Introduction

We are using a Black-Scholes stochastic model to forecast the behavior of the stock market by calculating the option pricing at various time intervals. Black-Scholes is the most widespread mathematical model used in financial markets, for pricing options on various assets such as equities, stock options and so on. Other numerous models (like the Heston model) can be formulated by modifying the assumptions of the Black-Scholes model. Black-Scholes is often criticized for its strict assumptions. This can be alleviated by pairing it up with Monte-Carlo simulations.

Performing Monte-Carlo not only provides a better approximation, but is also a practical method for forecasting stock prices. These samples can then be extended to calculating prices of various options such as the American or the European call and put, Asian markets, etc. Black-Scholes model in itself is a continuous time-driven stochastic process but since computer simulations require discrete time processes, we are discretizing Black-Scholes by what is known as Euler discretization.

The Black–Scholes model assumes that the market consists of at least one risky asset, usually called the stock, and one riskless asset, usually called the money market, cash, or bond. The rate of return on the riskless asset is constant and thus called the risk-free interest rate.