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Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models

Abstract:

We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox{Ingersoll{Ross model, is multiplied by a (leverage) function of the spot process, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for the spot process with the full truncation Euler scheme or the backward Euler{Maruyama scheme for the squared stochastic volatility component. Under some mild regularity assum...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1137/17M1136754

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Catherines College; St Catherines College
ORCID:
0000-0003-4027-5298
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM Journal on Numerical Analysis Journal website
Volume:
56
Issue:
6
Pages:
3430–3458
Publication date:
2018-12-11
Acceptance date:
2018-09-07
DOI:
EISSN:
1095-7170
ISSN:
0036-1429
Pubs id:
pubs:919062
URN:
uri:0861ecd1-0cbe-4c14-b255-9854ea79138e
UUID:
uuid:0861ecd1-0cbe-4c14-b255-9854ea79138e
Local pid:
pubs:919062

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