1. Solving partial differential equations related to option pricing
with numerical methods.
In these Master's thesis projects you solve partial differential equations (pdes) or partial integro-differential equations in financial mathematics with numerical methods.
It is possible, under certain assumptions on the development of stock prices, to compute the value of an option with the help of pdes. The basic equation is the well-known Black-Scholes equation. A standard option is a contract to buy or sell stocks at a certain time in the future for a prescribed amount of money. Nowadays, there are many different option variants on the market. Some of them lead to interesting numerical aspects in the discretization and numerical solution of the pde, like discontinuous final conditions or higher
dimensionality. An additional integral term is appearring in the differential equation if jumps are included in the model for the stock prices. This brings other interesting numerical issues.
In these Master's thesis projects you will get acquainted with the world of stocks and options by a literature studies.Furthermore, you will solve a pde accurately and efficiently. We are interested in options on more than one stock, but also in other exotic options.