
The
Conference
LECTURES ON MATHEMATICAL FINANCE, II
June, 7 – 8, 2002
will
take place at the Department of Science of the University of Chieti "G.
D’Annunzio", Aula Conferenze of the Facoltà di Economia, Viale Pindaro 42,
Pescara.
The
conference is supported by funds of the Business School of the University of
Chieti and by MURST funds for the COFIN project "Processi Stocastici,
Calcolo Stocastico e applicazioni" (University of Chieti and University of
RomaTor Vergata local units).
PROGRAM
LECTURES ON MATHEMATICAL FINANCE, II
Pescara, June 78, 2002

15.0015.10: Opening 15.1016.40: P. Protter, Cornell University Liquidity risk and arbitrage pricing theory (abstract) 16.4017.00: Coffee break 17.0018.30: V. Bally, Université Paris VI Numerical quantization for pricing and hedging american options (abstract) 20.30: Social dinner 
Saturday, June 8 
9.3011.00: C. Albanese, University of Toronto Models with jumps and stochastic volatility (abstract) 11.0011.30: Coffee break 11.3013.00: R. Cont, Ecole Polithecnique, Paris Calibration of option pricing models (abstract) 13.0013.10: Closing 
On Friday June 7, a social dinner will take place (expected cost: about
30 Euro). If you wish to attend the social dinner, please send an email BEFORE
May 20 (with subject: SOCIAL DINNER) to the address:
antonf@sci.unich.it
Click HERE for
practical information (such as hotels, how to reach Pescara, etc.)
Finally,
no registration fee is requested and, as usual, a certificate of participation
will be given if needed.
For
further information, please contact
Fabio
Antonelli (University of Chieti) – email: antonf@sci.unich.it
Lucia Caramellino (University of RomaTor Vergata) – email: caramell@mat.uniroma2.it
Carlo Mari (University of Chieti) – email: mari@sci.unich.it
Sergio Scarlatti (University of Chieti) – email: scarlatt@sci.unich.it
ABSTRACTS
LIQUIDITY RISK AND
ARBITRAGE PRICING THEORY
Philip
Protter
Department of Mathematics
Cornell University
email: protter@orie.cornell.edu
Classical theories of financial markets assume implicitly an infinitely
liquid market, and that all traders are price takers. This theory is a good
approximation for highly liquid stocks, although even there it does not apply
well for large traders, or for modeling transaction costs. We propose a new
model that takes into account questions of degree of liquidity, while extending
the classical model. Alternatively, or even simultaneously, one can use our
model for transaction costs. In essence, we are relaxing the standard
assumption of a competitive market, where each trader can either buy or sell
unlimited quantities of a stock at the market price. Our approach is to
hypothesize a stochastic supply curve for a security's price as a function of
trade size. This leads to some interesting mathematical issues, as well as
natural restrictions on hedging strategies.
The talk will be based on joint work with Umut Cetin and Robert Jarrow.
NUMERICAL
QUATIZATION FOR PRICING AND HEDGING AMERICAN OPTIONS
Vlad Bally
Equipe Statistique et Processus
Université du Maine
and
INRIARoquencourt
email: bally@ccr.jussieu.fr
The price of an american option appears as the Snell envelope of
the obstacle process and is computed using the Dynamical Programing
Principle. The difficulty in performing an efficient algorithm using the
DPP is that one has to compute a large number of conditional
expectations.
Several methods of doing it has been proposed in the last years. We
present an algorithm using the numerical quantization method. This
employes grids and weights as the classical finite element method, but
it
is a stochastic method for two reasons: it relays on the Faynman Kac
formula and the weights coming on in the algorithm are computed using
the
Monte Carlo method. Two special ingredients lead to an improved
algorithm:
on one hand one employes the optimal quantization theory in order to
produce optimal grids and on the other hand one employes the Malliavin
calculus in order to produce some correctors. These two ingredients
permit
to pass from schemes of order zero to schemes of order one.
MODELS
WITH JUMPS AND STOCHASTIC VOLATILITY
Claudio
Albanese
Department of Mathematics
University of Toronto
email: albanese@mathpoint.ca
The talk reviews option pricing models with jumps and state dependent
volatility which admit either exact solutions or exact numerical schemes. The
models extend known and popular models such as the CEV and quadratic volatility
models and the variancegamma model. Recent applications to the credit risk
process are also discussed.
CALIBRATION
OF OPTION PRICING MODELS
Rama Cont
Centre de Mathematiques Appliquees
CNRS  Ecole Polytechnique, Paliseau
email: Rama.Cont@polytechnique.fr
With the
development of sophisticated models for
option pricing, the problem of infering their parameters from data becomes
increasingly complex. Moreover, the procedure of "marking to market"
requires users to "calibrate" model parameters to match current market
prices of benchmark options, leading to an 'inverse option pricing problem'
which is usually ill posed. While algorithms for pricing are relatively well
developed and implemented with great precision, less care is taken in
implementing the calibration method, leading to paradoxical situations where
high precision pricing algorithms are used in a poorly calibrated model. We
study this inverse problem, the existence, uniqueness and stability of
solutions and review some regularization procedures available for coping with
its ill posedness in the case of local volatility/ diffusion models and
discuss algorithms and numerical aspects for calibrating such models. We then
study the impact of the calibration method on the pricing and hedging of
options in a general context illustrated by some examples.