Steps Ahead

MOSAIC SMART DATA IS PROUD TO BE A SPONSOR OF FRONTIERS IN QUANTITATIVE FINANCE

Points of discussion:

May 7th

May’s Frontiers in Quantitative Finance webcast, co-sponsored by Mosaic Smart Data, was led by Dr Brian Healy from Decision Science Ltd and Professor Andrew Papanicolaou from New York University, who gave a joint presentation on Principal Component Analysis (PCA) of Implied Volatility Surfaces.

The presentation was based on new research carried out in collaboration with Professor Marco Avellaneda from New York University and Professor George Papanicolaou from Stanford University.

As an introduction to the subject, Dr Healy began by explaining how they applied PCA to U.S. equities’ returns. He discussed issues such as how many components should be removed for the residuals to be random, how to construct the explanatory factors and the natural structure of the data. He then demonstrated this by applying some results from random matrix theory to the data.

Professor Andrew Papanicolaou followed by discussing the application of PCA using tensors to implied volatility surface data, which is a higher-dimensional problem. When performing matrix PCA on the volatility surface data, they concluded that the number of significant components is 9. As a result of the structure contained in option prices, this is lower than is typical for equity returns, where the number is usually 20.

In a similar approach to a market capitalisation weighted equity factor or index, Healy and Papanicolaou used the open interest on the option and its vega to create a portfolio of implied volatility returns that tracks the volatility surface ‘EigenPortfolio’ – suggesting this can be used in similar ways to the VIX, the S&P 500 volatility index.

Healy and Papanicolaou concluded the talk by explaining how retaining the tensor structure in the ‘EigenPortfolio’ improves how well it tracks the open interest weighted implied volatility returns portfolio.

The online event was hosted by the Oxford Mathematical and Computational Finance Group and was attended by more than 130 participants from around the world. Follow Mosaic Smart Data on LinkedIn to ensure you don’t miss information on the next Group meeting which will be in June.

To read the full presentation of Hedging with Neural Networks, by Professor Johannes Ruf and Weiguan Wang, click here.

Frontiers in Quantitative Finance

A monthly event hosted by the Oxford Mathematical and Computational Finance Group. Providing a forum for academics and practitioners to discuss and debate new ideas in the modelling, management and regulation of financial risks and an opportunity for networking. Students, academics and professionals from the finance and government sector are welcome to join the online seminar.

Attendance is free of charge but requires prior registration.

Date:
Thursday, 7 May, 18:00-19:00

Speaker:
Marco Avellaneda, New York University
Marco Avellaneda is a Professor of Financial Mathematics at New York University and a Managing Partner at Finance Concepts, a financial risk-management consultancy.

Event synopsis:
‘Hierarchical Principal Component Analysis and applications to portfolio management’

Professor Avellaneda will discuss the risk factors derived from Principal Component Analysis (PCA) and how they are generally difficult to interpret and use in practical portfolio management. He will explore an alternative approach – Hierarchical Principal Component Analysis (HPCA) – which makes strong use of the partition of the market into sectors. He will show that this approach leads to no loss of information with respect to PCA in the case of equities (constituents of the S&P 500) and also that the associated common factors admit simple interpretations. The model can also be used in markets in which the sectors have asynchronous price information, such as single-name credit default swaps, generalising the work of Cont and Kan (2011) and Ivanov (2016).

FUTURE EVENTS

Machine Learning in Finance Conference 2020
Friday 25th September

Points of discussion:

April 16th

In April’s Frontiers in Quantitative Finance webcast, co-sponsored by Mosaic Smart Data, Professor Johannes Ruf from the London School of Economics (LSE) spoke about the use of neural networks as estimation tools for the hedging of options.

As Professor of Mathematics at the LSE, he has conducted research with one of his PhD students, Weiguan Wang. The aim of Ruf and Wang’s work was to investigate the application of neural networks (NNs) as a tool for non-parametric estimation, discussing their implementation, comparing the results to several benchmarks and analysing the results, giving possible explanation.

Professor Ruf discussed how NNs have been applied to the pricing and hedging of derivatives over the past 30 years, commenting that most research papers have claimed that NNs have superior performance over other benchmarks.

He and Wang have implemented a NN, ‘HedgeNet’, which is trained to minimise the hedging error rather than the pricing error. Professor Ruf described their implementation of the model, the choice of input features and time periods. The data sets used were the end-of-day and tick prices of S&P 500 and Euro Stoxx 50 options.

He compared their results using Black-Scholes and linear regression as benchmarks. The results showed that HedgeNet outperformed the Black-Scholes benchmark significantly but not the linear regression model, which incorporated the leverage effect. 

Professor Ruf argued that the outperformance of NNs previously reported in mathematical literature is most likely due to a lack of data hygiene such as the incorrect treatment of the time series data or using an incorrect split of the test and training data.

The online event was hosted by the Oxford Mathematical and Computational Finance Group and was attended by 167 people from around the world.

To read the full presentation of Hedging with Neural Networks, by Professor Johannes Ruf and Weiguan Wang, click here.

Points of discussion:

February 20th

In February’s Frontiers in Quantitative Finance event co-sponsored by Mosaic Smart Data, Professor Olivier Guéant from the Université Paris 1 spoke about how automation in financial trading is taking the next step in market making.

Professor Guéant discussed research that he and his team have conducted on how to build market making algorithms for options on liquid assets. He discussed problems faced by market makers and the models that price-setting is based upon.

He formulated the problem as one of optimisation which is complicated due to the ‘curse of dimensionality’. His research uses ‘The Greeks’ to obtain dimensionality reduction, reducing the problem down to a system of linear ordinary differential equations which becomes easier to solve.

In giving numerical results he referred to assumptions he and his team have made, as well as ideas for further work in the algo market making space.

The event was hosted by the Oxford Mathematical and Computational Finance Group and held at Citi Stirling Square.

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