Applied Mathematics: Introduction to C++ Scientific Computing Project
Geometric Brownian Motion and Stock Prices: Geometric Brownian motion (GBM) can be simulated using a numerical solution to a stochastic differential equation, using schemes such as the Euler-Maruyama Method that are similar to the Euler method we used to solve an ODE in assignment 2 and 3 but have an additional random noise term (note that the std library contains implementations of almost any random number distribution you might wish, for example std::normal_distribution would be helpful for this project). GBM is used to model stock-prices in the Black-Sholes model. In this project you would investigate using simulations of many realizations of a GBM in order to model stock and option pricing. For a mini-project you could implement a generic GBM for a stock and work out the expectation values for the price of the stock at some later time, along with it's standard deviation (related to the risk or volatility). For the main project you would add some option pricing, and potentially some other functions related to the Black-Sholes model. Extensions would include constructing a local volatility model (perhaps based on some historical data such as index prices you could download from somewhere) or a stochastic volatility model.
Textbook - Undergraduate Topics in Computer Science - Guide to Scientific Computing in C++ by Joe Pitt-Francis and Jonathan Whiteley.