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Small-Time Asymptotics for Gaussian Self-Similar Stochastic Volatility Models

Small-Time Asymptotics for Gaussian Self-Similar Stochastic Volatility Models Appl Math Optim https://doi.org/10.1007/s00245-018-9497-6 Small-Time Asymptotics for Gaussian Self-Similar Stochastic Volatility Models 1 2 3 Archil Gulisashvili · Frederi Viens · Xin Zhang © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We consider the class of Gaussian self-similar stochastic volatility models, and characterize the small-time (near-maturity) asymptotic behavior of the correspond- ing asset price density, the call and put pricing functions, and the implied volatility. Away from the money, we express the asymptotics explicitly using the volatility pro- cess’ self-similarity parameter H, and its Karhunen–Loève characteristics. Several model-free estimators for H result. At the money, a separate study is required: the asymptotics for small time depend instead on the integrated variance’s moments of 1 3 orders and , and the estimator for H sees an affine adjustment, while remaining 2 2 model-free. Keywords Stochastic volatility models · Gaussian self-similar volatility · Implied volatility · Small-time asymptotics · Karhunen–Loève expansions Mathematics Subject Classification 60G15 · 91G20 · 40E05 B Archil Gulisashvili gulisash@ohio.edu Frederi Viens viens@purdue.edu Xin Zhang zhang407@math.purdue.edu Department of Mathematics, Ohio University, Athens, OH 45701, USA Department of Statistics, Purdue University, West Lafayette, IN 47907, USA Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Small-Time Asymptotics for Gaussian Self-Similar Stochastic Volatility Models

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References (84)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-018-9497-6
Publisher site
See Article on Publisher Site

Abstract

Appl Math Optim https://doi.org/10.1007/s00245-018-9497-6 Small-Time Asymptotics for Gaussian Self-Similar Stochastic Volatility Models 1 2 3 Archil Gulisashvili · Frederi Viens · Xin Zhang © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We consider the class of Gaussian self-similar stochastic volatility models, and characterize the small-time (near-maturity) asymptotic behavior of the correspond- ing asset price density, the call and put pricing functions, and the implied volatility. Away from the money, we express the asymptotics explicitly using the volatility pro- cess’ self-similarity parameter H, and its Karhunen–Loève characteristics. Several model-free estimators for H result. At the money, a separate study is required: the asymptotics for small time depend instead on the integrated variance’s moments of 1 3 orders and , and the estimator for H sees an affine adjustment, while remaining 2 2 model-free. Keywords Stochastic volatility models · Gaussian self-similar volatility · Implied volatility · Small-time asymptotics · Karhunen–Loève expansions Mathematics Subject Classification 60G15 · 91G20 · 40E05 B Archil Gulisashvili gulisash@ohio.edu Frederi Viens viens@purdue.edu Xin Zhang zhang407@math.purdue.edu Department of Mathematics, Ohio University, Athens, OH 45701, USA Department of Statistics, Purdue University, West Lafayette, IN 47907, USA Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Apr 30, 2018

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