Forecasting fractional rough volatility - a machine learning approach

Description

It is well-known that the hypothesis of constant volatility in the celebrated Black-Scholes-Merton (BSM) model for pricing financial derivatives is wrong and may lead to drastic mispricing, in particular for any exotic derivative contracts. Apart from the classic [Dupire1994] deterministic local volatility approach, recently, the concept of rough stochastic volatility [Gatheral, et. al. 2018] massively emerged in the academic research by replacing a fractional Brownian motion with Hurst parameter less than half instead of using a Brownian motion for the stochastic volatility process. In the past years there has been a big amount of research on rough volatility model in quantitative finance as a substitute for the traditional stochastic volatility. However, recently, Rogers [2019] and, later on, Cont and Das [2022] raise the important question of whether using a rough volatility model is useful from a practical point of view. In fact, they argue that the Hurst roughness index measured based on high-frequency observations is different for the realized volatility – even based on very short sampling intervals – and the instantaneous (spot) volatility. Their critics entirely based on the discretization error or microstructure noise. In this project, we aim at studying the pivotal issue of the validity of rough fractional stochastic volatility in quantitative finance via a machine learning perspective. The central goal is to understand in depth the universality of the volatility formation process via fully non-parametric and model-free approaches with well-developed machine learning techniques. More precisely, we aim to analyze the volatility formation mechanism by trying to forecast the next daily realized volatility by using recurrent neural networks (RNN) such as long short-term memory (LSTM) networks in order to take into account the presence of the memory reflecting the non-Markovian structure.

Start Date: 1st October 2023

Further Details:

This PhD project is funded by The Faculty of Science & Engineering at The University of Liverpool and will start on 1st October 2023.

Successful candidates who meet the University of Liverpool eligibility criteria will be awarded a Faculty of Science & Engineering studentship for 3.5 years, covering UK tuition fees and an annual tax-free stipend (e.g. £17,688 p.a. for 2022-23).

Faculty of Science & Engineering students benefit from bespoke graduate training and £5,000 for training, travel and conferences.

The Faculty of Science & Engineering is committed to equality, diversity, widening participation and inclusion. Academic qualifications are considered alongside non-academic experience. Our recruitment process considers potential with the same weighting as past experience. Students must complete a personal statement profoma and ensure this is included in their online application.

How to Apply:

All applicants must complete the personal statement proforma. This is instead of a normal personal/supporting statement/cover letter. The proforma is designed to standardise this part of the application to minimise the difference between those who are given support and those who are not. The proforma can be found here: https://tinyurl.com/ym2ycne4. More information on the application process can be found here: https://tinyurl.com/mwn5952t. When applying online, students should ensure they include the department name in the ‘Programme Applied For’ section of the online form, as well as the Faculty of Science & Engineering as the ‘studentship type’ in the finance section.

Application Web Address: https://www.liverpool.ac.uk/study/postgraduate-research/how-to-apply/