## Workshop "Rough volatility: regularity structures and deep learning"

- Wed, September 4, 2019 (afternoon) - Fri, September 6, 2019 (morning)
- FAM @ TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien
- Room "Zeichensaal 3", Freihaus building, 7th floor, green section

- Speakers:
- Organiser:
**Stefan Gerhold**, FAM @ TU Wien

Participationis free and there is no registration necessary.

## Schedule

Wed, September 4th | ||
---|---|---|

15:00-16:30 | Peter Friz"Rough paths, rough volatility, regularity structures" (part I) | |

evening | Joint Dinner * | |

Thu, September 5th | ||

9:15-10:45 | Peter Friz"Rough paths, rough volatility, regularity structures" (part II) | |

11:00-12:30 | Christian Bayer"Calibration of rough volatility models by deep learning" (part I) | |

afternoon | free to avoid collision with WPI event | |

Fri, September 6th | ||

10:00-11:30 | Christian Bayer"Calibration of rough volatility models by deep learning" (part II) |

## Abstracts

### Christian Bayer

"Calibration of rough volatility models by deep learning"

Rough stochastic volatility models have been successfully used to explain various stylized facts of financial markets. In particular, they recover the power-law explosion of skews of implied volatilities of put and call options when maturity goes to zero, and generally provide excellent fits to implied volatility surfaces in the market.

This model class is, however, difficult to treat computationally, usually because the underlying processes fail to satisfy the Markov property. This impacts both asymptotic analysis (see the talk of Peter Friz) and numerical approximation. Indeed, many typical numerical option pricing methods either are not applicable at all, or are more difficult to implement and analyze. As option pricing is difficult in these models, standard model calibration procedures become difficult, as they typically require huge numbers of price calculations due to the iterative nature of the optimization algorithms involved.

In this talk, we propose to calibrate rough volatility models using deep learning methods. In the literature, model calibration by machine learning has been suggested before, usually in the sense of learning the map from market prices to model parameters. In contrast, we use deep learning to approximate the option price function within the model, i.e., the forward rather than the inverse problem. The actual calibration is then done using a standard calibration procedure.

Based on joint work with Blanka Horvath, Aitor Muguruza, Ben Stemper and Mehdi Tomas.

### Peter Friz

"Rough paths, rough volatility, regularity structures"

We will run through the basic of rough path theory and point out the corresponding objects in Hairer's theory of regularity structures. Rough volatility actually provides us with some stochastic objects whose pathwise interpretation has many common aspects with the pathwise approach to singular stochastic partial differential equations. As financial application we will consider the pricing of short-dated options under rough volatility. Time permitting, I will also talk about a new class of stochastic processes called rough semimartingales.

## Joint Dinner

In order to have time to talk to each other there will be a joint dinner in the evening of Wednesday, September 4th, 2019, near TU Wien (time/place t.b.a.).

In case you want to join the dinner on Wednesday please write an email to Stefan Gerhold <sgerhold@fam.tuwien.ac.at>.