What does this research mean for the field?

Rigorous mathematical proofs substantiate the foundational theorems of stochastic calculus and their applications in quantitative finance models, including the Black-Scholes framework, Heston model, and SABR expansion. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish complete and rigorous mathematical proofs for foundational stochastic calculus and advanced option pricing models.

September 8, 2026Open Access

Proofs and Derivations for the Math Journey to Black-Scholes, Greeks and Beyond

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Authors

YDY Diawara

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Implication

Theoretical derivation demonstrates rigorous mathematical foundations in financial derivative pricing models, highlighting unified analytical verification for quantitative finance frameworks.

Key Points

To establish complete and rigorous mathematical proofs for foundational stochastic calculus and advanced option pricing models.
Derived measure-theoretic and stochastic integration principles from Jensen's inequality and the Radon-Nikodym theorem through Itô's lemma and martingale representation.
Formulated rigorous derivations for the full Black-Scholes apparatus, including Feynman-Kac, Girsanov, Novikov conditions, and the Greeks.
Proved key formulations for extended models, including Dupire's formula, Heston characteristic functions via Riccati ODEs, SABR expansions, and Fundamental Theorems of Asset Pricing.
Provided complete analytical verifications for core stochastic calculus tools and classical derivative pricing mechanisms without heuristic shortcuts.
Established formal proofs for advanced pricing frameworks, including Merton jump-diffusion pricing and Cox-Ross-Rubinstein convergence to Black-Scholes.

Cite This Study

Y Diawara (2026) studied this question.

synapsesocial.com/papers/6a9fd78a58e84d0ff5b463e6 https://doi.org/10.5281/zenodo.22503437

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Implication

Theoretical derivation demonstrates rigorous mathematical foundations in financial derivative pricing models, highlighting unified analytical verification for quantitative finance frameworks.

Proofs and Derivations for the Math Journey to Black-Scholes, Greeks and Beyond

Discussion

Member takes

Implication

Key Points

Cite This Study

Proofs and Derivations for the Math Journey to Black-Scholes, Greeks and Beyond

Discussion

Member takes

Implication

Key Points

Cite This Study

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