Christian Hassold

The Valuation of Multivariate Options Christian Hassold

Diplomarbeit, die am 17.06.2004 erfolgreich an einer Universität in Deutschland im Fachbereich Wirtschafts- und Sozialwissenschaftliche Fakultät eingereicht wurde. Abstract: During the last decades, capital markets have transformed rapidly. Derivative securities - or more simply derivatives - like swaps, futures, and options supplemented the trading of stocks and bonds. These financial products can frequently be seen in the media: Due to derivatives, Procter & Gamble lost $150 million in 1994, Barings Bank lost $1.3 billion in 1995 and Long-Term Capital Management (LTCM) lost $3.5 billion in 1998. Though these figures seem daunting, derivatives can be useful financial instruments. Applications include risk management, speculation, reduced transaction costs, and regulatory arbitrage. Theory and practice of option valuation were revolutionized in 1973, when Fischer Black and Myron Scholes published their celebrated Black Scholes formula in the landmark paper "The pricing of options and corporate liabilities". Afterwards, a vast amount of papers on option valuation was published which employ all kinds of stochastic processes. Thereby, the special features of financial return data are tried to be taken into account. Advancing option valuation theory to options with multiple underlyings, lead to the problem that the dependence structure of the underlying securities needs to be considered. Though linear correlation is a widely used dependence measure, it may be inappropriate for multivariate return data. Throughout the last years, dependence modelling through copulas has become common. Copulas are multivariate distributions on the d-dimensional unit-hyper-square which couples d marginal distributions to a joint distribution. Copulas can be used to construct dependence measures like the rank correlation coefficients of Spearman or Kendall. They are also a useful tool in the context of option valuation. The prices of