A hybrid model is a model, where two markets are studied jointly such that stochastic dependence can be taken into account. Such a dependence is well known for equity and interest rate markets on which we focus here. Other pairs can be considered in a similar way. Two different versions of a hybrid approach are developed. Independent time-inhomogeneous Lévy processes are used as the drivers of the dynamics of interest rates and equity. In both versions, the dynamics of the interest rate side is described by an equation for the instantaneous forward rate. Dependence between the markets is generated by introducing the driver of the interest rate market as an additional term into the dynamics of equity in the first version. The second version starts with the equity dynamics and uses a corresponding construction for the interest rate side. It is stressed that the dependence can be quantified in both cases by a single parameter. Numerically efficient valuation formulas for interest rate and equity derivatives are developed. As an example for a hybrid derivative a performance basket is discussed. Using market quotes for liquidly traded derivatives we show that the hybrid approach can be successfully calibrated.
Cass Business School, 106 Bunhill Row
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Ernst Eberlein is professor emeritus at the University of Freiburg. He studied mathematics and physics at the Universities Erlangen-Nürnberg and Paris and received the Dr. rer. nat. at the University of Erlangen-Nürnberg. As a postdoc he held positions at the University of Bonn, IMPA Rio de Janeiro and ETH Zürich where he got his habilitation in mathematics. He has published about eighty articles on topics in probability theory and mathematical finance, and he is editor of a number of conference proceedings. In the early 90s he stood in the forefront to apply Lévy processes for more realistic modeling in finance. More than 20 Ph.D. thesis were finished under his supervision. He served as Dean and as Dean of Study Affairs for his Faculty. He held sabbatical visiting positions at Stanford University, the University of California, San Diego (UCSD) and the University of Technology Sydney (UTS). Ernst Eberlein is one of the founding members of the Freiburg Center for Data Analysis and Modeling (FDM). He is an elected member of the International Statistical Institute and honorary member of the Bachelier Finance Society. He spent the academic year 2009/10 as a fellow at FRIAS with a project on Information, Liquidity, and Trust in Incomplete Markets and was John-von-Neumann professor at TU Munich in 2015. Currently he is a senior fellow at FRIAS with a project Linking Finance and Insurance: Theory and Applications. He served as co-editor of Mathematical Finance and Applied Mathematical Finance. He is a frequent speaker at conferences on topics in mathematical finance. His current research interests and consulting activities focus on modeling of financial markets, risk management, as well as the valuation of derivative financial products.
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