Black-Scholes for scientific computing students

Revisiting Black-Scholes Equation

In 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 ...

Markovian Black and Scholes

We generalize the classical binomial approach of the model of Black and Scholes to a Markov binomial approach. This leads to a new formula for the cost of an option.

The use of iterative methods for solving Black-Scholes equation

Confidence Interval for Solutions of the Black-Scholes Model

The forecast is very complex in financial markets. The reasons for this are the fluctuation of financial data, Such as Stock index data over time. The determining a model for forecasting fluctuations, can play a significant role in investors deci-sion making in financial markets. In the present paper, the Black Scholes model in the prediction of stock on year later value, on using data from mel...

Numerical Solutions for Fractional Black-Scholes Option Pricing Equation

In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.