Quadratic Hedging of Basis Risk
AbstractThis 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.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 225.
Date of creation: 01 Jun 2008
Date of revision:
Option hedging; incomplete markets; basis risk; local risk minimization; mean-variance hedging;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-07-20 (All new papers)
- NEP-FMK-2008-07-20 (Financial Markets)
- NEP-RMG-2008-07-20 (Risk Management)
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