Applications in Mathematical Finance

Abstract

This chapter covers financial applications. First a brief survey is given on the specific Levy processes that are frequently used to model financial processes (such as the evolution of an asset price); special attention is paid to the normal inverse Gaussian process, the variance gamma process, and the generalized tempered stable process (which also covers the CGMY process). Then we explain how Levy processes can be estimated from data. A substantial part of this chapter focuses on the computation of prices of exotic options, such as the barrier option and the lookback option, whose payoff functions can be expressed in terms of the extreme values (over a given time horizon) that are attained by the price of the underlying asset. The chapter is concluded by an account of the use of Levy fluctuation theory in non-life insurance.