Podcast: Piterbarg on medians and machine learning

This episode of Quantcast features Vladimir Piterbarg, head of quantitative analytics and quantitative development at NatWest Markets, and a two-time winner of Risk.net’s Quant of the year award.

His latest work, The arcsine law for quantile derivatives, deals with the implications of using the median – or, more broadly, quantiles – for defining the payoff of a derivative product.

The paper was inspired by the fallback rate for Libor contracts developed by the International Swaps and Derivatives Association. Under this protocol, Libor-linked contracts will switch to a risk-free rate plus a Libor Adjustment Spread (LAS), which is calculated by taking the median of the difference between Libor and a replacement risk-free rate over a given period of time.

“As is often the case with my papers, it came from a question from a trader,” says Piterbarg. “He was looking at what spread was being implied by the market that day and he saw numbers that he couldn’t quite understand.”

Piterbarg realised that calculating LAS using the median could lead to inaccurate estimates, chiefly because of the dependence of such measures on volatility. In the paper, he proposes a fast and stable alternative to estimate the expected value of quantiles.

The LAS for various currencies was fixed on March 5, de facto ending the uncertainty around it, but the applications of Piterbarg’s paper extend beyond these specifics; any derivative that uses quantile expectations may be affected by the same statistical bias. One example is a Napoleon option, which pays the return of a security selected by its rank within the underlying basket.

Piterbarg also explains his scepticism of machine learning: applying it to finance, he says, often resembles a hammer looking for a nail.

It is, however, a field he cannot ignore. Piterbarg concedes that machine learning is excellent at interpolating data, though its ability to extrapolate from data is somewhat more uncertain. Earlier this year, he published Deep asymptotics, a paper co-authored with Alexandre Antonov and Michael Konikov, in which they propose a mathematical technique to control the extrapolation boundaries of neural networks.

He is equally unconvinced by recent developments in volatility modelling, which he believes have generated more hype than meaningful results. While models such as rough volatility added new weapons to the quant armoury, he thinks that, at least in rates markets, they are unlikely to lead to a major paradigm shift.

Index

00:00 Intro

01:28 The motivation for researching quantile derivatives

04:42 The results of the study

08:10 The arcsine law and its relevance to derivatives pricing

13:40 Application to Napoleon options and other quantile derivatives

15:15 Is machine learning in finance more hype than substance?   

20:25 Current research projects

24:50 The biggest open challenges in quant finance

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