The Black-Scholes Equation is a mathematical model described by a second-order parabolic partial derivative equation. This model enables the theoretical calculation of a financial option’s price at a future date using the current stock price. Its applicability extends to different situations within the economic field, including company valuation, stock simulation, valuation of a real estate project portfolio, and risk management in financial institutions, among others. In this research, the numerical solution of the Black-Scholes Equation is obtained using finite differences and a Crank-Nicolson scheme. Also, a financial application is developed, allowing the user, after entering specific parameters, to get the solution of the equation for an interval of the present stock price value. After the validation of the program, it is used to evaluate Ecuadorian companies and a portfolio of Peruvian real estate projects. When the application user has the numerical solution of the Black-Scholes Equation, he can make an appropriate financial decision.

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Numerical Solution of the Black-Scholes Equation and Examples of Application in Financial Decision-Making

  • Nury-Gabriela Ortiz-Moya,
  • Santiago-David Quinga-Socasi,
  • Héctor-Alejandro Calvopiña-Enriquez

摘要

The Black-Scholes Equation is a mathematical model described by a second-order parabolic partial derivative equation. This model enables the theoretical calculation of a financial option’s price at a future date using the current stock price. Its applicability extends to different situations within the economic field, including company valuation, stock simulation, valuation of a real estate project portfolio, and risk management in financial institutions, among others. In this research, the numerical solution of the Black-Scholes Equation is obtained using finite differences and a Crank-Nicolson scheme. Also, a financial application is developed, allowing the user, after entering specific parameters, to get the solution of the equation for an interval of the present stock price value. After the validation of the program, it is used to evaluate Ecuadorian companies and a portfolio of Peruvian real estate projects. When the application user has the numerical solution of the Black-Scholes Equation, he can make an appropriate financial decision.