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

 

 

 

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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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