The  13th Annual CAP Workshop on  

Derivative Securities and Risk Management

Co-sponsored by ERM Institute International

Friday, November 3rd, 2006

Davis Auditorium, Columbia University

Schedule of Events

View Poster of Conference (pdf)

• 9:00 - 9:45 Optimal Risk Sharing for Law Invariant Monetary Utility Functions    [DOWNLOAD]                                                                                        

Walter Schachermayer
Professor, Mathematics Department
Vienna University of Technology

We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law-invariant monetary utility functions or equivalently, law-invariant risk measures. We first prove existence of an optimal risk sharing allocation which is in addition increasing in terms of the total risk. We next provide an explicit characterization in the case where both agents' utility functions are comonotone. The general form of the optimal contracts turns out to be given by a sum of options (stop-loss contracts, in the language of insurance) on the total risk. In order to show the robustness of this type of contracts to more general utility functions, we introduce a new notion of strict risk aversion conditionally on lower tail events, which is typically satisfied by the semi-deviation and the entropic risk measures. Then, in the context of an AV@R-agent facing an agent with strict monotone preferences and exhibiting strict risk aversion conditional on lower tail events, we prove that optimal contracts again are European options on the total risk.

• 9:45 - 10:30 Making Proactive Use of Risk Management an Integral Part of Strategic Decisions    [DOWNLOAD]        
  
  Leo Tilman
  Chief Institutional Strategist
  Bear Stearns

  When it comes to executive-level strategic decisions in both investment and corporate finance realms, risk management often remains an afterthought - a passive safety and soundness verification. This talk discusses dominant financial industry, market, and macroeconomic trends as well as resulting real-life challenges facing institutional investors and financial institutions worldwide. In the process, opportunities and potential benefits of proactive utilization of advanced risk management frameworks and tools are illuminated.

• 11:00 - 11:45 Affine Markov Chain Model of Multi-firm Credit Migration   [DOWNLOAD]   
  
  Tom Hurd
  Professor, Mathematics & Statistics
  McMaster University
  
  This talk will explore a natural extension of the intensity based doubly stochastic framework for credit default. The essential addition is to introduce a Markov chain for the ``credit rating'' of each firm, which are independent conditioned on one or more stochastic time changes, or equivalently, stochastic intensities. Stochastic time change is then combined with other stochastic factors, for example, the interest rate and the recovery rate, into a multidimensional affine process. The resulting AMC framework has the computational effectiveness of the intensity based models. Already, the minimal version of the AMC framework which combines stochastic interest rates, stochastic recovery rates and the multifirm migration process gives very good qualitative reproduction of essential features of dynamic credit spread curves, default correlations and multifirm default distributions. At the end of the talk, we show how the same framework extends to large scale basket credit derivatives, particularly CDOs.

• 11:45 - 12:30 Real-time Volatility Estimation Under Zero Intelligence    [DOWNLOAD]   
  
  Jim Gatheral
  Managing Director in Global Equities
  Merrill Lynch

  Accurate real-time volatility estimates are needed for many applications, including the real-time pricing of options. Also, high-frequency market data is widely available. The question then arises: given a time series of tick data, how can realized volatility be estimated? The obvious estimator - the sum of squared returns between trades - is very biased by microstructure effects such as bid-ask bounce and so typically, practitioners are advised to drop most of the data and sample at most every five minutes or so. On the other hand, the fewer points that are used, the greater the estimation error. The search for a practical solution to this tradeoff between microstructure bias and estimation error has become a very active area of econometric research.

  Various authors have suggested estimators and optimal sampling approaches based on a priori assumptions on the nature of the "microstructure noise" process. They often also confirm their results through Monte-Carlo simulation. However, it's not clear that the price process can be neatly decomposed into true price and noise processes and even if this were possible, it's not clear what the specification of the "microstructure noise" process should be.

  We attempt to shed some light on this problem by simulating an artificial (zero-intelligence) market that has been shown to mimic some key properties of actual markets. Because our generating model parameters are constant, we know that the "true volatility" must also be constant and we can determine the "true volatility" through Monte Carlo simulation. It is then straightforward to take one realization of the price process and check to see how the various proposed estimators perform in estimating the "true volatility".

  We conclude with firm practical recommendations on data sampling and efficient estimators.
  



• 2:00 - 2:45 Research Problems in Enterprise Risk Management    [DOWNLOAD] 
  
  Shaun Wang
  Executive Director
  ERM Institute International
  
  Enterprise risk modeling must capture dominant risk dynamics at various levels of the firm, which calls for an operational research type of approach to the major players, forces, and their interactions. Indeed, arbitrage-free pricing is only a special case whereas the dominant force is the law of one price via frictionless portfolio replication. In general, valuation can be driven by both fundamentals and speculative forces; Moreover, valuation can be sticky under some circumstances, which requires modeling of behavioral aspects of friction, incomplete information and competitive game. We need to develop an expanded portfolio theory for enterprise risks, and to make a clear distinction between statistical correlation and cost-implied correlation in economic capital calculations.

• 2:45 - 3:30 Risk Adjusted Profitability by Business Unit: How to Allocate Capital and How Not to    [DOWNLOAD]   
  
  Gary Venter
  Managing Director
  Guy Carpenter Inc.
  
  A goal of ERM is to adjust business unit profitability for risk. This might be approached by allocating capital to the units for the denominator of return rate. Several drawbacks of this approach have been raised, but some of them can be mitigated if the allocation is equal to marginal risk impact. Ways to risk-adjust profit without allocating capital will be discussed as well.
  


• 4:00 - 4:45 Innovations in Enterprise Risk Management: Enhancing Analytical Ratings Frameworks    [DOWNLOAD] 
  
  David Ingram
  Director of Enterprise Risk Management
  Standard & Poor's
  
  Rating agencies are all increasing attention to risk management in their view of insurance company's credit ratings. Standard & Poor's has instituted a robust process for evaluating the Enterprise Risk management (ERM) of insurers as a major category of the analysis that leads to a credit rating decision. That process looks at Risk management Culture, Risk Control Processes, Emerging Risks Management, Risk & Capital Models and Strategic risk management to determine a view of an insurers ERM. Overall ERM quality is viewed as Weak, Adequate, Strong or Excellent. In 2007, S&P will begin to look at Economic Capital Models of Insurers with Strong or Excellent ERM to better inform our view of Capital Adequacy of the insurers. (Capital Adequacy is another of the main components of analysis that supports our insurer credit analysis) This talk will describe the elements of this program, the findings to date and some of the areas where we see the need for further research and development in related topics.

• 4:45 - 5:30 Risk Neutral Compatibility with Option Process    [DOWNLOAD] 
  
  Phillip Protter
  Professor, Operations Research
  Cornell University
  
  A common problem is to choose a "risk neutral" measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique equivalent local martingale measure'' by completing the market with option prices. We do this by modeling the behavior of the stock price X, together with the behavior of the option prices for a relevant family of options which are (or can theoretically be) effectively traded. In doing so, we need to ensure a kind of `compatibility'' between X and the prices of our options, and this poses some interesting mathematical difficulties.

        Registration :

        REGISTRATION FEES:

        Academic Rates:

        Before Oct. 12: $125 ($40 student)

        On site: $175 ($100 student)

        Corporate Rates:

        Before Oct. 12: $225

        On site: $325

        Credit Cards (Visa/Mastercard), Checks (made payable to Center for Applied Probability), or Money Orders are accepted.

        Please contact Administrative Coordinator Emmanuel Casuscelli at emc2135@columbia.edu or (212)-854-8404 to register.

        Hotel Arrangements:

        For hotels near Columbia University, please visit:   http://www.campustravel.com/university/columbia/

        Directions & Parking Information: please click here for directions and parking information.

        For Inquiries:
        chris@wald.stat.columbia.edu (Chris Heyde, Director of CAP)
        sigman@ieor.columbia.edu (Karl Sigman, Secretary of CAP)