Economics at your fingertips  

Hedging with Stochastic and Local Volatility

Carol Alexander () and Leonardo Nogueira ()
Additional contact information
Leonardo Nogueira: ICMA Centre, University of Reading

ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading

Abstract: We derive the local volatility hedge ratios that are consistent with a stochastic instantaneous volatility and show that this 'stochastic local volatility' model is equivalent to the market model for implied volatilities. We also show that a common feature of all Markovian single factor stochastic volatility models, (log)normal mixture option pricing models and 'sticky delta' models is that they predict incorrect dynamics for implied volatility. As a result they over-hedge the Black-Scholes model in the presence of a market skew and this explains the poor delta hedging performance of these models reported in the literature. Whilst the traditional 'sticky tree' local volatility models do not possess this unfortunate property, they cannot be used for pricing without exogenous and ad hoc smoothing of results. However the stochastic local volatility framework allows one to extend a good pricing model into a good hedging model. The theoretical results are supported by an empirical analysis of the hedging performance of seven models, each with different volatility characteristics, on the SP500 index skew.

Keywords: Local volatility; stochastic volatility; implied volatility; hedging; dynamic delta hedging; volatility dymamics (search for similar items in EconPapers)
JEL-codes: C16 G12 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2004-07, Revised 2004-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3) Track citations by RSS feed

Downloads: (external link) (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found ( [302 Found]-->

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:

Access Statistics for this paper

More papers in ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading Contact information at EDIRC.
Bibliographic data for series maintained by Marie Pearson ().

Page updated 2021-10-13
Handle: RePEc:rdg:icmadp:icma-dp2004-10