The 14th Annual CAP Workshop on Derivative Securities and Risk Management

Co-sponsored by the Center for Financial Engineering

Friday, November 9th, 2007

 

Davis Auditorium

 

Columbia University

Schedule of Events

 

View Poster of Conference (pdf)
  • 9:00 - 9:45 Local Volatility Dynamic Models   [DOWNLOAD]                                                                                      

Rene Carmona
Professor, Operations Research & Financial Engineering
Princeton University Bendheim Center for Finance


This paper is concerned with the characterization of arbitrage free dynamic stochastic models for the equity markets when Ito stochastic differential equations are used to model the dynamics of a set of basic instruments including, but not limited to, the underliers. We study these market models in the framework of the HJM philosophy originally articulated for Treasury bond markets. The approach to dynamic equity models which we follow was originally advocated by Derman and Kani in a rather informal way. The present paper can be viewed as a rigorous development of this program, with explicit formulae, rigorous proofs and numerical examples.

  • 9:45 - 10:30 H2: A New Concept in Risk Management    

    Bruno Dupire
    Senior Researcher
    Bloomberg LP

How risky is an ITM barrier option? How can we hedge a basket or spread options with options on the components? Pricing by perfect replication is a very potent tool but real markets are far from being complete and most contingent claims cannot be perfectly hedged. We define a measure of hedge efficacy, H2 (in reference to the R2 of a regression), which reflects the reduction of tracking error variance when using a certain set of hedging instruments/strategies. We illustrate the approach in the case of discrete time hedging, stochastic volatility and multi-asset  models.

  • 11:00 - 11:45 Pricing Swaps and Options on Quadratic Variation Under Stochastic Time Change Models   [DOWNLOAD]      

    Andrey Itkin
    Head of Quantitative Strategies / Adjunct Professor 
    Volant Trading / Rutgers University


    Swaps and options on quadratic variation recently became very popular instruments at financial markets. However, there exists a known observation that simple models are not able to replicate the price of the quadratic variation contract for all maturities. Therefore, one can see a steadfast interest to applying more sophisticated jump-diffusion and stochastic volatility models to pricing swaps and options on the quadratic variation. Usually Monte-Carlo methods are used to price the quadratic variation products under this approach, because analytical and semi-analytical (like FFT) results are available only for the simplest models. In the present paper we consider a class of models that are known to be able to capture at least an average behavior of the implied volatilities of the stock price across moneyness and maturity time-changed Levy processes. For these models we derive an analytical expression for the fair value of the quadratic variation and volatility swap contracts as well as use a modifyed Carr-Madan FFT approach proposed by Roger Lee to price options on these products. The results are compared with the market data.
  • 11:45 - 12:30 Default Correlation, Cluster Dynamics and Single Names: The GPCL Dynamical Loss Model   

    Damiano Brigo
    Managing Director & Global Head, Quantitative Structured Credit Innovation
    DerivativesFitch

We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil (2003) to a formulation avoiding repeated defaults, thus obtaining a model that can account consistently for single name default dynamics, cluster default dynamics and default counting process. This approach allows one to introduce significant dynamics, improving on the standard “bottom-up” approaches, and to achieve true consistency with single names, improving on most “top-down” loss models. Furthermore, the resulting GPCL model has important links with the previous GPL dynamical loss model in Brigo, Pallavicini and Torresetti (2006a,b), which we point out. Model extensions allowing for more articulated spread and recovery dynamics are hinted at. Calibration to both DJi-TRAXX and CDX index and tranche data across attachments and maturities shows that the GPCL model has the same calibration power as the GPL model while allowing for consistency with single names.

  • 2:00 - 2:45 Latest Research on Liquidity Risk - Topic to be Announced   [DOWNLOAD]

    Lasse Pedersen
    Professor, Finance
    NYU Stern School of Business


    TBA
  • 2:45 - 3:30 Equity Correlation Swaps: A New Approach for Modeling & Pricing   [DOWNLOAD] 

    Sebastien Bossu
    Vice President, Equity Derivatives Structuring
    Dresdner Kleinwort


    Correlation Swaps were introduced in the early 2000's to allow investors to bet on realized correlation against a strike, and help exotic derivative desks to recycle their correlation risk. In practice the strike is driven by supply and demand and may differ significantly from the implied correlation derived from the prices of vanilla options on indices and their constituent stocks. In this presentation we introduce some fundamental relationships for realized and implied correlation, propose a simple model for derivatives on variance and proceed to derive the arbitrage strike of index correlation swaps based on dynamic trading of variance dispersions. The conclusion is that the fair strike is close to implied correlation, revealing potential dynamic arbitrage opportunities in the market.
  • 4:00 - 4:45 Efficient Risk Management in Monte Carlo   [DOWNLOAD]   

    Luca Capriotti
    Global Modeling & Analytics Group
    Credit Suisse

    Monte Carlo simulations are an indispensable tool for pricing and hedging derivatives securities due to the ever increasing level of sophistication of the instruments traded in the Financial Markets. Although generally straightforward to implement, Monte Carlo approaches carry a very significant computational cost. In this talk, I will describe some recent research aimed at improving the efficiency of the Monte Carlo calculation of Option Prices and Sensitivities (so-called Greeks) by means of Importance sampling, Likelihood Ratio Methods, and Adjoint techniques. 
  • 4:45 - 5:30 Optimal Disclosure and Operational Risk: Evidence from Hedge Fund Registration    [DOWNLOAD]

    William Goetzmann
    Professor, Fiance
    Yale School of Management

    Required disclosure is an important regulatory tool in that it allows market participants to assess manager risks without constraining manager actions. This trade-off between freedom of activity and transparency is particularly relevant to hedge funds, which rely often rely on proprietary models and positions. We use the recent, unsuccessful SEC attempt to increase hedge fund disclosure through registration in order to examine the value of disclosure to investors. We test the potential value and materiality of operational risk and conflict of interest variables disclosed in Form ADV filed by a large number of hedge funds in February 2006. We find that operational risk indicators are conditionally correlated to conflict of interest variables, indicating a potential value of disclosing such conflicts to investors. Operational risk factors are also correlated to lower leverage and concentrated ownership, suggesting that the 2006 disclosure requirements may have been redundant for lenders and equity investors in hedge funds. In contrast, operational risk factors had no ex-post effect on the flow-performance relationship, suggesting that investors either lack this information, or they do not regard it as material. The findings suggests that any consideration of disclosure requirements should take into account the endogenous production of information within the industry, and the marginal benefit of required disclosure on different investment clienteles.

 

        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 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 Heyde, Director of CAP)
        (Karl Sigman, Secretary of CAP)