主讲人：Peter W. Duck，School of Mathematics, The University of Manchester
The seminal work of Black & Scholes (1973) and Merton (1973) has led to an explosion of ideas in the theory of the pricing of financial derivatives,in particular options (and a joint Nobel price for economics). A put (call) option is a contract between two parties, in which one party, the holder, has the right to sell (buy) an asset from the other party, the writer. Obviously the right implies some value to this contract, and this is what option pricing theory is all about. In this talk a brief overview of the subject is given,Monte-Carlo simulation methods are described, and a short derivation of the now well known Black-Scholes equation is presented. This equation, which is pivotal in numerous studies of this kind is of backwards parabolic type, although a series of routine transformations can reduce the basic form to the heat-conduction equation.
The first case considered is that of European options (which can only be exercised on a prescribed date), for which exact solutions exist.
The second case considered is that of American options. This class of option is one where the holder of the option has the right to exercise at any time during the lifetime of the option. These lead to free boundary problems (basically the location in asset space where the option should be exercised), and as such these are nonlinear problems. Nonetheless, these are amenable to standard computational techniques.
No prior knowledge of Mathematical Finance will be assumed!
报告人简介：Professor Duck is the Head of the School of Mathematics, a Professor in Applied Mathematics. More information can be found on his personal website: http://www.maths.manchester.ac.uk/~duck/