Abstract
During the last two decades there has been an explosion in the number of complex financial instruments that are traded on the financial markets. Naturally, being able to value the increasing number of traded complex financial instruments has an academic interest. Such valuation methods are, however, certainly not only of interest to academics. For agents on the financial markets, it is of crucial importance to be able to assess the value of new exotic securities. This is equally true for financial services firms that construct and promote the instruments, borrowers that sell the products for the financing of their activities and investors that buy the products. Many new financial instruments have attributes that make Contingent Claims Analysis (CCA) superior to other currently known valuation methods. CCA is a technique for determining the price of an asset whose payoffs depend upon the evolution of one or more underlying state variables. One problem that often arises when this framework is used is that it is not possible to find a closed-form solution for the price. Numerical methods must therefore be relied on. Furthermore, in many cases and especially in cases where there is more than one underlying state variable, which many complex financial instruments require for accurate valuation, numerical methods become computationally laborious. Hence, research concerning and development of efficient numerical methods that can be used in the CCA context is important. This dissertation consists of four different papers (papers A to D). Paper A provides discussion of the process of financial innovation. A lengthy appendix is attached to paper A. In this appendix, more thn 100 more or less complex financial instruments are described briefly. Papers B to D have a common theme, which is valuation of complex financial instruments with the help of CCA and numerical methods. The research task of paper B is to answer a question that has unclear status in academic literature. The question is "How do errors (or different modelling choices) in boundary conditions affect solutions when the implicit finite difference method is used?". In papers C and D, numerical methods which can be used to price financial instruments with several underlying state variables are developed and tested. The methods in paper C are finite difference methods, and the method in paper D is a lattice (or tree) approach.