At the same time, a student at our institute did her Master thesis on the old publications of Jacobi. On numerical issues related to partial differential equation models for option pricing in financial mathematics Dr. C.W. Oosterlee German Nat. In the first part of this seminar an introduction will be given to the mathematical models that are used in financial mathematics for option pricing. In particular, we will derive and discuss the so-called Black and Scholes partial differential equation. The second part of the seminar will deal with numerical methods for solving the equation.
European options are typically the simplest to solve.
An analytic solution can even be determined for many options of this type. For American options, we have to deal with obstacle problems. Here, an additional feature is that in one of the dimensions only a first order derivative appears. This leads to specific considerations for an accurate discretization. The resulting discretization can first be evaluated, for example for European options and can there be compared to an analytic solution.