Bewertung eingebetteter Optionen - ein Replikationsansatz

From a financial mathematics point of view, German building savings contracts are complex financial instruments. In particular the valuation of embedded options places specific demands on actuaries due to the dynamic interactions between these multiple options and the partial lack of financial rationality of the contract holders. To date, German building societies use various models for the risk valuation of embedded options in building savings contracts. For this work, the concept of the replication portfolio, which has been used in life insurance for some time, was transferred to building savings contracts and implemented in a Jupyter Notebook framework. A specific cash flow approach and filtering algorithms were developed to deal with the problems arising in a standard approach. Initial test results on the contract portfolio of Bausparkasse Schwäbisch Hall AG are very promising. Further research and development work is required for practical application, but the authors believe that in the long term the approach has the potential to develop into a standard for the (risk) assessment of embedded building savings options. Furthermore, the developed concept might be helpful for other applications not restricted to German building societies.