Deep Learning Profit & Loss

19 Pages Posted: 10 Jul 2020 Last revised: 27 Aug 2020

See all articles by Pietro Rossi

Pietro Rossi


Flavio Cocco

Prometeia Calcolo

Giacomo Bormetti

University of Bologna - Department of Mathematics

Date Written: June 17, 2020


Building the future profit and loss (P&L) distribution of a portfolio holding, among other assets, highly non-linear and path-dependent derivatives is a challenging task. We provide a simple machinery where more and more assets could be accounted for in a simple and semi-automatic fashion. We resort to a variation of the Least Square Monte Carlo algorithm where interpolation of the continuation value of the portfolio is done with a feed forward neural network. This approach has several appealing features not all of them will be fully discussed in the paper. Neural networks are extremely flexible regressors. We do not need to worry about the fact that for multi assets payoff, the exercise surface could be non connected. Neither we have to search for smart regressors. The idea is to use, regardless of the complexity of the payoff, only the underlying processes. Neural networks with many outputs can interpolate every single assets in the portfolio generated by a single Monte Carlo simulation. This is an essential feature to account for the P&L distribution of the whole portfolio when the dependence structure between the different assets is very strong like the case where one has contingent claims written on the same underlying.

Keywords: feed-forward neural networks, profit & loss distribution, non-linear portfolios

JEL Classification: C45, C63, G13, G32

Suggested Citation

Rossi, Pietro and Cocco, Flavio and Bormetti, Giacomo, Deep Learning Profit & Loss (June 17, 2020). Available at SSRN: or

Pietro Rossi (Contact Author)

Prometeia ( email )


Flavio Cocco

Prometeia Calcolo ( email )

Via G. Marconi, 43
I-40122 Bologna

Giacomo Bormetti

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126

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