Large-maturity regimes of the Heston forward smile

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Title: Large-maturity regimes of the Heston forward smile
Author(s): Jacquier, A
Roome, PR
Item Type: Journal Article
Abstract: We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the higher-order terms highly depends on the parameters, and diff erent powers of the maturity come into play. As a by-product of the analysis we provide new implied volatility asymptotics, both in the forward case and in the spot case, as well as extended SVI-type formulae. The proofs are based on extensions and re finements of sharp large deviations theory, in particular in cases where standard convexity arguments fail.
Publication Date: 21-Nov-2015
Date of Acceptance: 29-Oct-2015
URI: http://hdl.handle.net/10044/1/27704
DOI: https://dx.doi.org/10.1016/j.spa.2015.10.012
ISSN: 0304-4149
Publisher: Elsevier
Start Page: 1087
End Page: 1123
Journal / Book Title: Stochastic Processes and Their Applications
Volume: 126
Issue: 4
Replaces: 10044/1/18587
http://hdl.handle.net/10044/1/18587
Copyright Statement: © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M008436/1
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Stochastic volatility
Heston
Forward implied volatility
Asymptotic expansion
Sharp large deviations
STOCHASTIC VOLATILITY MODELS
IMPLIED VOLATILITY
ASYMPTOTIC FORMULAS
MOMENT EXPLOSIONS
EXTREME STRIKES
OPTION PRICES
EXPANSIONS
DEVIATIONS
BEHAVIOR
JUMPS
q-fin.PR
q-fin.PR
math.PR
60F10, 91G99, 91G60
Stochastic volatility
forward implied volatility
asymptotic expansions
sharp large deviations
0104 Statistics
1502 Banking, Finance And Investment
Statistics & Probability
Publication Status: Published
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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