Quadratic hedging of basis risk

Hulley, H; McWalter, T

Quadratic hedging of basis risk

Hulley, H

McWalter, T

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Publisher:: MDPI
Publication Type:: Journal Article
Citation:: Journal of Risk and Financial Management, 2015, 8 (1), pp. 83 - 102
Issue Date:: 2015-03-02

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Field	Value	Language
dc.contributor.author	Hulley, H https://orcid.org/0000-0002-6684-8309	en_US
dc.contributor.author	McWalter, T	en_US
dc.date.issued	2015-03-02	en_US
dc.identifier.citation	Journal of Risk and Financial Management, 2015, 8 (1), pp. 83 - 102	en_US
dc.identifier.issn	1911-8074	en_US
dc.identifier.uri	http://hdl.handle.net/10453/37828
dc.description.abstract	Research Paper Number: 225 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.	en_US
dc.publisher	MDPI	en_US
dc.relation.ispartof	Journal of Risk and Financial Management	en_US
dc.relation.isbasedon	10.3390/jrfm8010083	en_US
dc.title	Quadratic hedging of basis risk	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	8	en_US
utslib.for	010406 Stochastic Analysis and Modelling	en_US
utslib.for	010404 Probability Theory	en_US
utslib.for	010205 Financial Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Finance Discipline
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access
pubs.consider-herdc	true	en_US
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	8	en_US

Abstract:

Research Paper Number: 225 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.

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http://hdl.handle.net/10453/37828