ABSTRACTS - Plenary Speakers
Challenges of the Emissions Markets
We review recent attempts to provide rigorous mathematical analyses
of the cap-and-trade schemes used as market mechanisms to control
greenhouse gas emissions. We include equilibrium models as well
as reduced form models proposed to price options. We conclude with
a set of new mathematical results showing that some of the singular
BSDEs occurring in the pricing of emission allowance can have pathological
Itô Calculus and Applications
present an extension of Itô calculus to functionals of price
paths. It leads to a Black-Scholes like PDE for path dependent
options, even if the path dependency cannot be summarized by a
finite number of state variables, with the classical Gamma/Theta
(properly defined) trade-off. It also gives an alternative expression
of the Clark-Ocone formula for the Martingale Representation Theorem
and a non Markov extension of the Feynman-Kac formula.
We apply the functional Itô Formula to obtain the difference
of price of an exotic option in two different models and deduce
the sensitivity of the price to local deformations of the implied
volatility surface. It leads to a decomposition of the volatility
risk across strikes and maturities and the associated hedge in
terms of a portfolio of European options.
We also apply it in the context of super-replication and show
it leads to a refinement of the Kramkov optional decomposition
by splitting the increasing process into a convex component and
a time component, with trading interpretations.
Ecole Polytechnique Fédérale de Lausanne and Swiss
Variance Swap Models: Theory and Evidence
We introduce a quadratic term structure model for the variance
swap rates. The latent multivariate state variable is shown to follow
a quadratic process characterized by linear drift and quadratic
diffusion functions. The univariate case turns out to be a parsimonious
and flexible class of models. We provide a complete classification
and canonical representation, and discuss model identification.
We fit the model to the cross section of variance swap rates and
returns of the S&P 500 Index, and perform a specification analysis.
This is joint work with Elise Gourier and Loriano Mancini.
University of California, Santa Barbara
Stochastic Volatility Models
Stochastic volatility modeling plays a central role in academic
research as well as in practice for various markets: equity, fixed
income, foreign exchange, credit, energy,... These models present
the advantage of being very flexible and being able to fit the data
(returns and options) quite well with two or three factors. Choice
of one particular model, its calibration, and computation of exotic
option prices are very challenging problems. Asymptotic methods
have been proposed in various regimes (short or long maturities,
small vol-vol, large strikes, ...).
In this talk, I will present a combination of regular and singular
asymptotics for multiscale models where stochastic volatility factors
are identified by their time scales. I will explain how we address
the challenging problems mentioned above as well as the mathematical
difficulties inherent to singular payoffs of financial contracts.
Joint work with George Papanicolaou, Ronnie Sircar, and Knut Solna.
University of Toronto
Ratings and Securitization
rating agencies have come under criticism for assigning AAA ratings
to the senior tranches of the ABSs and ABS CDOs that were created
from subprime mortgages. This presentation will consider whether
the criteria used by rating agencies involved appropriate measures
of credit quality and whether the criteria were applied appropriately.
It will propose a no-arbitrage condition that a credit quality measure
should satisfy and examine whether the measures that were used satisfy
this condition. It will also use one-and two-factor copula models
to examine whether the AAA ratings assigned by rating agencies were
ex ante reasonable. It will reach conclusions on the future of structured
University of Illinois at Chicago
Market Making: Potential Profits and Research Opportunities
the emergence of electronic markets for stocks and other securities,
market makers migrated from the trading floor to computer terminals,
each manually posting quotes in one or a handful of securities.
But as it became apparent that speed was of the essence, market
makers developed computer algorithms for automatically posting their
quotes. Not only did speeds increase, but market makers became capable
of managing more securities, trading costs decreased, and bid-ask
spreads narrowed. This talk will describe the speaker's experience
with a Chicago trading firm that does electronic market making.
The issue is how to devise optimal algorithms for posting bid and
ask quotes. In one sense it is a familiar issue: a trade-off between
expected return and risk. But the real-time dynamics of bid and
ask prices are very complex, due to the very high, but irregular,
frequency of the updated quotes. So to address expected profits
it is necessary to employ new statistical techniques that fall outside
of the familiar frameworks of continuous-time and classical discrete-time
models. And to deal with risk one has to confront numerous issues,
some of which can be very subtle such as the presence of traders
doing volatility or pairs trading. As far as optimization is concerned,
there is little hope for "simple" approaches such as Markov
decision theory, because an unmanageable number of state variables
would be required in order for the underlying processes to be Markovian.
More appealing are approaches like adaptive control, reinforcement
learning, and genetic algorithms that deal with incomplete information
about the underlying statistical dynamics. We conclude with a step
in this direction.
Conic Finance and Accounting: The Static Case
up the modeling of two price markets developing closed forms for bid
and ask prices. Applications include capital policy, debt valuation
adjustments, new perspectives on stocks and bonds, and the formulation
of balance sheets that explicitly recognize the value of the taxpayer
put option as an asset owned and reported by the .rm. We further illustrate
with the construction of conic hedges for multidimensional risks.
The presentation closes with a decomposition of pro.ts and capital
reserves as an actvity weighted integral of exposure charges for gains
and losses over all quantile levels.