We count on the suggestions and comments left by advanced readers in the linkedIn thread to quickly complete this work with the quality expected from the Modern Computational Finance series.
The draft, co-authored by Jesper Andreasen and Antoine Savine, covers cash-flow scripting, a critical technology in modern Derivatives pricing and risk management, not covered in any alternative literature. Mathematically, scripting turns arbitrary descriptions of Derivatives cash-flows into a functional of the path of the market state so the prices and risks of arbitrary transactions may be computed in arbitrary stochastic models. Computationally, scripting produces a computation graph for the cash-flows of arbitrary transactions, which is then optimized and executed for the computation of prices and risks, in a similar manner to machine learning systems like TensorFlow.
Cash-flow scripting has been around for twenty-five years. It was invented in Societe Generale and Banque Paribas for the purpose of structuring exotic transactions and computing prices and risks in real-time. Since then, scripting has considerably evolved into a central piece in all Derivatives pricing, risk management and regulatory calculation platforms.
Jesper Andreasen and I have been working with cash-flow scripting since the mid 1990s, bringing this technology to production at BNP-Paribas, General Re Financial Products, BAML, Nordea, Danske Bank and Saxobank, among other places. We put in this book the sum of our experience, along with our views for the future of this technology. The book comes with an implementation in C++ available on GitHub. Scripting has strong ties to modern technologies like smart contracts or computation graphs for machine learning, although this is a chapter yet to be written.
We have just presented our latest Risk paper Differential Machine Learning at QuantMinds International 2020. The presentation includes a live demo of how differential ML is implemented in production, and combined with cash-flow scripting to provide truly general means of learning the pricing and risk function of arbitrary financial instruments. See the 5min demonstration below:
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.