Quadratic Hedging of Basis Risk

Hardy Hulley () and Thomas McWalter
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Hardy Hulley: Finance Discipline Group, UTS Business School, University of Technology Sydney, https://www.uts.edu.au/staff/hardy.hulley

No 225, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: 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 Follmer-Schweizer decomposition of 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 closed-form pricing and hedging formulae for put and call options are derived. 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 recent results achieved using a utility maximization approach.

Keywords: Option hedging; incomplete markets; basis risk; local risk minimization; mean-variance hedging (search for similar items in EconPapers)
Pages: 22 pages
Date: 2008-06-01
New Economics Papers: this item is included in nep-fmk and nep-rmg
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Citations: View citations in EconPapers (6)

Published as: Hulley, H. and McWalter, T. A., 2015, "Quadratic Hedging of Basis Risk", Journal of Risk and Financial Management, 8(1), 83-102.

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