James Johnston

Dr Pavel Gapeev

This course is available on the MSc in Financial Mathematics, MSc in Mathematics and Computation and MSc in Quantitative Methods for Risk Management. This course is available with permission as an outside option to students on other programmes where regulations permit.

Knowledge of Stochastic Processes (as for example provided in ST409) and Ordinary Differential Equations (as for example provided in MA209).
 

Optimal stopping problems form an important and well-developed part of stochastic control theory which have the pricing of real options as their immediate application. Their objectives are to identify the times at which such claims depending on the continuously observable underlying asset prices should be exercised with the aim of optimising the expected rewards. The optimal exercise times in such problems in Markovian models normally represent the first times at which the underlying asset price processes exit the appropriate continuation regions determined by certain boundaries. Such optimal exercise boundaries are particularly found in an explicit form for the (perpetual) real options with payoffs depending on the running asset values as well as their running maxima/minima or integral processes in the classical Markovian (jump-)diffusion models for the underlying asset prices. The course develops the methods for solutions to the real option and related pricing problems (such as pricing of callable and convertible bonds and defaultable options) including the derivations of explicit expressions for the optimal exercise boundaries in various Markovian models of financial markets.

10 hours of seminars and 20 hours of lectures in the Winter Term.

There will be regular homework assignments.

A reading list will be provided in a syllabus that will be available to students at the beginning of the academic year.

Essay (100%).

100% Coursework (More details will be provided in a syllabus that will be available to students at the beginning of the academic year.)