Hedging Large Portfolios of Options in Discrete Time

B. Peeters, C. L. Dert and Andre Lucas

Applied Mathematical Finance, 2008, vol. 15, issue 3, 251-275

Abstract: The problem studied is that of hedging a portfolio of options in discrete time where underlying security prices are driven by a combination of idiosyncratic and systematic risk factors. It is shown that despite the market incompleteness introduced by the discrete time assumption, large portfolios of options have a unique price and can be hedged without risk. The nature of the hedge portfolio in the limit of large portfolio size is substantially different from its continuous time counterpart. Instead of linearly hedging the total risk of each option separately, the correct portfolio hedge in discrete time eliminates linear as well as second and higher order exposures to the systematic risk factors only. The idiosyncratic risks need not be hedged, but disappear through diversification. Hedging portfolios of options in discrete time thus entails a trade-off between dynamic and cross-sectional hedging errors. Some computations are provided on the outcome of this trade-off in a discrete-time Black-Scholes world.

Keywords: Option hedging; discrete time; preference free valuation; hedging errors; cross-sectional hedging; static hedging; JEL Codes: G13; G12 (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.tandfonline.com/doi/abs/10.1080/13504860701718471 (text/html)
Access to full text is restricted to subscribers.

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:taf:apmtfi:v:15:y:2008:i:3:p:251-275

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RAMF20

DOI: 10.1080/13504860701718471

Access Statistics for this article

Applied Mathematical Finance is currently edited by Professor Ben Hambly and Christoph Reisinger

More articles in Applied Mathematical Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().