# Pricing under rough volatility

@article{Bayer2015PricingUR, title={Pricing under rough volatility}, author={Christian Bayer and Peter K. Friz and Jim Gatheral}, journal={Quantitative Finance}, year={2015}, volume={16}, pages={887 - 904} }

From an analysis of the time series of realized variance using recent high-frequency data, Gatheral et al. [Volatility is rough, 2014] previously showed that the logarithm of realized variance behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable timescale. The resulting Rough Fractional Stochastic Volatility (RFSV) model is remarkably consistent with financial time series data. We now show how the RFSV model can be used to price claims on…

## 302 Citations

### Volatility is rough

- Economics
- 2014

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional…

### Weak error rates for option pricing under linear rough volatility

- Mathematics
- 2020

In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [Bayer, Friz,…

### Rough volatility: Evidence from option prices

- Economics, MathematicsIISE Transactions
- 2018

ABSTRACT It has been recently shown that spot volatilities can be closely modeled by rough stochastic volatility-type dynamics. In such models, the log-volatility follows a fractional Brownian motion…

### Is Volatility Rough

- Economics, Mathematics
- 2019

Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have…

### Perfect hedging in rough Heston models

- EconomicsThe Annals of Applied Probability
- 2018

Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However,…

### Decoupling the Short- and Long-Term Behavior of Stochastic Volatility

- EconomicsJournal of Financial Econometrics
- 2021

We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including…

### The characteristic function of rough Heston models

- Mathematics
- 2016

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to…

### Short-time at-the-money skew and rough fractional volatility

- Mathematics, Economics
- 2015

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process…

### Weak error rates for option pricing under the rough Bergomi model

- MathematicsArXiv
- 2020

In quantitative finance, modeling the volatility structure of underlying assets is a key component in the pricing of options. Rough stochastic volatility models, such as the rough Bergomi model…

### Impact of rough stochastic volatility models on long-term life insurance pricing

- EconomicsEuropean actuarial journal
- 2022

The Rough Fractional Stochastic Volatility (RFSV) model of Gatheral et al. (Quant Financ 18(6):933–949, 2014) is remarkably consistent with financial time series of past volatility data as well as…

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