Erhan Bayraktar
Professor of Mathematics
Department of Mathematics
University of Michigan
Title: On the Market Viability under Proportional Transaction Costs [Download Slides]
Abstract: This paper studies the market viability with proportional transaction costs in the sense that the utility maximization problems defined on terminal liquidation values admit optimal solutions. Instead of requiring the existence of strictly consistent price systems (SCPS) as in the literature, we show that strictly consistent local martingale systems (SCLMS) can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABP). In particular, we reveal that the NUPBR and NLABP conditions in the robust sense for the smaller bid-ask spreads is the equivalent characterization of the existence of SCLMS for general market models. As a consequence, the relationship between NUPBR and NLABP conditions in the robust sense and the market viability is examined. Moreover, different types of arbitrage opportunities with transaction costs are discussed and the comparison between our setting and the frictionless market models is also presented.
Joint work with Xiang Yu.
D
amiano Brigo
Chair in Mathematical Finance
Department of Mathematics
Imperial College London
Title: Coordinate-free Stochastic Differential Equations as 2-Jets. [Download Slides]
Abstract: We explain how Ito Stochastic Differential Equations on manifolds may be defined as 2-jets of curves. We use jets as a natural language to express geometric properties of SDEs and show how jets can lead to intuitive representations of Ito SDEs, including three different types of drawings. We explain that the mainstream choice of Fisk-Stratonovich-McShane calculus for stochastic differential geometry is not necessary and elaborate on the relationships with the jets approach. We consider the two calculi as being simply different coordinate systems for the same underlying coordinate-free stochastic differential equation. If the extrinsic approach to differential geometry is adopted, then Stratonovich calculus may appear to be necessary when studying SDEs on submanifolds but in fact one can use the Ito/2-jets framework proposed here by recalling that the curvature of the 2-jet follows the curvature of the manifold. We argue that the choice between Ito and Stratonovich is a modelling choice dictated by the type of problem one is facing and the related desiderata. We also discuss the forward Kolmogorov equation and the backward diffusion operator in geometric terms, and consider percentiles of the solutions of the SDE and their properties, leading to fan diagrams and their relationship with jets. In particular, the median of a SDE solution is associated to the drift of the SDE in Stratonovich form for small times. Finally, we prove convergence of the 2-jet scheme to classical Ito SDEs solutions in L2. This is joint work with John Armstrong, Dept. of Mathematics, King’s College London.
Paul Embrechts
Professor of Mathematics
Department of Mathematics
ETH Zürich
Title: Quantile-based risk sharing [Download Slides]
Abstract: We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first present an inequality for RVaR aggregation, showing that a special form of subadditivity is satisfied by RVaR. Then, the risk sharing problem is solved by explicit construction. Three relevant issues in the optimal allocations are investigated: extra sources of randomness, comonotonicty, and model uncertainty. We show that in general, a robust optimal allocation exists if and only if none of the underlying risk measures is a VaR. Practical implications of the main results for risk management and policy makers are discussed, including gambling behaviour, moral hazard, regulatory arbitrage, and model misspecification. In particular, in the context of regulatory capital reduction, we provide some general guidelines on how a regulatory risk measure can lead to certain desirable or undesirable properties of risk sharing among firms, and show novel advantages of ES from the perspective of a regulator. This talk is based on joint work with Hailyan Liu and Ruodu Wang (University of Waterloo).
Anne Eyraud-Loisel
Director of the
Institute in Financial and Actuarial Sciences (ISFA)
University of Lyon
Title: How does asymmetrical information create market incompleteness?
[Download Slides]
Abstract: We present a hedging problem from an informed trader point of view. The model where the informed trader is supposed to have an influence on asset prices leads to a complete market model, which appear to be incomplete from a non-informed trader's point of view. This is a surprising example where the incompleteness of the market is not due to a lack of available assets. This incompleteness of the market is interesting to study, as well as the difference of investment whether the agent has the information or not. Tools used for this modeling are backward and forward-backward stochastic differential equations and enlargement of filtration.
Robert Fernholz
Founder of
INTECH
Wikipedia entry
Title: Volatility and arbitrage. [Download Slides]
Abstract: In an equity market, if there is "adequate volatility", then there is relative arbitrage. We shall investigate what "adequate volatility" might mean, when there is long-term arbitrage, and when there is arbitrage over arbitrarily short intervals.
Christian Julliard
Associate Professor of Finance
Department of Finance
LSE
Title: Network Risk and Key Players: A Structural Analysis of Interbank Liquidity
[Download Slides]
Abstract: We model banks’ liquidity holding decision as a simultaneous game on an interbank borrowing network. We show that at the Nash equilibrium, the contributions of each bank to the network liquidity level and liquidity risk are distinct functions of its indegree and outdegree Katz-Bonacich centrality measures. A wedge between the planner and the market equilibria arises because individual banks do not internalize the effect of their liquidity choice on other banks’ liquidity benefit and risk exposure. The network can act as an absorbent or a multiplier of individual banks’ shocks. Using a sterling interbank network database from January 2006 to September 2010, we estimate the model in a spatial error framework, and find evidence for a substantial, and time varying, network risk: in the period before the Lehman crisis, the network is cohesive and liquidity holding decisions are complementary and there is a large network liquidity multiplier; during the 2007-08 crisis, the network becomes less clustered and liquidity holding less dependent on the network; after the crisis, during Quantitative Easing, the network liquidity multiplier becomes negative, implying a lower network potential for generating liquidity. The network impulse-response functions indicate that the risk key players during these periods vary, and are not necessarily the largest borrowers.
Pablo Koch-Medina
Director of the Centre for Finance and Insurance (CFI)
Department of Banking and Finance
University of Zurich
Title: Diversification and protection of liability holders [Download Slides]
Abstract: Any solvency regime for financial institutions should be aligned with one of the fundamental objectives of regulation: protecting liability holders. From these objective we derive a normative requirements for capital adequacy tests, called surplus invariance. We characterize capital adequacy tests that satisfy surplus invariance and highlight an inherent tension between the ability to meet this requirement and the desire to give credit for diversification.
Nicolas Perkowski
Junior Professor of Stochastic Analysis
Institute of Mathematics
Humboldt University Berlin
Title: Game-theoretic martingales and applications to model free financial mathematics
[Download Slides]
Abstract: Vovk recently introduced a pathwise approach to continuous time financial mathematics which does not require any measure-theoretic modeling and allows us to describe properties of “game-theoretic martingales" by only relying on superhedging arguments. I will present the basic ideas of this approach and several applications, in particular a pathwise pricing-hedging duality for derivatives which are invariant under time reparametrization. Based on joint works with Mathias Beiglböck, Alexander Cox, Martin Huesmann, and David Prömel.
Eckhard Platen
Professor of Quantitative Finance
School of Mathematical and Physical Sciences
University of Technology Sydney
Title: Benchmark Approach to Finance [Download Slides]
Abstract: This lecture introduces into the benchmark approach that provides a general framework for financial modelling by employing the numeraire portfolio as benchmark and numeraire. It provides a unified treatment of portfolio optimization, derivative pricing and risk management. A diversification theorem allows forming a proxy for the numeraire portfolio. The benchmark approach extends the classical asset pricing theories, opening new possibilities for long term risk management, relevant to e.g. pensions, insurance, financial planning and regulation. The real world price is characterising the minimal possible price, below those of other pricing rules. The richer modelling framework of the benchmark approach leads naturally to tractable, realistic long term models. It will be explained how the approach differs from the classical risk neutral approach. Examples on long term and extreme maturity derivatives demonstrate how long dated contracts can be less expensively priced and hedged than suggested by classical theory.
References:
Platen, E. and Heath, D.: A Benchmark Approach to Quantitative Finance. Springer Finance (2010).
Claudia Ravanelli
Senior Research Associate
Department of Banking and Finance
University of Zurich
Title: Ambiguity Aversion in Ellsberg Frameworks [Download Slides]
Abstract: We study optimal portfolio choice and equilibrium asset prices induced by alpha-maxmin expected utility (alpha-MEU) models. In the standard Ellsberg framework we prove that alpha-MEU preferences are equivalent to either maxmin, maxmax or subjective expected utility (SEU). We show how ambiguity aversion impacts equilibrium asset prices, and revisit the laboratory experimental findings in Bossaerts et al. (2010). Only when there are three or more ambiguous states the alpha-MEU, maxmin, maxmax and SEU models induce different portfolio choices. We suggest criteria to discriminate among these models in laboratory experiments. Finally, we find that ambiguity seeking alpha-MEU agents may prevent the existence of market equilibrium. Our results indicate that ambiguity matters for portfolio choice and does not wash out in equilibrium.
W
olfgang Runggaldier
Professor of Mathematical Statistics
Department of Mathematics
University of Padua
Title: Optimal arbitrage and portfolio optimization for market models satisfying NUPBR but not NFLVR [Download Slides]
Abstract: The classical no-arbitrage condition of NFLVR is often too strong and can be weakened thereby still allowing to solve meaningfully standard problems in mathematical finance. A weaker condition to this effect is NUPBR (NA1). For market models satisfying NUPBR, but where NFLVR does not hold, classical arbitrage is thus possible. We discuss the construction of such market models and how to obtain for them optimal arbitrage. In particular, we consider models with insider information and for such models we discuss, besides optimal arbitrage, also the possibility of solving portfolio optimization problems by analogy to classical duality even under absence of an ELMM.
(Joint work with N.H.Chau and P.Tankov)
Michael Schmutz
Specialist in Market Risks
Part-Time Lecturer
FINMA, University of Bern, EPFL
Title: Risk-based solvency frameworks in a low interest rate environment
Abstract: Solvency II, in force since the beginning of this year, and the Swiss Solvency Test (SST), in force in Switzerland since 2011, seek to assess the financial health of insurance companies by quantifying capital adequacy based on a risk evaluation of the economic balance sheet modelled after one year. Companies can use their own economic capital models (internal models) for this evaluation, provided that the internal model has been approved by the insurance supervisor. The development and also the supervision of these models are complex and related to numerous challenges. These challenges are compounded by recent changes in the market environment leading to very low and even negative interest rates in many countries. This market environment is particularly difficult for life insurance companies offering capital guarantees so that many of them have started to take action, also triggering changes in their internal models. Some of the most important resulting challenges will be discussed, along with a number of attempts to tackle them.
Affiliation: University of Bern and Swiss Financial Market Supervisory Authority (FINMA)