# 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. April**: Zeno 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. Ma****i: 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. Juni**: Christian 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. Juli**: Rudi 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.