Podcast: UBS’s Gordon Lee on conditional expectations and XVAs

Conditional expectations have long been the bane of XVA desks. They are an integral part of virtually every derivatives product, from vanilla swaps to exotics such as Bermudan swaptions. But the standard way of calculating them – the least square Monte Carlo method – is notorious for its computational intensity.

In this episode of Quantcast, Gordon Lee, senior XVA and capital management quant at UBS, discusses an alternative estimation method he developed with Jörg Kienitz, Nikolai Nowaczyk and Nancy Qingxin Geng. This approach combines a number of existing techniques: kernel density estimation; Gaussian process regression; and the control variate.

Lee describes the method with analogies and nicknames: “Surely you have a nickname for your favourite mathematical technique, right?”

The kernel density estimation, which Lee calls the ‘neighbour’, provides an estimate for the variable under consideration based on neighbouring data points. The Gaussian process regression – a Bayesian technique, which Lee nicknames the ‘reverend’ – serves to stabilise the regression, making it smoother and less prone to errors. The control variate technique, or the ‘trader’, uses a related estimate – which, in the case of an option in the Black-Scholes world would be the delta of the option – to reduce variance and allow for quicker convergence.

“The estimation method can be retrofitted into existing systems and gives good results,” says Lee, and can produce an accurate estimate with significantly fewer simulated paths, thereby saving time.

Lee also shares his views on signatures and as well as quant finance education and the future of XVA desks.

Index

00:00 Dynamically controlled kernel estimation

05:30 Combining the three techniques

18:20 How does it perform?

21:55 Applications of signatures

24:36 Quant finance master’s and the demand for new skills

31:11 How XVA desks have changed in the recent past

To hear the full interview, listen in the player above, or download. Future podcasts in our Quantcast series will be uploaded to Risk.net. You can also visit the main page here to access all tracks, or go to the iTunes store or Google Podcasts to listen and subscribe.

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