Lectures on
Mathematical Finance, II

PESCARA
June 7 – 8, 2002

(versione italiana) 

 

                                                                                       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 Roma-Tor Vergata local units).

 

PROGRAM

 
LECTURES ON MATHEMATICAL FINANCE, II
Pescara, June 7-8, 2002




 


Friday, June 7

 
15.00-15.10: Opening
15.10-16.40: P. Protter, Cornell University
     Liquidity risk and arbitrage pricing theory  (abstract)
16.40-17.00: Coffee break
17.00-18.30: V. Bally, Université Paris VI
     Numerical quantization for pricing and hedging american options  (abstract)
20.30: Social dinner

Saturday, June 8

 
9.30-11.00: C. Albanese, University of Toronto
     Models with jumps and stochastic volatility  (abstract)
11.00-11.30: Coffee break
11.30-13.00: R. Cont, Ecole Polithecnique, Paris
     Calibration  of option pricing models  (abstract)
13.00-13.10: 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 e-mail 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 Roma-Tor 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
INRIA-Roquencourt
e-mail: 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 variance-gamma 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 posed-ness 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.