Si avvisa che il giorno mercoledì 12 ottobre 2016 alle ore 15 presso l’Università di Milano- Bicocca (via degli Arcimboldi 8 - edificio U7, quarto piano- aula seminari 4026) si terrà il seguente seminario:
Speaker: Dott. Federico Severino (Università Bocconi, Milano)
Titolo: “Weak time-derivatives and no arbitrage pricing”
Abstract: The risk-neutral pricing formula is a central result of asset pricing theory that provides the proper valuation of European derivatives in absence of arbitrages. Despite the variety of option payoffs, price dynamics are driven by the same interest rate process. We formalize this intuition by showing that no arbitrage prices constitute the weak solution of a differential equation, where the risk-free rate has a prominent role. To achieve this goal, we introduce the notion of weak time-derivative, which permits to differentiate functions of Markov processes. It generalizes the infinitesimal generator and provides a characterization of martingales, submartingales and supermartingales; in particular, martingales are characterized by a null weak time-derivative. Through the weak time-derivative, we formulate the no arbitrage pricing differential equation and we prove existence and uniqueness of the solution with both deterministic and stochastic interest rates. Finally, we reformulate the eigenvalue-eigenvector problem of Hansen and Scheinkman (2009) and we retrieve a decomposition of the stochastic discount factor, well-known in the long-term risk literature.
This is joint work with Massimo Marinacci.
Tutti gli interessati sono invitati a partecipare.
Un saluto e a presto,
Emanuela
******************************************************************************************* Emanuela Rosazza Gianin Dipartimento di Statistica e Metodi Quantitativi Università di Milano-Bicocca Edificio U7 – 4° Piano Via Bicocca degli Arcimboldi, 8 20126 Milano
Tel. 02 64483208 Fax. 02 64483105 e-mail: emanuela.rosazza1@unimib.it
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