*** Apologies for cross-posting ***
Dear Colleagues, we would like to invite you to the following Probability seminar that will take place at the Department of Mathematics, University of Padova (via Trieste, 63), on February 21 h. 15.30 room 1BC/45.
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NICOLA SECOMANDI Tepper School of Business, Carnegie Mellon University
Quadratic Hedging and Optimization of Option Exercise Policies in Incomplete Markets and Discrete Time
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.
Paper available at https://arxiv.org/abs/2001.05788?context=q-fin
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All the best 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 --------------------------------------------------------------------------