The Pricing of Options and Corporate Liabilities.¶
Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
Cited by¶
8 citations across 8 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Arbitrage (Generalized)
- Black and Scholes (1973) similarly derive option pricing from the requirement that a replicating portfolio admit no arbitrage, anchoring the cross-instrument case.
This sourceFoundational option pricing paper: derives the convex payoff structure of European options under continuous hedging and formalizes the asymmetric risk-return profile (capped downside, unlimited upside) as the consequence of payoff convexity.
- Black and Scholes (1973) similarly derive option pricing from the requirement that a replicating portfolio admit no arbitrage, anchoring the cross-instrument case.
- Discounting (Present Value)
- Black-Scholes (1973)
This sourceDerives option pricing via continuous riskless hedging and the no-arbitrage principle; supports the T5 claim that Black-Scholes resolved time/risk handling in derivatives pricing through continuous-time discounting and risk-neutral measures.
Supported in partVerified against the publisher's abstract
The paper's own abstract derives the option valuation formula from the no-arbitrage/portfolio-duplication principle and extends it to corporate liabilities, but says nothing of continuous-time discounting or risk-neutral measures.
“If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived.”
- Black-Scholes (1973)
- Optionality
- The core insight, formalized by Black and Scholes (1973), is that optionality has positive value precisely because the future is uncertain and the right to choose later is worth more than forced commitment now.
This sourceFoundational option pricing paper: derives the convex payoff structure of European options under continuous hedging and formalizes the asymmetric risk-return profile (capped downside, unlimited upside) as the consequence of payoff convexity.
Supported in partVerified against the publisher's abstract
The abstract confirms Black-Scholes derives an option valuation formula and treats corporate liabilities as options, but it does not state that optionality's value rests on uncertainty or on deferring commitment.
“Using this principle, a theoretical valuation formula for options is derived.”
- The core insight, formalized by Black and Scholes (1973), is that optionality has positive value precisely because the future is uncertain and the right to choose later is worth more than forced commitment now.
- Random Walk
- The diffusion limit transfers the heat-equation toolkit from physics to finance: Black–Scholes is the heat equation in disguise because the log-price is a random walk whose continuum limit is Brownian motion, so first-passage-time results for diffusing particles become barrier-option and default-time results for prices without re-derivation.
This sourceModels the log-price as Brownian motion (the continuum limit of the return walk), turning option pricing into a heat-equation problem.
Supported in partVerified against the publisher's abstract
Black-Scholes (1973) supplies the derivative-pricing framework that treats corporate liabilities, including bond default, as options; the abstract we hold does not state the heat-equation or first-passage mapping.
“Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.”
- The diffusion limit transfers the heat-equation toolkit from physics to finance: Black–Scholes is the heat equation in disguise because the log-price is a random walk whose continuum limit is Brownian motion, so first-passage-time results for diffusing particles become barrier-option and default-time results for prices without re-derivation.
- Stochasticity vs. Determinism
- Risk management, hedging, and portfolio theory rely on stochastic modeling, as Black and Scholes (1973) operationalized in their option-pricing framework.
This sourceFoundational option pricing paper: derives the convex payoff structure of European options under continuous hedging and formalizes the asymmetric risk-return profile (capped downside, unlimited upside) as the consequence of payoff convexity.
Supported in partVerified against the publisher's abstract
The paper's own abstract supplies the option-pricing formula and its extension to corporate liabilities, but says nothing about risk management, hedging or portfolio theory relying on stochastic modeling.
“Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants.”
- Risk management, hedging, and portfolio theory rely on stochastic modeling, as Black and Scholes (1973) operationalized in their option-pricing framework.
Domain-specific¶
- Black–Scholes Model
- The Black–Scholes model is the closed-form option-pricing formula derived by Fischer Black, Myron Scholes, and Robert Merton (1973) for European options on a non-dividend-paying stock, under the assumption that the underlying price follows geometric Brownian motion with constant volatility
This sourceBlack and Scholes's derivation of the closed-form value of a European option on a non-dividend-paying stock whose price follows a lognormal random walk with constant variance. The result that the option's value, as a function of the stock price, is independent of the expected return on the stock.
Supported in partVerified against the source
- The Black–Scholes model is the closed-form option-pricing formula derived by Fischer Black, Myron Scholes, and Robert Merton (1973) for European options on a non-dividend-paying stock, under the assumption that the underlying price follows geometric Brownian motion with constant volatility
- Derivative
- The Black–Scholes framework gives closed-form expressions for these derivatives
This sourceThe Black–Scholes derivation of a closed-form theoretical option valuation formula.
Supported in partVerified against the publisher's abstract
“Using this principle, a theoretical valuation formula for options is derived.”
- The Black–Scholes framework gives closed-form expressions for these derivatives
- Differential equation
- . Electromagnetism — fields from sources: Maxwell's equations as a first-order PDE system giving the electric and magnetic field everywhere. Fluid dynamics and diffusion — transport and spreading: Navier–Stokes and the heat equation ∂u/∂t = α∇²u governing flow and conduction. Population biology and epidemiology — growth and spread: the logistic equation dy/dt = ry(1 − y/K) approaching carrying capacity, and SIR-type compartmental models with threshold dynamics. Mathematical finance — fair-value evolution: the Black–Scholes parabolic PDE for option prices driven by drift and the curvature of the price function
Supported in partVerified against the publisher's abstract
“If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.”
- . Electromagnetism — fields from sources: Maxwell's equations as a first-order PDE system giving the electric and magnetic field everywhere. Fluid dynamics and diffusion — transport and spreading: Navier–Stokes and the heat equation ∂u/∂t = α∇²u governing flow and conduction. Population biology and epidemiology — growth and spread: the logistic equation dy/dt = ry(1 − y/K) approaching carrying capacity, and SIR-type compartmental models with threshold dynamics. Mathematical finance — fair-value evolution: the Black–Scholes parabolic PDE for option prices driven by drift and the curvature of the price function
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 7 of 8 citations: 7 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:2d6b83ecb168 · see in the full table