Finance and Insurance Seminar SS 2010


15. April:  Frank Seidfried (Universität Kaiserslautern)

                   “A Stochastic Control Approach to Portfolio Optimization with   
                   Recursive Utility in IncompleteMarkets”
                  
                   Abstract:

                   We study the optimal portfolio and consumption decision of an investor 
                   with recursive preferences of Epstein-Zin-type in an incomplete market.
                   Following a classical dynamic programming approach, we formulate
                   the associated Hamilton-Jacobi-Bellman equation and provide a
                   suitable verification theorem. The proof of this verification theoreom is
                   complicated by the fact that the Epstein-Zin aggregator is non-Lipschitz,
                   so standard verification results (e.g.,in [Duffie, Epstein 1992]) are not
                   applicable. We then apply our results to obtain explicit solutions for
                   certain combinations of risk aversion and elasticity of intertemporal
                   substitution (EIS) in the stochastic excess return model of [Wachter
                   2002] and the stochastic volatility models of [Liu 2007] and [Chacko,
                   Viceira 2005]. Our results complement those of [Schroder, Skiadas
                   2003], who obtain explicit solutions for unit EIS with a utility gradient
                   approach. Our contribution is twofold: First, we find explicit solutions for
                   portfolio optimization problems with recursive preferences and non-unit
                   EIS. Second, our approach is based on classical stochastic control
                   methods and we provide a rigorous verification theorem.   

 

22. April Nicole Branger (Universität Münster)

                   "Expected Option Returns and the Structure of Jump Risk Premia"

                   Abstract:

                   The paper analyzes expected option returns in models with stochastic  
                    volatility and jumps. A comparison with empirically documented returns 
                   shows that the ability of the model to explain these returns can differ 
                   significantly depending on the holding period and depending on               
                   whether we consider call or put options. Furthermore, we show that the
                   size of  the jump risk premium and its decomposition into a premium for
                   jump intensity risk, jump size risk, and jump variance risk has a
                   significant impact on expected option returns. In particular, expected
                   returns on  OTM calls can even become negative.

29. AprilZeno Enders (Universität Bonn)

                   "The Birth and Burst of Asset Price Bubbles"

                   Abstract:

                   We develop a model of rational bubbles, based on the assumptions of  
                   an unknown potential market size and delegation of investment
                   decisions. In a bubble, the price of an asset rises above its steady-state
                   value, which must be justified by rational expectations about possible
                   future price developments. The higher the expected future price
                   increase, the more likely is the market potential reached, in which case
                   the bubble will burst. Depending on the interaction of uncertainty about
                   the market potential, fundamental riskiness of the asset, the
                   compensation scheme of the fonds manager, and the risk-free interest
                   rate, we give a condition for whether rational bubbles are possible.
                   Based on this analysis, several widely-discussed policy measures are
                   investigated with respect to their effectiveness to prevent bubbles. A
                   modified Taylor rule,long-term compensation, and capital requirements
                   can have the desired effect. Caps on bonuses and a Tobin tax can
                   create or destroy the possibility of bubbles, depending on their
                   implementation.
  

    6. Mai:   Mogens Steffensen (Universität Kopenhagen)

                  “Some solvable portfolio problems with quadratic and collective                   objectives”

 

                  Abstract:

                  We present a verification result for a general class of portfolio problems, 
                  where the standard dynamic programming principle does not hold.
                  Explicit solutions to a series of cases are provided. They include
                  dynamic mean-standard deviation, endogenous habit formation for
                  quadratic utility, and group utility. The latter is defined by adding up the
                  certainty equivalents of the group members, and the problem is solved
                  for exponential and power utility.

 

  20. Mai:   Annarita Bacinello (Universität Trieste)

                   "Variable annuities: Risk identification and riskassessment"                 

                   Abstract:

                   Life annuities and pension products usually involve a number of
                   'guarantees', such as, e.g., minimum accumulation rates, minimum
                   annual payments and minimum total payout. Packaging different
                   types of guarantees is the feature of so-called Variable Annuities.
                   Basically, these products are unit-linked investment policies providing
                   deferred annuity benefits. The guarantees, commonly referred to as
                   GMxBs (namely, Guaranteed Minimum Benefits of type 'x'), include
                   minimum benefits both in case of death and in case of survival.           
                   Following a Risk Management-oriented approach, this paper first aims 
                   at singling out all sources of risk affecting Variable Annuities ('risk
                   identification phase'). Critical aspects arise from the interaction between
                   financial and demographic issues. In particular, the longevity risk may
                   have a dramatic impact on the technical equilibrium within a portfolio.
                   Then, we deal with risk quantification ('risk assessment phase'), mostly
                   via stochastic simulation of financial and demographic scenarios. Our
                   main contribution is to present an integrated approach to risks in             
                   Variable Annuity products, so providing a unifying and innovative point of
                   view.


 10. Juni:   Sven Balder (Universität Duisburg)

                   "The too-big-to-fail option"

 

                   Abstract:

                   The recent financial crisis has shown that some nancial institutions are 
                   considered to be systemically relevant. This implies that governments
                   are expected to bail out distressed institutions. These firms are deemed
                   "too big to fail". The costs for an bail-out can be interpreted as an
                   insurance to the debt holders. Therefore regulation authorities should
                   ask for a premium for this insurance. The talk discusses how this
                   premium can be calculated. The too-big-to-fail option can be interpreted
                   as a credit default swap (cds). Unfortunately, if financial markets expect
                   that a financial institution is too big to fail this will be reflected by a cds
                   premium which is too low. Using the structural model approach it will be
                   discussed how stock and equity-option prices can be used for
                   calculating the insurance premium. Different parametric and
                   non-parametric methods are presented and discussed.

 

 17. JuniChristian Schlag (Universität Frankfurt)

                   “Long-Run Risk Models: Stochastic Volatility versus Stochastic                    Intensity”                                      Abstract:

                   Long-run risk (LRR) models introduced by Bansal and Yaron (2004) 
                   represent an important class of approaches to explain a number of
                   classical asset pricing puzzles. In a recent paper Drechsler and Yaron
                   (2009) extend the LRR model by including jumps in the state variables
                   and a stochastic long-run mean level for the conditional variance. The
                   resulting model explains the observed large and positive variance risk
                   premium as well as performance of this variance risk premium as a
                   predictor for future excess returns. Furthermore the model is also able
                   to match the patterns of time variation both in the level and in the
                   variance of excess returns on dividend claims. In this model the jump
                   intensity is specified as an affine function of the conditional variance, so
                   that these two state variables are assumed to be perfectly correlated.
                   The empirical validity of this assumption is highly questionable, as
                   shown by Santa-Clara and Yun (2008), who find that the estimated
                   correlation between the increments of the diffusive volatility and jump
                   intensity is quite low. This suggests that a model where the stochastic
                   jump intensity is perfectly correlated with conditional variance is
                   potentially misspecified.

                   Our paper investigates the impact of the specification of jump intensities
                   in LRR models. We introduce an additional, autonomous jump-diffusion
                   factor into the LRR model of Drechsler and Yaron (2009) and consider
                   different scenarios with respect to the weight of this additional factor in
                   the jump intensity dynamics. In this new model we then study asset
                   pricing moments and predictability characteristics to analyze the impact
                   of the intensity specification on the overall performance of the LRR
                   model.

     1. JuliRudi Zagst (Technische Universität München)

                   "The Crash-NIG copula model: modeling dependence in credit                    portfolios through the crisis"

 

                   Abstract:

                
                   It is well known that the one-factor copula models are very useful for risk
                   management and measurement applications involving the generation
                   of scenarios for the complete universe of risk factors and the inclusion
                   of CDO structures in a portfolio context. For this objective, it is necessary
                   to have a simple and fast model that is also consistent with the
                   scenario simulation framework. In this paper we present three
                   extensions of the NIG one-factor copula model which jointly have not
                   been considered so far: (i) tranches with dierent maturities modeled in
                   a consistent way, (ii) a portfolio with dierent rating buckets, relaxing
                   the assumption of a large homogeneous portfolio, and (iii) dierent 
                   correlation regimes. The regime-switching component of the proposed
                   Crash-NIG copula model is especially important in view of the current
                   credit crisis. We also introduce liquidity premiums into the Crash-NIG
                   copula model and show that the actual credit crisis is substantially 
                   driven by liquidity eects.


    8. Juli:    Victoria Steblovskaya (Bentley University, Boston, USA)

                   "Alternative Approach to Optimal Hedging in a Discrete Time
                   Incomplete Market and Applications to Finance and Insurance"

                   (Part I)

                   Abstract:
                   Over the last decades, a variety of approaches to pricing and hedging
                   financial derivatives in incomplete markets, both for discrete and 
                   continuous models, have appeared in the literature. A significant
                   proportion of research constructs self-financing trading strategies that 
                   satisfy both a primary no-arbitrage condition and secondary conditions 
                   on portfolio risk and return. Less prevalent is the study  of non-self-
                   financing trading strategies in similar economic environments.

                   Within a discrete model that generalizes the Cox-Ross-Rubinstein
                   binomial model, we build an algorithm that chooses an optimal
                   non-self-financing trading strategy from the set of admissible (market 
                   calibrated) trading strategies based on risk minimization principles.
                   Interesting links to a risk-minimization hedging theory developed by H.
                   Foellmer et al. will be discussed.

                   Along with theoretical description of our model and algorithm, 
                   encouraging numerical results using real market data will be  
                   presented. Some applications to equity-linked life insurance 
                   products will be discussed.

    13. Juli: Victoria Steblovskaya (Bentley University, Boston, USA)

                   "Alternative Approach to Optimal Hedging in a Discrete Time
                    Incomplete Market and Applications to Finance and Insurance"
                   (Part II)


                   Abstract:
                   Over the last decades, a variety of approaches to pricing and hedging
                   financial derivatives in incomplete markets, both for discrete and
                   continuous models, have appeared in the literature. A significant
                   proportion of research constructs self-financing trading strategies that
                   satisfy both a primary no-arbitrage condition and secondary conditions
                   on portfolio risk and return. Less prevalent is the study of
                   non-self-financing trading strategies in similar economic environments.

                   Within a discrete model that generalizes the Cox-Ross-Rubinstein
                   binomial model, we build an algorithm that chooses an optimal
                   non-self-financing trading strategy from the set of admissible (market
                   calibrated) trading strategies based on risk minimization principles.

                   Interesting links to a risk-minimization hedging theory developed by H.
                   Foellmer et al. will be discussed.

                  Along with theoretical description of our model and algorithm,
                  encouraging numerical results using real market data will be presented.
                  Some applications to equity-linked life insurance products will be
                  discussed


    15. Juli : Chris Rogers (Universität Cambridge)

                  "Diverse beliefs"

                    Abstract:

                  This paper presents a general framework for studying diverse beliefs in
                  dynamic economies. Within this general framework, the characterization
                  of a central-planner general equilbrium turns out to be very easy to
                  derive, and leads to a range of interesting applications. We show how
                  for an economy with log investors holding diverse beliefs, rational
                  overconfidence is to be expected; volume-of-trade effects are
                  effectively modelled; a range of sample moments from macroeconomic
                  growth data can be closely approximated; and the Keynesian `beauty
                  contest' can be modelled and analysed. We remark that models where
                  agents receive private information can formally be considered as
                  models of diverse beliefs.