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Option pricing model
A local volatility model, in mathematical finance and financial engineering, is an option pricing model that treats volatility as a function of both the
Local_volatility
Researcher and lecturer in quantitative finance
maturities, establishing the so-called Dupire's approach to local volatility for modeling the volatility smile. The Dupire equation is a partial differential
Bruno_Dupire
Implied volatility patterns that arise in pricing financial options
Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that needs to be modified
Volatility_smile
Degree of variation of a trading price series over time
deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived
Volatility_(finance)
When variance is a random variable
security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert
Stochastic_volatility
South African economist and physicist
interest-rate models, and the Derman–Kani local volatility or implied tree model, a model consistent with the volatility smile. Derman, who first came to the
Emanuel_Derman
Stochastic volatility model used in derivatives markets
mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands
SABR_volatility_model
Pricing model
volatility model, although technically it would be classed more precisely as a local volatility model, that attempts to capture stochastic volatility
Constant elasticity of variance model
Constant_elasticity_of_variance_model
Continuous stochastic process
volatility smile problem, one can drop the assumption that the volatility ( σ {\displaystyle \sigma } ) is constant. If we assume that the volatility
Geometric_Brownian_motion
Type of option contract
continuous averaging: the local volatility model, including the Black-Scholes model as a limiting case with constant volatility. For the Black-Scholes model
Asian_option
Model in finance
the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a model assumes that the volatility of the asset is not
Heston_model
Partial differential equation
Semiparametric Modeling of Implied Volatility, 2005, Springer Verlag, ISBN 978-3-540-26234-3 Jim Gatheral (2008). The Volatility Surface. Wiley and Sons,
Fokker–Planck_equation
Right to buy or sell a certain thing at a later date at an agreed price
An alternate, though related, approach is to apply a local volatility model, where volatility is treated as a deterministic function of both the current
Option_(finance)
Concept in finance
option pricing More recently, the volatility surface-aware models in the local volatility and stochastic volatility families. The Black model extends
Valuation_of_options
Financial model
values. Local volatility and stochastic volatility models, including the SABR volatility model, are used to fit observed cap and swaption volatility smiles
Black_model
Application of mathematical and statistical methods in finance
Implied volatility, Volatility smile Local volatility Stochastic volatility Constant elasticity of variance model Heston model Stochastic volatility jump
Mathematical_finance
Academic discipline concerned with the exchange of money
The two main approaches are local volatility and stochastic volatility. The first returns the volatility which is "local" to each spot-time point of the
Financial_economics
How equities and debt instruments are valued
such as mean reversion, or will be "volatility surface aware", applying local volatility or stochastic volatility. Rational pricing is also applied to
Asset_pricing
Differential equations involving stochastic processes
stochastic differential equation Langevin dynamics Local volatility Stochastic process Stochastic volatility Stochastic partial differential equations Diffusion
Stochastic differential equation
Stochastic_differential_equation
Overview of finance and finance-related topics
model – Model in finance SABR volatility model – Stochastic volatility model used in derivatives markets Local volatility – Option pricing model Implied
Outline_of_finance
List of notable quantitative analysts
Prediction Company. Jim Gatheral, Scottish, known for work on the volatility smile and the volatility surface. Hélyette Geman French mathematician known for change
List_of_quantitative_analysts
Keyword used in some programming languages to tag variables
varies considerably among the programming languages that have the volatile keyword. Volatility can have implications regarding function calling conventions
Volatile (computer programming)
Volatile_(computer_programming)
Affine term structure modeling Fokker–Planck equation Dupire equation (local volatility) Hamilton–Jacobi–Bellman equation Merton's portfolio problem Optimal
List of named differential equations
List_of_named_differential_equations
Ongoing armed conflict in West Asia
of the natural gas, fertilizer, aviation, and tourism industries, and volatility in financial markets. As of September 2026[update], the US Department
2026_Iran_war
Investment product
varies among houses – popular choices are Dupire-type local volatility models, stochastic SABR Volatility Models, or models which allow mixing of the two.
Power reverse dual-currency note
Power_reverse_dual-currency_note
Method for evaluating stock options that divides time into discrete intervals
volatility for the Black-76-prices of each component caplet; see Interest rate cap § Implied Volatilities.) Given this functional link to volatility,
Lattice_model_(finance)
Italian mathematician (born 1966)
consistent with mixture models, applying this to volatility smile modelling in the context of local volatility models. He is also one of the main authors in
Fabio_Mercurio
Financial software
Machine. The Heston stochastic volatility model plug-in Archived 2012-06-11 at the Wayback Machine. The Dupire local volatility model plug-in Archived 2014-06-22
Fairmat
Georgian politician and military commander
local volatility. Before the October Revolution, a predominantly Ossetian Union of Revolutionary Peasantry was formed in South Ossetia to fight local
Valiko_Jugheli
Model used in financial mathematics
Probability Calculators Deloire et Roth 2024 "Multi-asset and generalised Local Volatility. An efficient implementation" [1] Phelim Boyle, 1986. "Option Valuation
Trinomial_tree
Measure of political volatility
dividing this total by two. The political volatility measured by the Pedersen index differs from the political volatility when parliamentary seats are considered
Pedersen_index
Gambling statistic
C.A., Russell, A.M.T., & Rockloff, M.J. House-edge information and a volatility warning lead to reduced gambling expenditure: Potential improvements to
Return_to_player
Businessman and entrepreneur (born 1971)
initial public offering (IPO) of SpaceX. Since then, his net worth has been volatile, largely because of changes in SpaceX’s valuation. His net worth reached
Elon_Musk
Model of asset returns
incorporates stochastic volatility components of heterogeneous durations. MSM captures the outliers, log-memory-like volatility persistence and power variation
Markov_switching_multifractal
Country in Eastern Europe and North Asia
W.; Roos, H.; Bekkers, F.; Usanov, A.; de Rave, R.; Jans, K. (2017). Volatility and friction in the age of disintermediation. The Hague Centre for Strategic
Russia
Intelligence in machines
data centers would generate sufficient profits, leading to increased volatility in technology and semiconductor stocks and to concerns about a potential
Artificial_intelligence
percentage volume of non-volatile matter ISO 3233-1:2019 Part 1: Method using a coated test panel to determine non-volatile matter and to determine dry-film
List of ISO standards 3000–4999
List_of_ISO_standards_3000–4999
Pedro Hernandez. Due to the past investigation, their relationship was volatile until the OSP's operational psychologist Nate Getz revealed to Gibbs that
List_of_NCIS_characters
Sandy Geographical Area in Poland
the desert was planted with pine and holly willow to consolidate the local volatile sands and protect the surrounding fields from being buried by sand.
Błędów_Desert
Municipal election in California
Spot". Emerson College Polling. May 13, 2026. Retrieved May 13, 2026. "Volatility Ahead in LA Mayor's Race; UCLA Luskin Poll Finds 40% of Voters Undecided"
2026 Los Angeles mayoral election
2026_Los_Angeles_mayoral_election
American television series
meant to inherit the 10 Petal Ranch Ed Harris as Everett McKinney, the local veterinarian in Rio Paloma and a Vietnam War Navy veteran Annette Bening
Dutton_Ranch
Technology hub in California, United States
John K. (2002). John Chambers and the Cisco Way: Navigating Through Volatility. John Wiley & Sons. p. 28. ISBN 9780471273554. W. Josephujjwal sarkar
Silicon_Valley
Ongoing armed conflict in the Middle East
fine particulate matter, 12% of particulate matter, 7% of non-methane volatile organic compounds, and 1% of emissions from ammonia, anitrogen and sulfur
Gaza_war
Decentralized digital cryptocurrency
include high costs, the inability to process chargebacks, high price volatility, long transaction times, and transaction fees (especially for small purchases)
Bitcoin
2024 shooting in Pennsylvania, U.S.
two from the Secret Service and two from local law enforcement. One of them, comprising three snipers (local SWAT officer Greg Nicol, SWAT team member
Attempted assassination of Donald Trump in Pennsylvania
Attempted_assassination_of_Donald_Trump_in_Pennsylvania
Holocene climate period during which northern Africa was wetter than today
to regional and local differences in vegetation. Africa is a diverse landscape and groundwater and local vegetation can modify local conditions; groundwater-fed
African_humid_period
2LAY15 5.99 The first responders deal with a suspected nerve agent leak at a local bank and Hen is trapped when she tries to help an unconscious victim inside
List_of_9-1-1_episodes
American rapper and actor (1971–1996)
(1996), the first hip-hop double album, abandoned introspective lyrics for volatile gangsta rap. It yielded two Billboard Hot 100-number one singles, "California
Tupac_Shakur
importers and vulnerable economies. The 2026 Iran war caused immediate volatility in energy markets, with Brent crude oil prices surging 10–13% to around
2026_Iran_war_fuel_crisis
Country in South Asia
three prime ministers served a full five-year term or more during this volatile period: P.V. Narasimha Rao (1991–1996), Atal Bihari Vajpayee (1999–2004)
India
Ongoing armed conflict in Southeast Asia
October 2022, Myanmar was blacklisted by the task force, which increased volatility in the value of the Burmese kyat. The war disrupted transport and stunted
Myanmar civil war (2021–present)
Myanmar_civil_war_(2021–present)
Australian murderer (born 1955)
Charles Knight (1927–2009), a friend and co-worker of her then-husband. The local backlash forced Barbara and Ken to move to Moree. None of her sons went
Katherine_Knight
British arsonist also convicted of attempted murder, manslaughter, assault and GBH
single mother born in England to an Irish family, who had left a previous volatile relationship. Duffy moved into Philpott's house shortly after, and the
Mick_Philpott
1974 familicide in New York, US
claimed during his interrogation that he had drugged his family. DeFeo had a volatile relationship with his father, but the motive for the killings remains unclear
Amityville_murders
Psychoactive drug, often called ecstasy
vascular smooth muscle tissue, stronger effects at the uterus, and no "local effect at the eye". MDMA was also found to have effects on blood sugar levels
MDMA
Indian-American film actor (born 1985)
said, "Oberoi's light-eyed cold-bloodedness lends credence to Gurgaon's volatility in a way that lets the film take any unresolved direction it chooses to
Akshay_Oberoi
East Asian liquid condiment
"special grade" is defined at ≥ 0.8 g/100 mL. Despite a large variety of volatile and odorant compounds that have been identified in soy sauce, the food
Soy_sauce
1997 American crime drama film by James Mangold
effectively untouchable by internal affairs, and are further protected by the local sheriff, Freddy Heflin. Having lost his hearing in one ear while rescuing
Cop_Land
Psychedelic drug
Administration than the large-scale groups because their product reaches only local markets. Many LSD dealers and chemists describe a religious or humanitarian
LSD
American billionaire hedge fund manager (born 1968)
compared to $982 million for the same period in 2019, due to increased volatility, volume and retail trader engagement. In January 2021, Griffin attracted
Ken_Griffin
Compressed form of cannabis resin
(Multidimensional analysis of cannabis volatile constituents: Identification of 5,5-dimethyl-1-vinylbicyclo[2.1.1]hexane as a volatile marker of hashish, the resin
Hashish
Premier of China since 2023
same month, he held a State Council meeting, where he alluded to the volatility in global oil and energy prices since the start of the 2026 Iran war,
Li_Qiang
Chinese automobile manufacturer
The BYD Dolphin was added to the local line-up in September 2023. All BYD models sold in Japan are adapted to local conditions by adopting the CHAdeMO
BYD_Auto
American video game retailer
from $17.25 to over US$500 per share. According to the SEC report, this volatility was only in part due to the massive buying power of retail investors.
GameStop
under the impact of a second salvo of direct hits which set fire to the volatile aircraft in Vincennes's hangar space, and the resultant flames became uncontrollable
List of U.S. Navy ships sunk or damaged in action during World War II
List_of_U.S._Navy_ships_sunk_or_damaged_in_action_during_World_War_II
Election to the 18th Legislative Assembly of the Indian state of West Bengal
of the peaceful transition of power in one of India's most politically volatile and populous states. Bangladesh, the neighboring country which borders
2026 West Bengal Legislative Assembly election
2026_West_Bengal_Legislative_Assembly_election
Species of fungus
day's mushrooms for genetic analysis should a poisoning outbreak occur. The local government also sends public alerts during mushroom season to warn about
Lanmaoa_asiatica
2022 U.S. Supreme Court case on abortion
2022. Wild, Whitney (June 7, 2022). "DHS bulletin warns US could see more volatile threats fueled by election misinformation and upcoming Supreme Court abortion
Dobbs v. Jackson Women's Health Organization
Dobbs_v._Jackson_Women's_Health_Organization
Indian businessman (born 1954)
Industries. He soon realised that the profitability of his business was volatile, fluctuating with the prices of his raw materials: copper and aluminium
Anil_Agarwal_(industrialist)
American actress
Wilson, Phil LaMarr, Wayne Knight". Variety. Retrieved April 5, 2024. Volatile Games. Dead to Rights: Retribution. Namco Bandai Games. Scene: Ending credits
Debra_Wilson
British television drama series
sought-after graduate. There, he struggles to reconnect with his father, a local publican, and breaks his sobriety. At dinner with the recruit, drunk, he
Industry_(TV_series)
internal ideological fractures, most notably regarding the politically volatile issue of Haredi military conscription. The instability reached a critical
2026 Israeli legislative election
2026_Israeli_legislative_election
Global stock market crash
altered implied volatility patterns that arise in pricing financial options. Equity options traded in American markets did not show a volatility smile before
Black_Monday_(1987)
рынках" [The dollar, unleashed by the uniquely growing US economy, promises volatility in the markets]. The Moscow Times (in Russian). 17 April 2024. Retrieved
Peace negotiations in the Russo-Ukrainian war (2022–present)
Peace_negotiations_in_the_Russo-Ukrainian_war_(2022–present)
Indian billionaire businessman (born 1959)
October 2024). "Class of 2024: India's Best CEOs Navigate Uncertainty, Volatility". Fortune India. Retrieved 13 October 2024. "JSW Group Chairman Sajjan
Sajjan_Jindal
Cohort born from 1997 to 2012
misguided and outdated. Living as young adults in what they perceive as a volatile world, they crave security. Compared to older cohorts, young voters of
Generation_Z
Political ideology promoting free-market capitalism
designed to counter the volatility of free markets. One motivation for the development of policies designed to mitigate the volatility of capitalist free markets
Neoliberalism
Welsh actor and presenter (born 1969)
to declare him "the most exciting young actor of his generation ... a volatile, electrifying and technically fearless performer". His 1993 turn as Perdican
Michael_Sheen
Type of derivative in finance
Girsanov theorem leading to a drift term which depends on its volatility, the FX rate volatility (FX rate between the pricing currency and the modeled variable
Quanto
TV documentary
her friend Liz are preparing for a sleepover when they meet a man at a local video store, and they both offer a ride. During the trip, the man turns
I_Survived...
How trading mechanisms and market design shape prices, liquidity, and transaction costs
fundamental volatility), or in response to the trading activity of impatient traders and its effect of liquidity (i.e. transitory volatility). This factor
Market_microstructure
Any of the fifteen lanthanides plus scandium and yttrium
as a price floor that bring stability to the market and reduce price volatility. On 21 October 2025, the Prime Minister of Australia, Anthony Albanese
Rare-earth_element
American crime drama television series
her ambitions on her younger cousin Lamar Kinsey and on Artillery, a volatile local rapper, while gang warfare escalates in South Los Angeles and record
The_Drop:_A_Snowfall_Saga
Prime Minister of Malaysia (1981–2003, 2018–2020)
Alor Setar-based seat of Kota Setar Selatan. Elected to parliament in a volatile political period, Mahathir, as a backbencher, launched himself into the
Mahathir_Mohamad
Mass shooting in Texas, U.S.
silhouette targets at distances of up to 100 yards. At approximately 1:34 p.m. local time, November 5, 2009, Hasan entered the Soldier Readiness Processing Center
2009_Fort_Hood_shooting
American actor (born 1943)
hunk of inept whimsey Bang the Drum Slowly will be unprepared for his volatile performance. De Niro does something like what Dustin Hoffman was doing
Robert_De_Niro
Class of CNS depressant drugs
of expired stock must be witnessed by a designated inspector (either a local drug-enforcement police officer or official from health authority). Benzodiazepine
Benzodiazepine
2015 film by Brian Helgeland
gangster) clashes with Reggie's restraint and insight. Ron's barely concealed volatility results in his publicly murdering George Cornell, an associate of the
Legend_(2015_film)
Anti-government protests
predictable business environment, and preventing losses caused by market volatility. There were no reported clashes with security forces on this day and it
2025–2026_Iranian_protests
American police procedural television series
N/A When a crisis erupts at a local hospital over a critical transplant error, Danny and Lena work to calm a volatile situation while the rest of the
Boston_Blue
Organomercury chemical compound
an extremely toxic organomercury compound with the formula (CH3)2Hg. A volatile, flammable, dense and colorless liquid, dimethylmercury is one of the strongest
Dimethylmercury
American singer and actor (1915–1998)
a lot" when he was a child. Dolly became influential in Hoboken and in local Democratic Party circles. During the Great Depression, Dolly provided money
Frank_Sinatra
City in Texas, United States
Mavericks owner and local entrepreneur Mark Cuban purchased land along Lamar Street near Cedars Station in September 2005, and locals speculate he is planning
Dallas
2024 video game
Jamboree "has the misfortune of not being very fun, and mistakes the volatility of chance and happenstance for being the same thing as competitive satisfaction
Super_Mario_Party_Jamboree
First suicide on live television
Gordon J. Acker described Chubbuck's new show to a local paper: "It will feature local people and local activities. It will give attention, for instance
Suicide_of_Christine_Chubbuck
Country in North America
expanded the northern presidios and missions into Alta California. The volatility of the urban poor in Mexico City was evident in the 1692 riot over the
Mexico
American professional wrestler and homicide victim (1946–1988)
hardly ever agreeing to lose matches and building a reputation of being volatile; he would on occasion intentionally hit or hurt opponents during a match
Bruiser_Brody
Financing rules for clubs in UEFA leagues
depend only on a rich benefactor however, then the financial model is too volatile." Despite broad approval across Europe, in early 2010, the European Club
UEFA Financial Fair Play Regulations
UEFA_Financial_Fair_Play_Regulations
Referendum held in Scotland
(...) The poll and count will be managed in the same way as [local] elections, by local returning officers (...) and directed by a Chief Counting Officer"
2014 Scottish independence referendum
2014_Scottish_independence_referendum
Eighteenth letter of the Greek alphabet
represent milliseconds. In finance, σ is the symbol used to represent volatility of stocks, usually measured by the standard deviation of logarithmic returns
Sigma
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LOCAL VOLATILITY
LOCAL VOLATILITY
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LOCAL VOLATILITY
LOCAL VOLATILITY
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