it would look all bumpy like the ...
Kire Lor's user avatar
3 votes
2 answers
406 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
355 views

FX ATM-volatility quotes

Is the implied volatility ATM the same for a currency pair as for the inverted currency pair. I.e, can I expect the same volatility quote ATM for (for an instance) EURUSD as for USDEUR? And does this ...
user361695's user avatar
3 votes
1 answer
741 views

Interpolating implied volatility term structure when IV is sampled at fixed delta points

According to the accepted answer to a question in this site on the interpolation in the term structure of volatility surface: A simple linear interpolation on implied variance along iso-moneyness ...
Special Sauce's user avatar
3 votes
1 answer
2k views

Smile Strangle and Market Strangle

What is the difference between Smile Strangle margin and Market Strangle Margin in fx derivative market? Is it just variation in convention or is there any mathematical relationship between the two?
Ussu's user avatar
  • 577
3 votes
1 answer
121 views

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 ...
Attack68's user avatar
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4 answers
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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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1 answer
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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
  • 747
3 votes
1 answer
464 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
  • 31
3 votes
1 answer
287 views

Calibration of a volatility smile model on a partial smile

I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/...
Hasek's user avatar
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3 votes
1 answer
200 views

How to parameterising Greek Surfaces?

I'm currently working on my master thesis, where I have data on option trading volume and flow (number of shares bought minus sold; i.e., net position), divided among three kinds of market ...
Dipanshu Gupta's user avatar
3 votes
1 answer
371 views

LIBOR market model with stochastic volatility

I have read that there are 3 types of pricing models: local volatility, stochastic volatility and stochastic-local volatility models (LSV). I am now looking at interest rates exotics pricing models ...
Diuoo's user avatar
  • 41
3 votes
1 answer
223 views

Options when there's no VolSurf - Emerging/Frontier Markets

Context: Most emerging/frontier markets have no or very thinly traded volatility surfaces for their equity markets (single name and indices alike), furthermore, they usually have restrictions on Short-...
Mercadian's user avatar
3 votes
0 answers
50 views

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 ...
KaiSqDist's user avatar
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3 votes
0 answers
55 views

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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3 votes
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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
  • 105
3 votes
0 answers
92 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
3 votes
0 answers
136 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
3 votes
0 answers
145 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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3 votes
1 answer
963 views

Dupire (Local Vol with Imp Vol)

I am trying to implement a local volatility pricer using Monte Carlo and Dupire's equation in function of implied volatilities and I was told that first of all I have to check Dupire is well ...
Nico Blanco's user avatar
2 votes
1 answer
1k 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
2 votes
2 answers
233 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
  • 123
2 votes
1 answer
376 views

Does shifting/scaling the IV surface relatively/absolutely introduce arbitrage?

I am fitting a volatility surface for vanilla call options. I do this by fitting low-degree polynomials (or cubic splines) along the strike dimension per maturity and then linearly interpolating ...
JMC's user avatar
  • 177
2 votes
1 answer
669 views

FX smile extrapolation

Typically, 5 points data is available for smile construction : 25D RR, 25D SM, 10D RR, 10D SM and ATM. Questions: 1. How is a smooth smile curve generated with the help of these? 2. How is ...
Ussu's user avatar
  • 577
2 votes
1 answer
295 views

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
  • 747
2 votes
1 answer
1k views

simulate volatility surface

Assuming I have a stochastic volatility model for an asset, if I wanted to use it for pricing I would proceed in the following way: Use Euler discretization to simulate a sample path of the price and ...
apocalypsis's user avatar
2 votes
1 answer
766 views

FX convention and volatility calibration

In general, call/put options are quoted with respect to their Black-Scholes volatility. In the FX market we define the risk reversal volatility as $$\sigma_{25-RR} = \sigma_{25-Call} - \sigma_{25-Put}...
DeepInTheQF's user avatar