Black–Scholes model
E59634
The Black–Scholes model is a fundamental mathematical framework in financial economics for pricing options and other derivatives by modeling asset prices as stochastic processes.
All labels observed (10)
How this entity was disambiguated
This entity first appeared as the object of triple T478470 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Black–Scholes model Context triple: [Itô calculus, usedIn, Black–Scholes model]
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
C.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
-
D.
Kolmogorov backward equation
The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
-
E.
Girsanov theorem
Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Black–Scholes model Target entity description: The Black–Scholes model is a fundamental mathematical framework in financial economics for pricing options and other derivatives by modeling asset prices as stochastic processes.
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
C.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
-
D.
Kolmogorov backward equation
The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
-
E.
Girsanov theorem
Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical model
ⓘ
option pricing model ⓘ stochastic process model ⓘ |
| appliesTo |
European call options
ⓘ
European put options ⓘ |
| assumes |
constant risk-free interest rate
ⓘ
constant volatility ⓘ continuous trading ⓘ frictionless markets ⓘ geometric Brownian motion for underlying asset price ⓘ lognormal distribution of asset prices ⓘ no arbitrage ⓘ no dividends on underlying asset in basic form ⓘ no transaction costs ⓘ |
| basisFor |
risk management techniques
ⓘ
volatility surface construction ⓘ |
| describes | dynamics of underlying asset price ⓘ |
| developedBy |
Fischer Black
ⓘ
Myron Scholes ⓘ Robert C. Merton ⓘ |
| extendedTo |
currency options
ⓘ
dividend-paying assets ⓘ index options ⓘ |
| field |
financial economics
ⓘ
mathematical finance ⓘ quantitative finance ⓘ |
| hasLimitation |
assumes constant volatility contrary to empirical evidence
ⓘ
assumes continuous trading and no transaction costs ⓘ cannot capture volatility smile ⓘ |
| influenced | modern derivatives markets ⓘ |
| involvesParameter |
cumulative normal distribution function
ⓘ
risk-free interest rate ⓘ strike price ⓘ time to maturity ⓘ underlying asset price ⓘ volatility of underlying asset ⓘ |
| publicationYear | 1973 ⓘ |
| publishedIn | Journal of Political Economy ⓘ |
| recognizedBy |
Nobel Memorial Prize in Economic Sciences
ⓘ
surface form:
Nobel Prize in Economic Sciences for Myron Scholes and Robert C. Merton in 1997
|
| relatedTo |
Black–Scholes model
self-linksurface differs
ⓘ
surface form:
Black–Scholes formula
Greeks (option sensitivities) ⓘ delta hedging ⓘ implied volatility ⓘ |
| uses |
Itô calculus
ⓘ
surface form:
Ito calculus
risk-neutral valuation ⓘ stochastic differential equation ⓘ |
| yields |
Black–Scholes model
self-linksurface differs
ⓘ
surface form:
Black–Scholes partial differential equation
closed-form solution for European call option price ⓘ closed-form solution for European put option price ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Black–Scholes model Description of subject: The Black–Scholes model is a fundamental mathematical framework in financial economics for pricing options and other derivatives by modeling asset prices as stochastic processes.
Referenced by (18)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Scholes
this entity surface form:
Black–Scholes partial differential equation
this entity surface form:
Black–Scholes formula
this entity surface form:
Black–Scholes–Merton model
this entity surface form:
Black–Scholes–Merton model
this entity surface form:
Black–Scholes option pricing model
this entity surface form:
“The Pricing of Options and Corporate Liabilities”
this entity surface form:
1973: The Pricing of Options and Corporate Liabilities
this entity surface form:
Black–Scholes–Merton model
this entity surface form:
Black–Scholes–Merton option pricing model
this entity surface form:
Black–Scholes option pricing model
this entity surface form:
The Pricing of Options and Corporate Liabilities