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Comparison results for stochastic volatility models via coupling
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Hobson, David (David G.). (2010) Comparison results for stochastic volatility models via coupling. Finance and Stochastics, Vol.14 (No.1). pp. 129152. ISSN 09492984
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Official URL: http://dx.doi.org/10.1007/s0078000800837
Abstract
The aim of this paper is to investigate the properties of stochastic volatility models, and to discuss to what extent, and with regard to which models, properties of the classical exponential Brownian motion model carry over to a stochastic volatility setting. The properties of the classical model of interest include the fact that the discounted stock price is positive for all t but converges to zero almost surely, the fact that it is a martingale but not a uniformly integrable martingale, and the fact that European option prices (with convex payoff functions) are convex in the initial stock price and increasing in volatility. We explain why these properties are significant economically, and give examples of stochastic volatility models where these properties continue to hold, and other examples where they fail.
The main tool is a construction of a timehomogeneous autonomous volatility model via a timechange.
Item Type:  Journal Article  

Subjects:  H Social Sciences > HG Finance Q Science > QA Mathematics 

Divisions:  Faculty of Science > Statistics  
Library of Congress Subject Headings (LCSH):  Stochastic processes, Econometrics  Mathematical models, Finance  Mathematical models  
Journal or Publication Title:  Finance and Stochastics  
Publisher:  Springer  
ISSN:  09492984  
Official Date:  January 2010  
Dates: 


Volume:  Vol.14  
Number:  No.1  
Number of Pages:  24  
Page Range:  pp. 129152  
Identification Number:  10.1007/s0078000800837  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
References:  1. Andersen, L.B.G., Piterbarg, V.V.: Moment explosions in stochastic volatility models. Finance Stoch. 

URI:  http://wrap.warwick.ac.uk/id/eprint/16942 
Data sourced from Thomson Reuters' Web of Knowledge
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