AAPL · 1 May 2025 total var (vol²·T)
In the News
Media & Research
The Vola Dynamics team is at the cutting edge of research in dividend and volatility surface modeling, volatility dynamics, and the design of super-fast and robust pricing and calibration algorithms.
Most of our research is available exclusively to clients.
Top Links
Real Time Implied Volatility Surfaces: A Practitioner's View of the Black Arts
A practitioner's tour of what a real-time vol surface infrastructure has to get right: implied discount rates, borrow costs, event modeling, and spot-vol dynamics. Worked throughout on IBIT, the Bitcoin ETF whose options went liquid in weeks, where SVI fits are 13-70x worse than a C9W.
Thetas and Time Conventions in the Vola Library
Why the Vola library exposes several different thetas. Interest accrues on one clock, variance on another, so the library carries both a rate time and a volatility time, with a theta for each.
Read post →Timothy Klassen, CEO and Founder, on Vola's Offerings and Founding
Tim Klassen on founding Vola, the product suite, and why a quant library integrates more easily than a vendor system. On the client mix: "roughly a third, a third, a third" across prop shops, hedge funds and banks.
State of the Smile: The Ever-Surprising Evolution of the Equity Options Market
How the listed options market became "sophisticated and opinionated," read through vol skews in 2008 versus 2020. Why liquid names cannot be fit with SSVI, SVI or SABR, and what a large-scale valuation infrastructure has to get right: discount rates, dividends, no-arbitrage metrics, and spot-vol dynamics.
Vola Dynamics' Greatest Hits
A curated roundup of Vola's most popular published content — market analyses, technical insights, and industry commentary.
Read post →Video Series
What is an Implied Volatility Surface?
Misha Fomytskyi explains implied vol as an engineering trick — not one Black-Scholes model but a sequence of models, one per strike. Option prices, implied vols, and probability densities are three representations of the same information. "Implied volatility is the wrong number that you plug into the wrong formula to get the correct price."
Watch on YouTube →Thetas and Time Conventions
Why theta is "the most important Greek" — it is the daily cost of insurance or leverage, and in dollars per day it aggregates across underliers and expiries. Variance and interest accrue on different clocks, so theta_v and theta_c are not fungible: a straddle carries mostly theta_v, a box only theta_c, and you cannot hedge one with the other.
Watch on YouTube →PnL Attribution by Greeks
Greek-based PnL decomposition using smart greeks with spot-vol dynamics. Using BS greeks leaks spot PnL into vega and vice versa — adjusted greeks produce a cleaner decomposition. Covers the double-counting risk when combining delta and vega adjustments.
Watch on YouTube →PnL Attribution by Factors
Scenario-based PnL attribution: exact re-pricing under spot, vol, time, rate, and model shifts — no Taylor approximation. Factor-by-factor methodology, vol surface comparison subtleties, and why permuting factor order and averaging destroys the unexplained residual that serves as your most powerful diagnostic.
Watch on YouTube →Spot-Vol Dynamics and the Skew Stickiness Ratio
Bruno Dupire showed in 2003 that both sticky-strike and sticky-delta are impossible: a market moving that way would be easy to arbitrage with a dynamic trading strategy. What desks use instead holds the shape fixed in normalized coordinates while ATM vol moves along a path steeper than the skew. The ratio of those two slopes is the Skew Stickiness Ratio, developed by Lorenzo Bergomi from 2009.
Watch on YouTube →Calibrating the Skew Stickiness Ratio
Part 2 on spot-vol dynamics. How calibration time horizon matters: intraday returns capture mechanical market-maker quoting updates, close-to-close returns capture slower institutional views. Three practical calibration recipes — from yesterday's intraday data to hard-coding a reasonable value — all outperform Black-Scholes deltas.
Watch on YouTube →Event Variance Fitter
How events like earnings and FOMC cause ATM vol spikes and negative curvature. The Event Variance Fitter smooths the term structure by calibrating event variance into a time converter — improving American option pricing, cross-name vol comparison, and PCA/term structure models.
Watch on YouTube →Event Modeling: Decomposing Volatility Surfaces Around Events
Decomposing dirty vol surfaces into clean (diffusive) surfaces plus discrete event jumps with calibrated probabilities and sizes. Two workflows — build a dirty surface by adding events to a hand-marked clean one, or extract event parameters and a clean surface from the observed dirty one. Covers the two-limits framework, the dimensionality reduction this buys, and why W-shapes arise when a bimodal jump sits on a fat-tailed clean surface.
Watch on YouTube →Press Coverage
An oral history of the fear index
FT Alphaville's oral history of the VIX. The "new VIX" the Cboe began disseminating in September 2003 was based on a proposal by Tim Klassen, Sandy Rattray and Devesh Shah, then all at Goldman Sachs.
Read article →The Swiss Army Knife of Options Analytics
A technical survey of the vol surface fitting problem in Wilmott Magazine: cash dividends, borrow costs, why public-domain curves cannot produce the negative ATM curvature that liquid names need, and no-arbitrage. Includes worked SPX and AMZN fits against SSVI, SVI and SABR.
View PDF →Innovators Pavilion 2016 – Where are they now?
FIA follow-up on the 2016 Innovators Pavilion cohort, tracking Vola's growth from early-stage startup to established institutional infrastructure provider.
Read article →Vola was at the GVS 2019
Vola exhibited at the Global Volatility Summit, one of the premier annual events for institutional volatility investors.
View event →How S&P 500 options may be used to manipulate VIX 'fear gauge'
MarketWatch on whether the VIX can be moved by trading the S&P 500 options it is computed from, a question Tim Klassen has a direct stake in as a co-designer of the 2003 methodology.
Read article →18 Startups Bringing New Products and Services to the Derivatives Markets
FIA's profile of the 18 startups selected for the 2016 Innovators Pavilion at FIA Expo, with Vola (then Volar Technologies) among them. Quotes Tim Klassen: pricing options in real time "has become a high-risk, deep-pocket sport."
Read article →Blog & Insights
Vola Dynamics' Greatest Hits
A curated roundup of Vola's most popular published content.
Read post →GameStop options trading during the short squeeze
How Vola's fitter handled the GME short squeeze — stable fits with implied vol exceeding 500% and extreme skew, when many in-house systems broke down.
Read post →SPX vol surfaces during the 2020 Coronavirus Crash
Published during the crash itself. ATF curvature went negative across all terms out to three years, a first for index options, with the most extreme shapes on March 13. "All fits were performed in a fully automated fashion and take a small fraction of a second for the whole vol surface," against traders at many banks who "spend hours every day managing the SPX vol surface 'by hand'."
Read post →Spot-Vol Dynamics and Deltas for SPX Options
How the empirical spot-vol relationship affects delta hedging for SPX options, including the minimum-variance delta correction and its P&L impact for market makers.
AAPL, FB vol curves around earnings
Apple and Facebook vol curves before and after earnings — the "vol crush" phenomenon and how Vola's multi-modal C10m curve captures the W-shaped smiles around binary events.
Read post →The Global Volatility Summit New York happens on March 13, 2019
Announcement of Vola's attendance at GVS 2019 in New York.
Read post →Pot is hot: Having fun with TLRY options and borrows
Tilray options during the cannabis mania — extracting the enormous implied borrow cost via put-call parity, revealing short-selling pressure the stock lending market doesn't show directly.
Read post →The option market thinks there is a 16% chance that Tesla will not exist in January 2020
Using Vola's fitted surfaces to extract what Tesla options implied about the probability of extreme downside scenarios, including near-zero stock price.
Read post →The option market thinks there is a 16% chance that Tesla will not exist in January 2020 (part 2)
Follow-up with deeper analysis across expiries and discussion of risk-neutral vs. physical probabilities.
Read post →Volatility Surface Fitting Buy vs Build
The case for buying vol surface infrastructure rather than building it in-house — the problem is harder than it looks, the maintenance never stops, and quant time is better spent on alpha.
Read post →The Most Interesting Volsurface in the World
The AEX (Amsterdam) index around the Brexit referendum — dramatic W-shaped vol curves with distinct Leave/Remain scenarios, fitted with Vola's multi-modal C10m curve using default settings.
Read post →Vol Dynamics Releases Vol Derivatives Module
Release announcement for Vola's Vol Derivatives module — VIX futures and options, variance swaps, and volatility swaps — three months after the February 2018 "Volmageddon" event.
Read post →How does a Bitcoin volatility curve look like?
An early look at Bitcoin vol curves during the 2017 bull run — more symmetric smiles, much higher absolute vol levels, and how Vola's fitting technology is asset-class agnostic.
Read post →Are you in the options business -- then ask yourself these questions
Diagnostic questions for options professionals to evaluate the quality of their vol surface infrastructure.
Read post →"Your Curves work like magic"
Why Vola's C-curves appear to "work like magic" — the right balance between flexibility and parsimony, proper data weighting, and no-arb constraints as natural regularization.
Read post →How can we extend the success of the VIX to the whole equity options market
Written by Tim Klassen, who co-designed the VIX. Argues that the VIX's success creating a standardized volatility measure should extend to the full equity options universe.
Valuing options on leveraged ETFs
The unique challenges of pricing options on leveraged ETFs — vol scaling by the leverage factor, mechanically linked skew, and volatility drag from daily rebalancing.
Read post →How dividends impact options greeks
How discrete cash dividends affect options Greeks — one of the most common and consequential errors in equity options pricing. Directly informs Vola's Div Fitter module.
Read post →Interviews & Podcasts
Navigating New Waters of Extreme Change in Quant Finance
Podcast on how unprecedented market events have changed the landscape for quant finance practitioners, and why robust analytical infrastructure matters more than ever.
Timothy Klassen, CEO and Founder, on Vola's Offerings and Founding
Tim Klassen covers Vola's founding story, product suite, library delivery model, and positioning as infrastructure for institutional options analytics.
Misha Fomytskyi's appearance on AD Derivatives' Podcast
Vola co-founder Misha Fomytskyi discusses how Vola's asset-class-agnostic fitting technology applies to the growing crypto options market.
Presentations
Real Time Implied Volatility Surfaces: A Practitioner's View of the Black Arts
Why S* curves (SVI, SSVI, SABR) cannot produce the W-shapes events require, and what replaces them. Covers "SPIBOR" implied discount rates, Merton-jump event modeling, the spot-vol dynamics myths of sticky-strike and sticky-delta, and settlement effects on SPX and SPY.
Secrets of the Implied Volatility Surface: Inferring Rates, Dividends, Events, and Risk-Neutral Densities from Options Prices
Vol surfaces contain far more than volatility: implied discount rates, borrow costs, dividends, event jumps, and full risk-neutral densities. Worked case studies on IBIT, GameStop during the 2021 squeeze, AEX before Brexit, AMZN earnings, and SPX through the COVID crash.
State of the Smile: The Ever-Surprising Evolution of the Equity Options Market
Curve statistics for the 2023 options universe: 73% of OPRA names fit with SSVI, while the 50 most liquid need C10-C16, and SPX/SPY/ES need 16-18 parameters per term. Also covers "SPIBOR" discount rates, event time for American vanillas, and the SPX SSR time series 2012-2023.
Robust Options Valuation and Risk Management Workflows with Vola Dynamics Analytics
Worked diagnostic examples on IBM, SPX, NDX, SPY, BTC and TLT. How a bad fit tells you which input is wrong: curve type, missing dividends, incorrect spot, or discount rates taken from the wrong curve. Also covers volatility time, including its effect on the SPY early exercise premium.
Optimal Portfolio Construction and Risk Premia in Options Markets
How well-fitted vol surfaces serve as the foundation for systematic options strategies — vol risk premium extraction, skew trading, calendar spread relative value, and dispersion.
Navigating New Waters of Extreme Change in Quant Finance
How unprecedented market events have changed the quantitative finance landscape and why robust analytical infrastructure is increasingly essential.
The New World of Options Trading: Valuation, Risk and Robust Workflows
How post-2020 market conditions require new approaches to options valuation, risk management, and production workflow design.
Tools for Options Trading in a Crazy World
Vol skews and parameter term-structure, 2008 versus 2020. Of 4,300 OPRA names in November 2020, 70% fit with SSVI, but none of the top 25 do; the SPX complex needs 14-16 parameters for some terms. The Robinhood/Reddit era bid up call wings while PMs bought puts, so both wings are now wide, structured, and close to butterfly arbitrage.
Tools for Options Trading in the New World - A Report from the Cutting Edge
First-hand account of how Vola's systems performed during the COVID crisis, delivered eight months after the crash.
View conference →Arbitrage-Free Parametric Implied Volatility Surfaces and Real-Time Fitting
One of Vola's earliest conference presentations — introducing C-curve families, calendar arb enforcement, real-time fitting, and comparison with SVI.
Research Publications
Relevant for Vola Dynamics Software Solutions
Pricing Vanilla Options with Cash Dividends
The mathematical framework for European option pricing with discrete cash dividends — the foundation for Vola's Div Fitter module.
View paper →Necessary and Sufficient No-Arbitrage Conditions for the SSVI/S3 Volatility Curve
Exact conditions for butterfly-arbitrage freedom in SSVI — the parameterization developed by Jim Gatheral, Vola's advisor. Also highlights why Vola's C-curves sidestep this problem entirely.
View paper →Earlier Articles about Pricing Models and Algorithms
Simple, Fast and Flexible Pricing of Asian Options
Efficient algorithms for pricing Asian (average-rate) options. Part of the foundational computational work behind Vola's Pricer.
View paper →Pricing Variance Swaps with Cash Dividends
How discrete dividends affect variance swap pricing and VIX computation. Implemented in Vola's Vol Derivatives and VIX Pricer modules.
View paper →Symmetries in Jump-Diffusion Models with Applications in Option Pricing and Credit Risk
Jiri Hoogland, Dimitri Neumann and Michel Vellekoop. Extends local scale invariance to markets driven by Poisson as well as Wiener processes, covering options with jumps, Lévy processes, and credit risk via restricted jump counts.
View paper →Scaling Invariance and Contingent Claim Pricing
Jiri Hoogland and Dimitri Neumann. Published as "Local Scale Invariance and Contingent Claim Pricing." Prices of tradables can only be expressed relative to one another at any instant, which yields a pricing framework based on local scale invariance as an alternative to martingale techniques.
View paper →Scaling Invariance and Contingent Claim Pricing II: Path-Dependent Contingent Claims
Jiri Hoogland and Dimitri Neumann. Published as "Local Scale Invariance and Contingent Claim Pricing II: Path-Dependent Contingent Claims," extending the framework to path-dependent claims.
View paper →Asians and Cash Dividends: Exploiting Symmetries in Pricing Theory
Jiri Hoogland and Dimitri Neumann, July 2000. Applies the symmetry framework to Asian options and to vanillas on stocks paying known cash dividends.
View paper →Tradable Schemes
Jiri Hoogland and Dimitri Neumann, 2000. Fitting a finite difference scheme to exact solutions of the pricing PDE, which the tradables formulation makes tractable because no drift terms appear. Applied to arithmetic Asian options and to vanillas on stocks paying known cash dividends.
View paper →Converting the Reset
Jiri Hoogland, Dimitri Neumann and D. Bloch, April 2001. An algorithm for the effects of resets in convertible bond prices without adding a factor to value the reset, and a straightforward treatment of notice periods and make-whole features.
View paper →