On behalf of the Scientific Committee of the de Finetti Risk Seminars, we are glad to invite you to participate at the following Lecture

Quadratic Hedging and Optimization of Option Exercise Policies in Incomplete Markets and Discrete Time

Nicola Secomandi

Tepper School of Business – Carnegie Mellon University

Abstract. This paper extends quadratic hedging from European to Bermudan options in discrete time when markets are incomplete and investigates its use for supporting exercise policy optimization. The key idea is to construct date specific approximate replicating portfolios. Hedging any given exercise policy can be done by solving a collection of stochastic dynamic programs. Optimizing the exercise policy based on the resulting martingale measure requires care. If this measure is risk neutral (RN), the value of an optimal such policy, which can be obtained by augmenting the hedging model with an exercise policy optimization step, is a no arbitrage one. Otherwise this approach must be refined by imposing time consistency on exercise policies, although the value of the resulting exercise policy may not be arbitrage free. Following the common pragmatic strategy of specifying quadratic hedging under an RN measure, e.g., one calibrated to market prices, avoids these issues. In particular, it provides a simple hedging policy with immediate practical applicability and is equivalent to exercise policy optimization under RN valuation, thus complementing it with a consistent hedging policy. A simple numerical example shows that this procedure generates effective hedging policies

LOCATION: The seminar will be held on Wednesday, January 15, at 18.00 at room 3-E4-SR03, Bocconi University, Via Rontgen 1, 3rd floor, Milano.

Scientific Committee:

Prof. Simone Cerreia-Voglio (Univ. Bocconi) Prof. Marco Frittelli (Univ. degli Studi di Milano) Prof. Fabio Maccheroni (Univ. Bocconi) Prof. Marco Maggis (Univ. degli Studi di Milano) Prof. Massimo Marinacci (Univ. Bocconi) Prof. Emanuela Rosazza Gianin (Univ. Milano-Bicocca)

******************************************************************************************* 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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