Podcast: Olivier Daviaud on P&L attribution for options

Profit and loss (P&L) attribution is widely used to explain portfolio returns and evaluate risk management models.

In vanilla options, the standard approach is the so-called Greeks decomposition, which explains the P&L in terms of gamma, theta, vega and other sensitivities of the option price to market variables. This accurately describes the P&L dynamics of one-day market movements and works well for banks and market-makers that hedge portfolios daily.

But this approach is not without limitations – the main one being that it cannot be used over arbitrary time intervals. “So, it doesn’t work over one month of three months,” explains Olivier Daviaud, a quantitative strategist at JP Morgan, and our guest for this episode of Quantcast.

That makes Greeks decomposition far from ideal for buy-side firms that have longer investment horizons. Daviaud recently proposed a new P&L attribution method for vanilla options that is designed to meet the needs of these participants.

“We take the traditional Greeks decomposition and we manipulate it using basic calculus to disentangle some of the blocks,” Daviaud explains. “And as a result, the P&L is expressed along a fresh new set of meaningful dimensions.”

Daviaud’s method is an extension of a formula he proposed in 2022 with Abhishek Mukhopadhyay, cross-asset quantitative strategist at Societe Generale, in which they connect the performance of a portfolio of vanilla options to the difference between realised and implied volatility.

We take the traditional Greeks decomposition and we manipulate it using basic calculus to disentangle some of the blocks

Olivier Daviaud

The approach has a number of benefits. Notably, it explains the P&L dynamics in terms of how much volatility is realised, where it is realised, and the change in implied volatility. This differs significantly from the Greeks decomposition method, which provides a breakdown of the P&L dynamics in terms of sensitivities to just three variables: the price of the underlying; the time to maturity; and the implied volatility.

Daviaud’s method also keeps the memory of the implied volatility at the inception of the contract, reduces the noise of the day-to-day volatilities, and explicitly describes the P&L as a tractable function, all of which facilitate better P&L analysis. 

The approach outlined by Daviaud can be used to achieve several objectives related to the management of an options portfolio, such as calculating the fair value of volatility, conducting risk analysis and delta hedging. But from conversations with clients, some of which have adopted the method for their portfolios, Daviaud says the main use-case is performing P&L attribution and analysis.

Daviaud is not done with this stream of research He next plans to dissect the terms of the Greeks decomposition that appear to contribute little to the overall output but deserve to be investigated further. He is also considering the possibility of generalising the results so far into a wider framework that might unveil new applications, as often happens in science when a higher level of abstraction is achieved, leading to a better vantage point that reveals uses that were previously hidden.   

Index:

00:00 Introduction to P&L attribution for options

07:25 Greeks decomposition

10:00 Daviaud’s P&L attribution formula

13:00 Applications of the formula

17:25 Extension to non-equity vanilla options and exotics

18:40 Next research projects

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