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¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Arbitrage (Generalized)
- … as Ross (1976) develops in his Arbitrage Pricing Theory, where no-arbitrage conditions across factor exposures pin down the structure of asset returns. 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.
- … as Ross (1976) develops in his Arbitrage Pricing Theory, where no-arbitrage conditions across factor exposures pin down the structure of asset returns. 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.
- 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.
- 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.
- 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.
- Risk management, hedging, and portfolio theory rely on stochastic modeling, as Black and Scholes (1973) operationalized in their option-pricing framework.
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