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Journal article
Probability Density of Lognormal Fractional SABR Model
Risks (Basel), v 10(8), pp 156-27
01 Jan 2022
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Abstract
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature. We show in this paper a bridge representation for the joint density of the lognormal fractional SABR model in a Fourier space. Evaluating the bridge representation along a properly chosen deterministic path yields a small time asymptotic expansion to the leading order for the probability density of the fractional SABR model. A direct generalization of the representation of joint density often leads to a heuristic derivation of the large deviations principle for joint density in a small time. Approximation of implied volatility is readily obtained by applying the Laplace asymptotic formula to the call or put prices and comparing coefficients.
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Details
- Title
- Probability Density of Lognormal Fractional SABR Model
- Creators
- Jiro AkahoriXiaoming SongWang Tai-Ho
- Publication Details
- Risks (Basel), v 10(8), pp 156-27
- Publisher
- MDPI AG
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000845333100001
- Scopus ID
- 2-s2.0-85136603751
- Other Identifier
- 991019173712204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Business, Finance