Modern Computational Finance: Parts I and II free on SSRN for a limited time

SSRN link now expired — download parts I and II here for a limited time:

part III to follow

parts i and ii free for a limited time on SSRN

The first two parts (out of three) of my book Modern Computational Finance (Wiley, 2018) are complimentarily available on SSRN only in December 2020.

Part I teaches necessary C++ foundations with a focus on parallel computing. Part II summarizes the theory of financial Derivatives and develops serial and parallel Monte-Carlo pricing and risk management engines.

Part III, not included in this preview, discusses and develops the critical adjoint differentiation (AD) technology, its professional implementation in C++ and its deployment in risk management platforms.

In recent years, AD revolutionized the field of quantitative finance. It brought us real-time risk reports and instantaneous calibration. It also enabled extremely promising new directions of research. For instance, the Risk article Differential Machine Learning by Brian Huge and I (also available on arXiv and SSRN) leverages pathwise gradients computed with AD to train a novel breed of deep learning models to effectively approximate pricing and risk functions of arbitrary financial products.

I implemented AD in production at Danske Bank with my colleagues of the Quantitative Research department. I also teach AD at Copenhagen University in the context of my graduate course on Computational Finance and Machine Learning in Finance. My book gives an exhaustive and pedagogical account of AD, its implementation in C++ and its deployment for the risk management of financial Derivatives.

Parts I and II are necessary pre-requisites to make the most of the critical part III.

QuantMinds e-magazine, June 2020

New research, new breakthroughs, and new opportunities

With the results of my latest work with Brian Huge on differential machine learning, along with the latest from Marcos Lopez de Prado, Alexander Antonov, Svetlana Borovkova, and Fabio Mercurio, who have shared their latest insights into machine learning (ML), neural networks, covid-19 and Libor.

Differential machine learning combines ML with automatic differentiation (AAD) to produce accurate pricing and risk approximations for arbitrary derivatives transactions or trading books, quickly, online, with convergence guarantees.

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QuantMinds e-magazine, June 2020

interactive magazine here

Differential Machine Learning

Risk management with AAD and ML: an unreasonably effective combination

Working paper: on ssrn
TensorFlow notebook: on Google Colab

Differential machine learning (ML) is an extension of supervised learning, where ML models are trained on examples of not only inputs and labels but also differentials of labels to inputs, applicable in all situations where high quality first order derivatives wrt training inputs are available.

In the context of financial Derivatives and risk management, pathwise differentials are efficiently computed with automatic adjoint differentiation (AAD). Differential machine learning gives us unreasonably effective pricing and risk approximation. We can produce fast pricing analytics in models too complex for closed form solutions, extract the risk factors of complex transactions and trading books, and effectively compute risk management metrics like reports across a large number of scenarios, backtesting and simulation of hedge strategies, or regulations like XVA, CCR, FRTB or SIMM-MVA.

The article focuses on differential deep learning (DL), arguably the strongest application. Standard DL trains neural networks (NN) on punctual examples, whereas differential DL teaches them the shape of the target function, hence the performance. We included numerical examples, both idealized and real world.

In the online appendices, we apply differential learning to other ML models, like classic regression or principal component analysis (PCA), with equally remarkable results.

We posted a TensorFlow implementation on Google Colab, including examples from the paper and a discussion of practical implementation.

Open In Colab
basket option price approximation from simulated data
with standard and differential deep learning