Black–Scholes model

E59634

mathematical model option pricing model stochastic process model

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.

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Observed surface forms (4)

Surface form	Occurrences
Black–Scholes–Merton model	2
Black–Scholes formula	1
Black–Scholes partial differential equation	1
Scholes	1

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 ⓘ

Referenced by (6)

Full triples — surface form annotated when it differs from this entity's canonical label.

Paul Scholes → familyName → Black–Scholes model ⓘ

this entity surface form: Scholes

Kiyoshi Itô → influenced → Black–Scholes model ⓘ

this entity surface form: Black–Scholes–Merton model

Itô’s lemma → isUsedIn → Black–Scholes model ⓘ

this entity surface form: Black–Scholes–Merton model

Black–Scholes model → relatedTo → Black–Scholes model self-linksurface differs ⓘ

this entity surface form: Black–Scholes formula

Itô calculus → usedIn → Black–Scholes model ⓘ

Black–Scholes model → yields → Black–Scholes model self-linksurface differs ⓘ

this entity surface form: Black–Scholes partial differential equation