(sorry for possible cross-posting)

We have the pleasure to announce the following two seminars, in

University of Padova, Italy Department of Mathematics, via Trieste 63 room 1BC/45, 1st floor Friday, April 24

9.00 Zorana GRBAC: "Discrete-tenor interest rate models based on polynomial preserving processes"

ABSTRACT:

Based on the class of polynomial preserving Markov processes, we construct families of positive martingales, which are monotone with respect to some parameter. Such martingales are particularly suitable for modeling of discretely compounded forward interest rates via additive constructions. This includes Libor-type models, as well as extensions to the multiple-curve term structure. The main advantage of this model class is the possibility to obtain semi-analytic pricing formulas for both caplets and swaptions that do not require any approximations. Moreover, additive constructions allow to easily ensure, if desired, properties such as positivity of interest rates and spreads and monotonicity of spreads with respect to the tenor - in view of the current market situation a model in which the reference OIS interest rates can become negative and the spreads still remain positive is of particular interest. Examples of tractable and flexible model specifications that we study include quadratic OU-Gaussian and OU-L?vy processes, as well as linear models. We discuss the efficient option pricing via Fourier methods and develop the necessary exponential transform formulas for polynomial preserving processes.

This is joint work with K. Glau and M. Keller-Ressel.

10.00 Antonis PAPAPANTOLEON: "An equilibrium model for spot and forward prices of commodities"

ABSTRACT

The aim of this project is to determine the forward price of a consumption commodity via the interaction of agents in the spot and forward commodity market. We consider a market model that consists of three agents: producers of the commodity, consumers and financial investors (sometimes also called speculators). Producers produce a fixed amount of the commodity at each time point, but can choose how much they offer in the spot market and store the rest for selling at the next time period. They also have a position in forward contracts in order to hedge the commodity price uncertainty. Consumers are setting the spot price of the commodity at each time point by their demand. Finally, investors are investing in the financial markets and, in order to diversify their portfolios, also in the forward commodity market. The equilibrium prices for the commodity are the ones that clear out the spot and forward markets. We assume that producers and investors are utility maximizers and have exponential preferences, while the consumers' demand function is linear. Moreover, the exogenously priced financial market and the demand function are driven by L?vy processes. We solve the maximization problem for each agent and prove the existence of an equilibrium. This setting allows to derive explicit solutions for the equilibrium prices and to analyze the dependence of prices on the model parameters and the agent's risk aversion.

This is joint work with Michail Anthropelos and Michael Kupper.

After the two seminars, the defenses of a PhD thesis will take place:

11.00 Giulio MIGLIETTA: "Topics in interest rate modeling" (supervisor: Martino Grasselli)

See you all in Padova! Tiziano

-------------------------------------------------------------------------- Tiziano Vargiolu Dipartimento di Matematica Phone: +39 049 8271383 Universita' di Padova Fax: +39 049 8271428 Via Trieste, 63 E-mail: vargiolu@math.unipd.it I-35121 Padova (Italy) WWW: http://www.math.unipd.it/~vargiolu --------------------------------------------------------------------------