Quadratic Hedging of Basis Risk

Hardy Hulley and Thomas McWalter
Additional contact information
Hardy Hulley: University of Technology Sydney, Finance Discipline Group, P.O. Box 123, Broadway, NSW 2007, Australia

JRFM, 2015, vol. 8, issue 1, 1-20

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 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.

Keywords: option hedging; incomplete markets; basis risk; local risk minimization; mean-variance hedging (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/1911-8074/8/1/83/pdf (application/pdf)
https://www.mdpi.com/1911-8074/8/1/83/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jjrfmx:v:8:y:2015:i:1:p:83-102:d:45402

Access Statistics for this article

JRFM is currently edited by Ms. Chelthy Cheng

More articles in JRFM from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().