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Quadratic Hedging of Basis Risk

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University of Technology Sydney, Finance Discipline Group, P.O. Box 123, Broadway, NSW 2007, Australia
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Department of Actuarial Science and the African Collaboration for Quantitative & Risk Research, University of Cape Town, Rondebosch, 7701, South Africa
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Faculty of Economic and Financial Sciences, Department of Finance and Investment Management, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa
*
Author to whom correspondence should be addressed.
Academic Editor: Michael McAleer
J. Risk Financial Manag. 2015, 8(1), 83-102; https://doi.org/10.3390/jrfm8010083
Received: 28 November 2014 / Revised: 5 January 2015 / Accepted: 20 January 2015 / Published: 2 February 2015
This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach. View Full-Text
Keywords: option hedging; incomplete markets; basis risk; local risk minimization; mean-variance hedging option hedging; incomplete markets; basis risk; local risk minimization; mean-variance hedging
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Hulley, H.; McWalter, T.A. Quadratic Hedging of Basis Risk. J. Risk Financial Manag. 2015, 8, 83-102.

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