Finance and Insurance Seminar WS 2011/12
“Variable Annuities and the Option to seek risk: Why should you diversify?”Abstract:We analyze the impacts of an additional rider which is incorporated in recent retirement planning products. The payoff of these products is linked to the performance of a multi asset investment strategy and includes a minimum interest rateguarantee on the contributions. In addition, the buyer receives the option to decide on the investments dynamically.Prominent examples are so called Variable Annuities, in particular guaranteed minimum accumulation benefits (GMABs). Due to the embedded guarantee, these products are interesting for risk averse investors who, in general, benefit from diversification. However, to stay on the safe side the price setting of the provider must take into account the most risky strategy.We show that, for an expected utility maximizing investor who also obtains terminal wealth from background assets, the additional rider gives the incentive to invest more aggressively. We quantify the trade--off between the utility of diversification and the utility of a more valuable guarantee. Surprisingly, it turns out that the overall utility loss which is caused by the additional rider is not necessarily increasing in the level of risk aversion. This is explained by the combined effects from background wealth and borrowing constraints. 3.November Prof. Marcus Christiansen, Universität Ulm "Safety margins for the unsystematic biometric risk in life and health"Abstract:
In multistate life and health insurances, the pattern of states of the policyholder is random, thus exposing the insurer to an unsystematic biometric risk. For this reason safety margins are added on premiums and reserves. But in contrast to non-life insurance, traditionally the safety margins are not chosen explicitly but implicitly in form of a valuation basis of first order. If we define the implicit margins bottom-up, we are not able to control the level of safety that we finally reach for premiums and reserves. If we use a top-down approach, that means that we directly calculate explicit margins for premiums and reserves and then choose implicit safety margins that correspond to the explicit margins, we are able
to control the total portfolio risk, but we have the problem that it is
unclear how to allocate the total margin to partial margins for different transitions at different ages. Although the allocation of the total margin to the partial (implicit) margins is not relevant for the total portfolio risk, we have to pay attention since it can have a great effect on the calculation of surplus.
In this paper we calculate asymptotic probability distributions for premiums and reserves of second order by using the functional delta method. As a result, we can not only determine the actual level of safety that is induced by given implicit safety margins, but we can also linearly decompose the total randomness of a portfolio to contributions that the different transition rates at different ages make to the total uncertainty. As a result we do not only get new insight into the sources of unsystematic biometric risk, but we also obtain a useful tool that allows to construct reasonable principles for the allocation of the total safety margin to implicit margins with respect to transitions and ages.
10.November Prof. Elena Vigna, Universita di Torino & Collegio Carlo Alberto "Efficiency of mean-variance based portfolio selection in DC pension schemes"Abstract:We consider the portfolio selection problem in the accumulation phase of a defined contribution (DC) pension scheme. We solve the mean-variance portfolio selection problem using the embedding technique pioneered by Zhou and Li (2000) and show that it is equivalent to a target-based optimization problem, consisting in the minimization of a quadratic loss function. We support the use of the target-based approach in DC pension funds for three reasons. Firstly, it transforms the difficult problem of selecting the individual's risk aversion coefficient into the easiest task of choosing an appropriate target. Secondly, it is intuitive, flexible and adaptable to the member's needs and preferences. Thirdly, it produces final portfolios that are efficient in the mean-variance setting.We address the issue of comparison between an efficient portfolio and a portfolio that is optimal according to the more general criterion of maximization of expected utility (EU). The two natural notions of Variance Inefficiency and Mean Inefficiency are introduced, which measure the distance of an optimal inefficient portfolio from an efficient one, focusing on their variance and on their expected value, respectively. As a particular case, we investigate the quite popular classes of CARA and CRRA utility functions. In these cases, we prove the intuitive but not trivial results that the mean-variance inefficiency decreases with the risk aversion of the individual and increases with the time horizon and the Sharpe ratio of the risky asset.Numerical investigations stress the impact of the time horizon on the extent of mean-variance inefficiency of CARA and CRRA utility functions. While at instantaneous level EU-optimality and efficiency coincide (see Merton, 1971), we find that for short durations they do not differ significantly. However, for longer durations -- that are typical in pension funds -- the extent of inefficiency turns out to be remarkable and should be taken into account by pension fund investment managers seeking appropriate rules for portfolio selection. Indeed, this result is a further element that supports the use of the target-based approach in DC pension schemes. 24.November Prof. Wolfgang Schmidt, Frankfurt School of Finance & Management "Credit Gap Risk in a First Passage Time Model"Abstract:The payoff of many credit derivatives depends on the level of credit spreads. In particular, credit derivatives with a leverage component are subject to gap risk, a risk associated with the occurence of jumps in the underlying credit spreads. Modelling those jumps requires a model for the dynamics of credit spreads. We investigate the credit dynamics in the framework of a first passage time model that is driven by a jump diffusion with exponentially distributed jumps. The model supports calibration to market data and to a wide range of dynamics. By valuing a leveraged credit-linked note we investigate the impact of different assumptions on the credit dynamics thereby highlighting the issue of model risk. 1. Dezember Prof. Dr. Svein-Arne Persson, NHH "Capital Requirement and Optimal Default in Insurance"Abstract:Our parsimonious model of default for insurance companies in the setting of Leland (1994), provides internally consistent combination of risk capital requirements (amount and coupon), pricing of insurance, and optimal default on insurance companies based on regulstory rules regarding the probability of default, and distributional characteristics of the insurance claims. 8. Dezember
|Prof. Dr. Tim Adam, Humboldt-Universität zu Berlin |
We examine whether mutual funds use derivatives to increase fund risk due to tournament behavior, and focus in particular on the use of credit default swaps (CDS) by the largest U.S. corporate bond fund. We find that by 2008, the majority of these funds are using CDS and are holding substantial CDS positions. On average funds are net sellers of both single- and multiple CDS. Funds that underperform during the first half of a calendear year sell more CDS during the second half of the year. Since funds do not appear to systematically change their asset allocations or trading behaviors we conclude that the increase in funds' short CDS positions leads to an increase in fund risk consistent with fund tournament behavior.
Stefan Ankirchner, Universität Bonn
Thomas Kruse, Universität Bonn
"Optimal Trade Execution under Price-Sensitive Risk Preferences"
We consider the stochastic control problem of how to optimally close a large asset position. Within a continuous-time model with a linear temporary price impact we show how to obtain an optimal trade off between liquidity costs and price risk. We measure risk with respect to a reference point making liquidation paths price sensitive and entailing that realized proceeds/costs are skewed. We characterize the optimal trading speed in terms of a PDE for which, in general, no closed-form solution exists. We show that trading rates from discrete model approximations converge to the unique viscosity solution of the PDE. Finally, we present some numerical experiments.
Christine Grün, University of Brest
“On stochastic differential games with incomplete information: BSDE approach and related approximative scheme”
We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the noninformed player can try to guess his missing information. Our aim is to quantify the amount of information the informed player has to reveal in order to play optimally: to do so, we show that the value function of this zero-sum game can be rewritten as a minimization problem over
some martingale measures with a payoff given by the solution of a backward stochastic differential equation. Furthermore we show how to construct an approximative scheme for the value function of this game.
Javier Suarez Ph.D., Center for Monetary and Financial Studies (CEMFI)
“Dynamic Maturity Transformation”
We develop an infinite horizon equilibrium model in which banks finance long term assets with non-tradable debt. Banks choose the amount of debt and its maturity taking into account investors' preference for short maturities (which better accommodate their preference shocks) and the risk of systemic liquidity crises (during which refinancing is especially expensive). Unregulated debt maturities are inefficiently short due to pecuniary externalities in the market for funds during crises and their interaction with banks' refinancing constraints. We show the possibility of improving welfare by means of limits to debt maturity, Pigovian taxes, and
private and public liquidity insurance schemes.
|Prof. Dr. Lukas Menkhoff, Leibniz Universität Hannover|
“Order Flow, Heterogeneous Information, and Currency Risk Premia”
We study the informational content of order flow for exchange rate movements based on a unique dataset covering a broad cross-section of currency pairs and distinguishing key customer types in currency markets. We find a significant role of order flow in predicting FX excess returns and we propose a novel way of measuring the economic value of order flow for exchange rates via a portfolio approach. There is substantial heterogeneity across customer types: trading by corporate and private clients is generally not informative and tends to generate negative payoffs. Order flow by asset managers has a permanent impact on exchange rates, suggesting superior information processing or forecasting ability. Flows by hedge funds, by contrast, have a transitory impact and we show that their FX trading is significantly
exposed to default, liquidity, and global volatility risk.
26.Januar Dr. Anja Richter, ETH Zürich “Explicit solutions to BSDEs and applications to utility maximization”Abstract:Over the past few years quadratic Backward Stochastic Differential Equations (BSDEs) have been a popular field of research. However there are only very few examples where explicit solutions for these equations are known. In this talk we consider a class of quadratic BSDEs involving affine processes and show that their solution can be reduced to solving a system of generalized Riccati ordinary differential equations. We then demonstrate how these results provide analytically tractable solutions to the problem of utility maximization and indifference pricing in in several affine stochastic volatility models like the Heston, Barndorff-Nielsen-Shephard and multivariate Heston setting. In particular we calculate the interesting quantity of the power utility indifference value of change of numeraire.
5.April Prof. Dr. Alexander Kempf, Univeristät Köln “The Valuation of Hedge Funds' Equity Positions”Abstract:We provide evidence on the valuation of equity positions by hedge fund advisors. Reported valuations deviate from standard valuations based on closing prices from CRSP for roughly seven percent of the positions. These deviations are economically significant for about 25 percent of the hedge fund advisors. Advisors with more pronounced valuation deviations show a stronger discontinuity in their reported returns around zero, manage a higher fraction of potentially fraudulent funds, show smoother reported returns, self-report to commercial databases, and are domiciled in offshore locations. Additional tests suggest that the documented equity valuation deviations respond to past performance.