Workgroup Financial Mathematics

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Research Projects

Dependencies in hybrid markets

hybrid_fm_math The securitization of risk in insurance and reinsurance offers an interesting alternative to more traditional actuarial schemes. To this purpose, insurance companies have tried to take advantage of the vast potential of capital markets by introducing exchange-traded insurance-linked instruments such as mortality derivatives and catastrophe insurance options. At the same time, insurance products such as unit-linked life insurance contracts, where the insurance benefits depend on the price of some specific traded stocks, offer a combination of traditional life insurance and financial investment. Furthermore, new kinds of insurance instruments, which provide insurance against risks, connected to macro-economic factors such as unemployment, are recently offered on the market. These new kinds of hybrid products originate a huge demand of investigation on the dependencies between financial and insurance markets, whose dynamic interplay must be modeled and estimated. In this project we focus on analysing and modeling dependency structures in hybrid markets both from the mathematical and statistical point of view.

Equilibrium models for insider trading with long memory

equ_fm_mathIn their seminal papers, Kyle and subsequently Back formulate and study an equilibrium model for insider trading, where the financial market has three agents:
the insider, who already from the initial time knows the value v at the terminal time T of a given stock, the noise traders, who trade randomly without any information about the market, and the market makers, who at any time t can observe the total traded volume. In this setting, the insider tries to find the trading intensity, which maximizes the expected terminal wealth. The dilemma for the insider is that an increased trading intensity at some time t will reveal more information about the value of v to the market makers and hence induce a price closer to v, which in turn implies a reduced insider advantage. In this project, we study how the introduction of persistence or memory among the noise traders influences the Kyle-Back model, in particular what effect it has on the optimal insider portfolio and maximal expected insider wealth.

Energy and related markets

electricity_fm_math3The global economic growth highly depends on sustainable supply of energy which has caused a strong worldwide increase in demand of energy related assets over the last decades. At the same time, in many parts of the world energy markets have been or are in the process of being deregulated in order to establish a free float of prices in a competitive environment. Furthermore, CO2 emission reduction targets, imposed by the Kyoto Protocol, and the trading of carbon allowances create an additional dimension of complexity and price uncertainty that energy market participants have to cope with. Hence, a reliable and sustainable valuation and management of energy risk created in this new and highly uncertain environment has to be a key consideration of decision makers from politics and industry. In particular, we focus on three relevant projects concerning:

  • commodity futures curve modeling,
  • optimal electricity purchase strategies,
  • consistent factor models for temperature markets.

Local risk minimization for mortality derivatives

local_risk_fm_mathAt the intersection of insurance and financial markets a new kind of financial insurance derivatives has recently been introduced in order to hedge against systematic mortality risk in life insurance contracts, so called mortality-linked securities. These new kinds of products introduce an additional source of randomness that cannot be hedged by self financing portfolios consisting of primary assets. Hence, it is natural to compute the price and hedging strategy of mortality-linked securities by means of a quadratic hedging criterion, specifically by using the local risk-minimization technique. The key idea of this approach is to find a replicating strategy with minimal cost. The results and techniques developed in this context may then also be applied to price and hedge more general kinds of hybrid financial products.

Pricing of unemployment products under the benchmark approach

Unemployment-USAInsurance against unemployment risk has recently been gaining increasing attention within many fields of actuarial research. As specific unemployment insurance products are currently at a rather early stage of introduction, to develop adequate mathematical models for the pricing and hedging of these kinds of contracts remains an open problem. A possible method to solve this problem is by means of the so called benchmark approach introduced by Platen (2004), which is a special martingale approach for the dynamic pricing of financial claims. In order to apply this method to model and calculate fair insurance premiums for unemployment products, it is necessary to investigate the dependency structures between the benchmark portfolio and the unemployment rate. The project is built on the close cooperation of an interdisciplinary research team from the fields of mathematical finance and stochastics, as well as statistics and economics.