Quant house of the year: Crédit Agricole CIB

Asia Risk Awards 2022

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In the derivatives business, a pricing model is good only if it allows for the risk management of the instruments it prices. A model that only delivers accurate pricing is not good enough. If the sensitivities it produces are unstable, the bank may need to re-hedge in a way that is costly and inefficient.

This is especially true for callable products such as Bermudan or American-style options. The Longstaff-Schwartz method, which has been the standard model for pricing these products over the past two decades, can be computationally intensive and produce unstable sensitivities, or Greeks. It nevertheless became ubiquitous in banks, chiefly because it was the best method available.

That was until quants saw the opportunity to use neural networks to approximate the continuation value, which is needed to decide whether to exercise the embedded optionality.

Crédit Agricole CIB has been named Asia Risk’s quant house of the year for developing a novel neural-network approach to price callable products in a comparably short timeframe and for gradually replacing Longstaff-Schwartz in its front-office functions.

The quant research team, based in Hong Kong, identified Greeks’ stability as one of the main issues in exotics, and made it a priority to improve on Longstaff-Schwartz pricing. The resulting method, optimal neural-network least squares Monte Carlo (ONLSM), builds on work outlined in two recent academic papers.

The first, Neural network regression for Bermudan option pricing, by Bernard Lapeyre and Jérôme Lelong (2020), approximates the continuation value by training a neural network on each call date. This leads to a non-convex optimisation, which can be computationally intensive.

The second, Optimal stopping via randomized neural networks, by Calypso Herrera, Florian Krach, Pierre Ruyssen and ETH Zurich’s Professor Josef Teichmann (2022), circumvents the non-convex optimisation problem by training the output layer instead of the hidden layer of the network, thereby speeding up the computation.

Wail El Allali, head of Asia quantitative research at Crédit Agricole CIB, says the new method “makes use of neural networks with only one hidden layer. The hidden layer parameters are optimised with stochastic gradient descent, while the output layer parameters are optimised with a convex optimisation similar to the least-squares method. The proof of convergence is based on Lapeyre and Lelong’s paper”.

The adoption of ONLSM has had a significant impact on how the bank prices callable products on its books. Fabien Lanneluc, head of Asia non-linear trading at Crédit Agricole CIB, who looks after rate options, structured notes and hybrid products, says: “The Longstaff-Schwartz model can be used to price different products, but to do so one has to adapt it to each product family individually. This neural network approach is more generic: it can be used on different products without having to modify it each time.”

He says the problem with Longstaff-Schwartz is not so much the prices, but rather the Greeks. Delta and gamma require a lot of calculations and are prone to estimation errors. Errors of the same sign can accumulate and create unwanted exposure, which is why stable Greeks are so important.

Beware Greeks bearing instability

With the more stable Greeks that ONLSM provides, hedging is more efficient and potentially cheaper. That is because noisy Greeks under the Longstaff-Schwartz model force banks to re-hedge their positions more frequently. As they re-calculate the hedging strategy, they might end up paying more for it, especially when operating in less liquid markets or at less liquid times of the day.

The quant team’s own research paper, Neural-network regression for pricing and hedging American-style options by El Allali, Arthur Semin and Ryan Kurniawan (2022), shows how their model works on a 20-year USD Bermudan swap. “We can see that prices are comparable to the Longstaff-Schwartz ones,” says Semin, a quantitative researcher in El Allali’s team. “But one can note that we achieved competitive computational cost and higher stability of the vegas.”

Similar results were obtained in a 20-year USD callable dual-range accrual, a complex product that is traded in significant volumes in Asian markets. The prices obtained through ONLSM were much closer to those reached through the benchmark PDE method than those calculated via Longstaff-Schwartz.

“We started the implementation phase in Q4 2021, and the model was available in production in Q2 2022,” says Christophe Michel, Crédit Agricole CIB’s global head of quantitative research. He explains that the new method is currently used for pricing and risk management, though its use in accounting and reporting is expected to be approved internally in the near future.

Having a framework for pricing American options already in place meant the team only had to work on top of the existing framework to implement the neural network solution. This made the whole process considerably easier than starting from scratch.

El Allali says that everyone, from the quant team to the business side to the IT team, collaborated to ensure the project progressed smoothly and swiftly.

Kurniawan, the quantitative researcher in El Allali’s team who was the chief architect of the import and the development of ONLSM’s code, says they were inspired by Herrera et al’s paper, which showed an efficient optimisation method for neural network applications.

“I did my PhD at ETH where Teichmann teaches, so I knew his works on neural network applications for financial pricing,” he says. “Professor Teichmann’s team gave very valuable feedback throughout our project. Their publicly available source code was especially helpful as it serves as the foundation of our code and therefore considerably speeds up our development.”

“Ryan and I graduated from the same master programme at ETH Zurich,” says El Allali. “When I started to work on this approach, I asked him to join our team. Arthur worked on a similar subject using neural networks for parametrised PDEs at EPFL [the Swiss Federal Institute of Technology Lausanne]. This project was a priority for us on our desk.”

The next step will be to expand the portion of the portfolio in which ONLSM is used. “We will study the expansion of this method to all callable products that cannot be priced with PDEs because of the high complexity,” Michel says.