Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ...Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.展开更多
一、期权定价理论的Black—Scholes模型:偏微分方法
期权定价理论是微观金融字的重要内谷之一,而Black—Scholes模型是期权定价理论乃至整个金融领域的一个重大突破。该模型的推导可以从两条线索展开而得到相同的结论:(1)由Black ...一、期权定价理论的Black—Scholes模型:偏微分方法
期权定价理论是微观金融字的重要内谷之一,而Black—Scholes模型是期权定价理论乃至整个金融领域的一个重大突破。该模型的推导可以从两条线索展开而得到相同的结论:(1)由Black and Scholes(1973)开创的偏微分方程;(2)由Harrison and Kreps(1979)以及Harrison and Pliska(1981)首先提出的鞅方法。展开更多
文摘Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.
文摘一、期权定价理论的Black—Scholes模型:偏微分方法
期权定价理论是微观金融字的重要内谷之一,而Black—Scholes模型是期权定价理论乃至整个金融领域的一个重大突破。该模型的推导可以从两条线索展开而得到相同的结论:(1)由Black and Scholes(1973)开创的偏微分方程;(2)由Harrison and Kreps(1979)以及Harrison and Pliska(1981)首先提出的鞅方法。