Revisiting the Black-Scholes equation

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dc.creatorWang, D. F.
dc.date1998-05-10
dc.date.accessioned2026-07-07T12:07:08Z
dc.date.available2026-07-07T12:07:08Z
dc.descriptionIn common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships among the securities in the asset market. In special case where the interest rate is constant, he rederived the Black-Scholes partial differential equation from the general equilibrium asset market. In this work, I follow Cox-Ingersoll-Ross formulation to consider an economy which includes (1) uncertain production processes, and (2) the random technology change. Assuming a random production stochastic process of constant drift and variance, and assuming a random technology change to follow a log normal process, the equilibrium point of this economy will lead to the Black-Scholes partial differential equation for option pricing.
dc.description12 pages, Revtex style
dc.identifierhttps://arxiv.org/abs/cond-mat/9805115
dc.identifierhttp://arxiv.org/abs/cond-mat/9805115
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208863
dc.subjectStatistical Mechanics
dc.subjectPricing of Securities
dc.titleRevisiting the Black-Scholes equation
dc.typetext

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