Asymptotics for multifactor Volterra type stochastic volatility models

Catalini, Giulia; Pacchiarotti, Barbara

doi:10.48550/arxiv.2109.09448

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…It is clear that x 0 = (log s (1) 0 , • • • , s (m) 0 ). Various sample path LDPs are known for log-processes (see, e.g., [14,15,28,32,35,37,38,39,40,44]). Our main goal in the present paper is to obtain a universal sample path LDP for log-processes in multivariate stochastic volatility models that unifies the results established in the above-mentioned publications and also provides new results.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Stochastic Volatility Models and Large Deviation Principles

Gulisashvili¹

2022

Preprint

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We establish a comprehensive sample path large deviation principle (LDP) for log-processes associated with multivariate time-inhomogeneous stochastic volatility models. Examples of models for which the new LDP holds include Gaussian models, non-Gaussian fractional models, mixed models, models with reflection, and models in which the volatility process is a solution to a Volterra type stochastic integral equation. The LDP for log-processes is used to obtain large deviation style asymptotic formulas for the distribution function of the first exit time of a log-process from an open set and for the price of a multidimensional binary barrier option. We also prove a sample path LDP for solutions to Volterra type stochastic integral equations with predictable coefficients depending on auxiliary stochastic processes.

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Section: Introductionmentioning

confidence: 99%

Multivariate Stochastic Volatility Models and Large Deviation Principles

Gulisashvili¹

2022

Preprint

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“…Short maturity local volatility under rough volatility is studied in Bourgey et al (2022). Pathwise large and moderate deviation principles for rough stochastic volatility models are established in Jacquier et al (2018Jacquier et al ( , 2022; Gulisashvili (2018Gulisashvili ( , 2020Gulisashvili ( , 2021Gulisashvili ( , 2022; Gulisashvili et al (2018a,b); Cellupica and Pacchiarotti (2021); Catalini and Pacchiarotti (2021).…”

Section: Introductionmentioning

confidence: 99%

Short-time asymptotics for non self-similar stochastic volatility models

Giorgio¹,

Pacchiarotti²,

Pigato³

2022

Preprint

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We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP holds under suitable conditions, but does not require any self-similarity assumption on the Volterra process. For this reason, we are able to apply such LDP to two notable examples of non self-similar rough volatility models: models where the volatility is given as a function of a log-modulated fractional Brownian motion [Bayer et al., Log-modulated rough stochastic volatility models. SIAM J. Financ. Math, 2021Math, , 12(3), 1257Math, -1284, and models where it is given as a function of a fractional Ornstein-Uhlenbeck (fOU) process [Gatheral et al., Volatility is rough. Quant. Finance, 2018, 18(6), 933-949]. In both cases we derive consequences for short-maturity European option prices and implied volatility surfaces. In the fOU case we also discuss moderate deviations pricing and simulation results.

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Asymptotics for multifactor Volterra type stochastic volatility models

Cited by 2 publications

References 19 publications

Multivariate Stochastic Volatility Models and Large Deviation Principles

Multivariate Stochastic Volatility Models and Large Deviation Principles

Short-time asymptotics for non self-similar stochastic volatility models

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