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Prof. Dr. Klaus Sandmann Publications

Research Profile

Term Structure of Interest Rates
The arbitrage theory of the term structure of interest rates serves as the main tool for the pricing and hedging of interest rate dependent derivatives. It provides the basis for the risk management of banks and financial institutions with regard to interest-rate-dependent derivatives such as options on bonds, financial futures and interest rates (caps, floors and swaptions). Many models of the term structure are formulated with respect to continuously compounded interest rates. These rates are not identical to observable interest rates. One observation is, that the expected roll over returns are finite even within in log-normal framework if instead of continuously compounded rates the stochastic dynamics of nominal rate are the modelling elements (Sandmann, Sondermann (1997). One of the most important term structure models, the so called LIBOR-Market Model (Miltersen, Sandmann, Sondermann (1997)) covers this case. Among others the famous Black formula for caps and floors has shown to be arbitrage free. In a recent study on the term structure of futures rates new no-arbitrage conditions on the volatility surface of the term structure of interest rates are derived (Miltersen, Nielsen, Sandmann (2006)).


Exotic Option Pricing
The market share of non exchange traded derivative securities exceeds by far that of exchange traded ones. Important examples are Barrier Options and options on the average of an underlying asset, exchange rate or interest rate. In many cases the value and the hedging can only be approximated by numerical methods or simulations. For average options this is analyzed in Nielsen, Sandmann (1996a, 2002, 2003).


Risk management of non-standard interest rate dependent claims
The pricing and hedging of standardized interest rate financial products like bond options, caps and floors and swaptions is well developed. Non-standard products with broken compounding periods, time delayed payment dates, barrier conditions or individual exercise opportunities are frequently offered by financial institutions. In many cases the pricing of these products is derived by numerical procedures relative to a specific model assumption. A more robust approach than the numerical approximation relies on super hedging ideas. These approaches are usually based on weaker model assumptions. One very promising approach is based on the uncertain volatility approach by Avellaneda, Levy and Paras (Pricing and Hedging Derivative Securities in Markets with Uncertain Volatilities, Applied Mathematical finance 2(2), 1995, 73-88). This approach refers to the price process of one underlying process. In case of interest rate risk we have to consider a full term structure model. The extension of the uncertain volatility approach to the term structure of interest rates is not yet derived. Furthermore as demonstrated in Chen, Sandmann (2012) for in- arrear term structure products well established practitioner rules like the convexity adjustment yields stunningly good model independent bounds for the pricing and hedging of in arrear contracts.


Equity linked pension and life insurance with guarantees
Equity linked life and pension insurance contracts are related to financial risk as well as to non-financial risk. The non-financial risk is among others related to the death and survival risk of the insured and to early exercise by the insured for example due to unemployment. The pricing and hedging of these contracts is related to the diversification technique within a cohort of insured persons and to the dynamic duplication by trading in a financial market. In addition periodic premium and long time to maturity complicates the hedging problem for the insurer. So far these problems are addressed only within very specific modelling framework. Within this research project we like to consider robust contract specifications in the sense of close approximation by super hedging strategies and model independency. The solution involves the contract design as well as the construction of the underlying financial portfolio (Nielsen, Sandmann (1995, 1996b, 2002), Nielsen, Sandmann, Schlögl (2011)).


Executives´ Stock Options Schemes
The financial crisis has pushed compensation policy like Executives´ Stock Options (ESOs) at the forefront of the public debate. An on-going discussion is whether ESOs have in fact encouraged the managers to take on too large risks which might improve their own benefits but jeopardize the firm. People doubt that ESOs have always positive effects on the firm's performance. Sustainability and incentive compatibility are the main qualitative keywords within the present discussion. In Chen, Pelger, sandman (2013) we advocate two executive non-traditional performance-based stock option schemes which discourage managers from excessive risk taking: Parisian and constrained Asian executives' stock option plans. Both options have a criterion on the terminal value similar to a call option, but in addition impose a restriction on the path of the firm's assets process. Both schemes make the exaggerated risk taking through the executives less likely.

Publications

Refereed Articles

  • Chen, An; M. Pelger; K. Sandmann (2013): New Performance-Vested Stock Option Schemes; Applied Financial Economics 23(8), 709-727.
  • Chen, A.; K. Sandmann (2012): In Arrear Term Structure Products: No Arbitrage Pricing Bounds and The Convexity Adjustments, International Journal of Theoretical and Applied Finance (IJTAF) 13(01), 139-161.
  • Nielsen, J. A.; K. Sandmann; E. Schlögl (2011): Equity-linked pension schemes with guarantees; Insurance, Mathematics and Economics 49; 547–564.
  • Sandmann, K.; M. Wittke (2010): It's Your Choice: A Unified Approach To Chooser Options, International Journal of Theoretical and Applied Finance (IJTAF) 13(01), 139-161.
  • Mahayni, A.; K. Sandmann (2008): Return guarantees with delayed payments, German Economic Review 9(2), 207-231.
  • Miltersen, K.R.; J.A. Nielsen; K. Sandmann (2006): New no-arbitrage conditions and the term structure of interest rate futures, Annals of Finance 2(3), 303-325.
  • Nielsen, J.A.; K. Sandmann (2003): Pricing Bounds on Asian Options; Journal of Financial and Quantitative Analysis 38(2), 449-473.
  • Nielsen, J.A.; K. Sandmann (2002): Asian Exchange Rate Options under Stochastic Interest Rates: Pricing as a Sum of Delayed Payment Options; Finance and Stochastics 6(3), 355-370.
  • Miltersen, K. R.; K. Sandmann; D. Sondermann (1997): Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates; The Journal of Finance 52(1), 409-430.
  • Sandmann, K.; D. Sondermann (1997): A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures; Mathematical Finance 7(2), 119-125.
  • Nielsen, J.A.; K. Sandmann (1996a): The Pricing of Asian Options Under Stochastic Interest Rates; Applied Mathematical Finance 3(3), 209-236.
  • Nielsen, J.A.; K. Sandmann (1996b): Uniqueness of the Fair Premium for Equity-Linked Life Contracts; The Geneva Papers on Risk and Insurance Theory 21(1), 65-102.
  • Sandmann, K.; E. Schlögl (1996): Zustandspreise und die Modellierung des Zinsänderungsrisikos; Zeitschrift für Betriebswirtschaftslehre 66 (7), 813-836.
  • Nielsen, J.A.; K. Sandmann (1995): Equity-linked Life Insurance - A Model with Stochastic Interest Rates; Insurance, Mathematics and Economics 16(3), 225-253.
  • Rady, S.; K. Sandmann (1994): The Direct Approach to Debt Option Pricing. The Review of Futures Markets; 13(2), 461-514;
  • Sandmann, K. (1993): The Pricing of Options with an Uncertain Interest Rate: A Discrete Time Approach; Mathematical Finance; 3(2), 201-216.
  • Sandmann, K.; D. Sondermann (1993): A Term Structure Model and the Pricing of Interest Rate Derivatives; The Review of Futures Markets; 12(2), 391-423.
  • Sandmann, K.; D. Sondermann (1990): Zur Bewertung von Caps und Floors; Zeitschrift für Betriebswirtschaftslehre, 11, 1205-1238.

Proceedings and Articles in Books

  • Sandmann, K (2006): Indexzertifikate mit Mindestgarantie. In T. Böttcher (ed): 50 Jahre BVB, Festschrift zum 50-jährigen Bestehen der Betriebswirtschaftlichen Vereinigung Bonn e.V., Rathgeber & Partner GmbH: Staufenberg, 80-108.
  • Sandmann, K (2005): Überschussbeteiligung fondsgebundener Lebens- und Rentenversicherungen. In W. Kürsten and B. Nietert (eds): Kapitalmarkt, Unternehmensfinanzierung und rationale Entscheidungen, Festsschrift für Jochen Wilhelm, Springer Verlag Heidelberg.
  • Nielsen, J.A.; K. Sandmann (2002): The Fair Premium of an Equity Linked Life and Pension Insurance. In P. Schönbucher and K. Sandmann (eds.): Advances in Finance and Stochastics: Essays in Honor of Dieter Sondermann, Springer Verlag, Heidelberg.
  • Miltersen, K.; K. Sandmann; D. Sondermann (2001): Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates. Reprint in George M. Constantinides and A.G. Malliaris (eds.): Options Markets. Vol. II, The International Library of Critical Writings in Financial Economics, Edward Elgar Publishing Lt.
  • Sandmann, K.; D. Sondermann (2001): A Term Structure Model and the Pricing of Interest Rate Derivatives. Reprint in Lane Hughston (eds.): The New Interest Rate Models, RISK Magazine Publications, 255-278.
  • Miltersen, K.; K. Sandmann; D. Sondermann (1995): Closed Form Term Structure Derivatives in a Heath-Jarrow-Morton-Model with Log-Normal Annually Compounded Interest Rates, Proceedings of the Seventh Annual European Futures Research Symposium, Chicago Board of Trade, 45-164.
  • Reimer, M.; K. Sandmann (1994): An Efficient Approach for Down-and-Out Calls in a Binomial Model. In: A. Karmann, K. Mosler, M. Schader und G. Uebe (eds.): Operations Research '93; Physica-Verlag; Heidelberg, 418-421.
  • Sandmann, K.; E. Schlögl (1994): Binomial Structure Model and the Forward Probability Measure: Algorithmic Model Specification and Simulation Results. In: A. Karmann, K. Mosler, M. Schader und G. Uebe (eds.): Operations Research '93; Physica-Verlag; Heidelberg, 434-437.
  • Sandmann, K.; D. Sondermann (1993): A Term Structure Model and Interest Rate Options. In: A. Karmann, K. Mosler, M. Schader und G. Uebe (eds.): Operations Research '92; Physica-Verlag; Heidelberg, 392-394.
  • Sandmann, K.; D. Sondermann (1992): Interest Rate Options. In: Wolf-Rüdiger Heilmann (eds.): Ergebnisband der 5. Tagung ``Geld, Banken und Versicherungen''; VVW; Karlsruhe, 739-759.

Books

  • Sandmann, K. (2010): Einführung in die Stochastik der Finanzmärkte. Springer Verlag, Heidelberg, 653 p., 3rd edition.
  • Schönbucher, P.; K. Sandmann (2002): Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann, Springer Verlag, Heidelberg.
  • Sandmann, K. (1991): Arbitrage und die Bewertung von Zinssatzoptionen (Ph.D. Thesis). Physica-Verlag, Heidelberg.

Unpublished Manuscripts/Lecture Notes

  • Sandmann, K (2020): Mathematische Methoden der Wirtschaftswissenschaften A, Lecture Note.
  • Sandmann, K (2017): Option Pricing, Lecture Note.
  • Sandmann, K (2016): Internationale Bankleistungen, Lecture Note.
  • Sandmann, K (2014): Investition und Finanzierung, Lecture Note.
  • Sandmann, K (2013): Financial Economics: Stochastic Financial Markets, Lecture Note.
  • Sandmann, K (2006): Einführung in die BWL: Produktion, Lecture Note.
  • Mahayni, A; K. Sandmann (2005): Asset Liability Management fondsgebundener Versicherungsverträge, University of Bonn, Discussion Paper.
  • Sandmann, K (2005): Risikomanagement in Versicherungsunternehmen, Lecture Note.
  • Sandmann, K (2005): Zinsstrukturtheorie, Lecture Note.
  • Sandmann, K. (1996): Derivative Asset Analysis under Stochastic Interest Rates, Habilitation Thesis, University of Bonn.
  • Reimer, M; K. Sandmann (1993): Down-and-Out Call: Bewertungstheorie, Konvergenz numerischer Verfahren und Simulationsstudie; University of Bonn, Discussion Paper B--239.

 

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