MATEO - Mannheimer Texte Online
The present work studies a combined model of the bond and stock market and its applications to actuarial science. To this extent a revolving generalization of the Heath-Jarrow-Morton bondmarket model is constructed.
Within the integrated model of bond and stock market the stock index is considered "as is", namely as the sum of its constituting shares. Pragmatic reasons led to the exemplifications on the German Stock Market Index DAX, a trade mark of the German Stock Exchange Deutsche Börse AG.
The interplay between actuarial and financial risk is stated in the form of a Principle of Actuarial and Financial Mathematics. Although new developments on this field make implicit use of it, it has never been stated in the literature at the authors disposition. The main statement of this Principle is the settlement of the settings for the actuarial and financial risk management. Based on this Principle the following risk analysis is possible:
The common approach in the literature used to skip the second step, i.e. identify the risk sources and take expectations. Into the authors opinion the detailed risk analysis based on the above Principle is a key factor in the competition on the insurance and financial markets. Depending on how extensive insurance companies will follow the growth on the financial markets to match their liabilities we may see in the next years a reassessment of the actuarial principles on the grounds of this Principle. This is already the case with the unit-linked life insurance with guarantee, which is dealt with in the last chapter of the present work due to its complexity.
The present work is divided in three chapters. The first chapter illustrates the role of the bond market in pricing derivatives, presents the HJM bond market methodology and makes it amenable to dynamic hedging strategies.
The second chapter is devoted to stock index arbitrage and exemplifies it on the DAX. The following three sections deal with the index arbitrage, in increasing order of model complexity:
The third chapter considers the implications of the bond and stock market to the actuarial mathematics. A programmatic Principle is stated in the second section. Based on it and on the assessment of cashflows within the HJM bond market the Hattendorff Theorem is generalized to include the interest rate risk. The chapter concludes with the unit-linked life insurance policies. For the pricing of the optional part of these policies the integrated part of the bond and stock market is used. Also, the stock index is more realistically considered as the sum of the constituting shares. In this general context the forward start options of [MR] are priced for the cliquet-style construction of the optional part of the unit-linked life insurance policy.
The no-arbitrage principle has been consequently followed in the choice of the input parameters, only market data has been used in the computations. This data consists of the volatilities of the DAX shares and the REX subindices together with their correlations and is listed in the tables of the appendix.
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