Questions tagged [volatility-surface]
The volatility-surface tag has no usage guidance.
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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}}...
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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) ...
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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 ...
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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++....
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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 ...
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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, ...
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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 ...
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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.
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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$ ...
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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). ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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Could a certain Volatility Surface generate two options with different strikes but the same Delta?
Is it possible for a volatility surface $\sigma(K,T)$ results in two options (both call or puts) with different strikes, but the same Delta, i.e., $\Delta(K_1,\sigma(K_1,T);S,T,r)$ = $\Delta(K_2,\...
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How to improve fit in American options vol surface?
I am trying to model the volatility surface of index etfs (spy, iwm and qqq). I am using the CRR model with discrete dividends and the spot model. I find that for some cases there is a noticeable ...
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SSVI butterfly arbitrage condition
I am reading the Notes and the Paper of SSVI. I see the author simply wrote the conditions for power-law SSVI $\phi = \eta\theta^{-\gamma}(1+\theta)^{\gamma -1}$, where $\gamma \in [0,1]$, $\theta >...
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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 ...
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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}) = \...
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Sticky Strike vs Sticky Delta - revisited [duplicate]
Given a time series of implied volatility smiles over the last 100 days for a given option (e.g. 1y S&P call, or 1y x 10y swaption), and the corresponding forward rates, what test should be ...
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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?
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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....
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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&...
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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 ...
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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 ...
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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 ...
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How to efficiently shift BlackVarianceSurface to compute the vega, volga and vanna of an option
I am working with a vol surface that was created as a BlackVarianceSurface.
Now I would like to compute the "vol" greeks for a product and as such I need to shift that surface by a small ...
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Reference request: Approximate mapping of a multi-factor stochastic volatility model to single-factor stochastic volatility model
I am looking for approaches to transform a more complicated stochastic volatility model such as the one shown in Section 2.2 of Smile Dynamics II to a single-factor model such as the one shown in ...
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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 ...
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Quantlib issue with BlackVarianceSurface diffusing with the wrong vol when there are either holes or arbitrages in early maturities
I'm new to Quantlib in Python and I'm running into a quite awkward situation.
I have a vol surface from the market on the SPX index. Not all strikes/maturities are populated. In addition, there could ...
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simple volatility surface interpolation
I'm trying to build an implied vol surface from some listed options. In particular I have data for calls and puts for different strikes and expiries. I'm not looking to price on the interpolated vols ...
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Why can't the curve find the least squares parameters when I used it in SABR model? (SABR Calibration)
Follow is the SABR function part of my code in python：
...
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Help needed in replicating FX Implied Vol Surface
I am relatively new to this area and am doing some self studying on SLV model. I am however getting stuck on trying to replicate this implied vol surface (which I will use to calculate the local vol)
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Deriving vol of vol from volatility futures price
From Colin Bennet's trading volatility (pg 117), he says:
"A forward on a volatility future is short vol of vol. This means it is possible to back out the implied vol of vol from the price of ...
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Market models of implied volatility and no arbitrage
Something has been bugging me for a while, and I can't really find an answer to it in papers. Maybe somebody can help me out.
In addition to modelling the instantaneous vol, or modelling forward ...
user34971
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How would one construct a volatility surface given only the spot price?
The traditional way to build a volatility surface is to pull options data and then do some form of interpolation. What happens if there is no existing options market and only a spot market for asset X?...
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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/...
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Bloomberg OVML| FX option pricing | Python
Wanted to check if any API for python is available to replicate Bloomberg's OVML.
The objective is to perform FX options pricing for multiple positions, and we are getting stuck in calculating ...
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May banks ignore the vol surface for far OTM, distantly-dated options, and make risk decisions only on near-term implied ATM vol?
Here is a difficult "real-life" skew / surface options problem that actually occurred. Please help me judge its validity or falsity.
In 2018 a Chinese communications stock was falling, and ...
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