Implied Volatility Structure in Turbulent and Long-Memory Markets
We consider fractional stochastic volatility models that extend the classic Black–Scholes model for asset prices. The models are general and motivated by recent empirical results regarding the behavior of realized volatility. While such models retain the semimartingale property for the asset price t...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2020-04-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fams.2020.00010/full |
| _version_ | 1818901989989285888 |
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| author | Josselin Garnier Knut Sølna |
| author_facet | Josselin Garnier Knut Sølna |
| author_sort | Josselin Garnier |
| collection | DOAJ |
| description | We consider fractional stochastic volatility models that extend the classic Black–Scholes model for asset prices. The models are general and motivated by recent empirical results regarding the behavior of realized volatility. While such models retain the semimartingale property for the asset price the associated European option pricing problem becomes complex, with no explicit solution. In a number of canonical scaling regimes it is possible, however, to derive asymptotic and sparse representations for the option price and the associated implied volatility, that are parameterized by a few effective parameters and that involve power law dependencies on time to maturity. These effective parameters may depend in a complicated way on the volatility model, but they can be easily estimated from the observation of a few option prices. The effective parameters associated with a particular underlying asset can be calibrated with respect to liquid contracts written on this asset and then used for pricing less liquid contracts written on the same underlying asset. Therefore, the effective parameters provide a robust link between financial products written on a particular underlying asset. |
| first_indexed | 2024-12-19T20:28:31Z |
| format | Article |
| id | doaj.art-eae2cd72494b4c8db99956281e6f400d |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-19T20:28:31Z |
| publishDate | 2020-04-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-eae2cd72494b4c8db99956281e6f400d2022-12-21T20:06:47ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872020-04-01610.3389/fams.2020.00010523591Implied Volatility Structure in Turbulent and Long-Memory MarketsJosselin Garnier0Knut Sølna1CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, FranceDepartment of Mathematics, University of California, Irvine, Irvine, CA, United StatesWe consider fractional stochastic volatility models that extend the classic Black–Scholes model for asset prices. The models are general and motivated by recent empirical results regarding the behavior of realized volatility. While such models retain the semimartingale property for the asset price the associated European option pricing problem becomes complex, with no explicit solution. In a number of canonical scaling regimes it is possible, however, to derive asymptotic and sparse representations for the option price and the associated implied volatility, that are parameterized by a few effective parameters and that involve power law dependencies on time to maturity. These effective parameters may depend in a complicated way on the volatility model, but they can be easily estimated from the observation of a few option prices. The effective parameters associated with a particular underlying asset can be calibrated with respect to liquid contracts written on this asset and then used for pricing less liquid contracts written on the same underlying asset. Therefore, the effective parameters provide a robust link between financial products written on a particular underlying asset.https://www.frontiersin.org/article/10.3389/fams.2020.00010/fullstochastic volatilitylong-memory processfractional processvolterra processasymptoticstime scales |
| spellingShingle | Josselin Garnier Knut Sølna Implied Volatility Structure in Turbulent and Long-Memory Markets Frontiers in Applied Mathematics and Statistics stochastic volatility long-memory process fractional process volterra process asymptotics time scales |
| title | Implied Volatility Structure in Turbulent and Long-Memory Markets |
| title_full | Implied Volatility Structure in Turbulent and Long-Memory Markets |
| title_fullStr | Implied Volatility Structure in Turbulent and Long-Memory Markets |
| title_full_unstemmed | Implied Volatility Structure in Turbulent and Long-Memory Markets |
| title_short | Implied Volatility Structure in Turbulent and Long-Memory Markets |
| title_sort | implied volatility structure in turbulent and long memory markets |
| topic | stochastic volatility long-memory process fractional process volterra process asymptotics time scales |
| url | https://www.frontiersin.org/article/10.3389/fams.2020.00010/full |
| work_keys_str_mv | AT josselingarnier impliedvolatilitystructureinturbulentandlongmemorymarkets AT knutsølna impliedvolatilitystructureinturbulentandlongmemorymarkets |