of cash‐flows that lends itself to a scalable production of risk, back‐testing, capital assessment, value adjustments, or even middle office processing for portfolios of heterogeneous financial transactions. We also focus on performance and introduce the key notion of pre‐processing, whereby a script is automatically analyzed, prior to its valuation or risk, to optimize the upcoming calculations. Our framework provides a representation of the cash‐flows and a way of working with them that facilitates not only valuation but also pre‐processing and any kind of query or transformation that we may want to conduct on the cash‐flows of a set of transactions.
Scripting makes a significant difference in the context of xVA, as explained in part V, and more generally, all regulatory calculations that deal with multiple derivatives transactions of various sophistication, written on many underlying assets belonging to different asset classes. Before xVA may be computed over a netting set,3 all the transactions in the netting set must be aggregated. This raises a very practical challenge and a conundrum when the different transactions are booked in different systems and represented under different forms. Scripting offers a consistent representation of all the transactions, down to their cash‐flows. Scripted transactions are therefore naturally aggregated or manipulated in any way. A key benefit of scripted cash‐flows is that scripts are not black boxes. Our software (more precisely, the visitors implemented in the software) can “see” and analyze scripts, in order to aggregate, compress, or decorate transactions as explained in part V, extract information such as path‐dependence or non‐linearity and select the model accordingly, implement automatic risk smoothing (part IV), or analyze a valuation problem to optimize its calculation. Our library is designed to facilitate all these manipulations, as well as those we haven't thought about yet.
The purpose of this publication is to provide a complete reference for the implementation of scripting and its application in derivatives systems to its full potential. The defining foundations of a well‐designed scripting library are described and illustrated with C++ code, available online on:
https://github.com/asavine/Scripting/tree/Book-V1
Readers will find significant differences between the repository code and the code printed in the book. The repository has been undergoing substantial modernization and performance improvements not covered in this edition of the text. Make sure you connect to the branch Book‐V1, not the master. Besides, the code base evolves throughout the book and the online repository contains the final version. It is advisable to type by hand the code printed in the text rather than rely on the online repository while reading the book.
This code constitutes a self‐contained, professional implementation of scripting in C++. It is written in standard, modern C++ without any external dependency. It was tested to compile on Visual Studio 2017. The library is fully portable across financial libraries and platforms and includes an API, described in section 3.7, to communicate with any model.
The code as it stands can deal with a model of any complexity as long as it is a single underlying model. It works with the Black and Scholes model of [5] and all kind of extensions, including with local and/or stochastic volatility, like Dupire's [9] and [10], or single underlying stochastic volatility models.4 The library cannot deal with multiple underlying assets, stochastic interest rates, or advanced features such as the Longstaff‐Schwartz algorithm of [22]. It doesn't cover the management of transactions throughout their life cycle or deal with past fixings. All those features, necessary in a production environment, would distract us from correctly establishing the defining bases. These extensions are discussed in detail in parts II and III, although not in code.
Our online repository also provides an implementation of Fuzzy Logic for automatic risk smoothing, an excel interface to the library, a tutorial for exporting C++ code to Excel, a prebuilt xll, and a demonstration spreadsheet.
The C++ implementation is discussed in part I, where we explore in detail the key concepts of expression trees and visitors. We show how they are implemented in modern C++ and define the foundations for an efficient, scalable scripting library. We also provide some (very) basic self‐contained models to test the library, although the library is model agnostic by design and meant to work with any model that implements an API that we specify. For clarity, the code and comments related to parsing (the transformation of a text script into an expression tree) are moved from the body of the text into an appendix.
We discuss in part II the implementation of some basic extensions, and in part III more advanced features like interest rates and multiple currencies and assets. We discuss the key notion of indexing simulated data. Indexing is a special flavor of pre‐processing, crucial for performance. We also discuss the support for LSM, the regression‐based algorithm designed by Carriere and Longstaff‐Schwartz in [6] and [22] to deal with early exercise in the context of Monte‐Carlo simulations, and later reused in the industry in the context of xVA and other regulatory calculations. These parts include extensive guidance for the development of the extensions, but not source code.
The rest of the publication describes some applications of scripting outside the strict domain of pricing and demonstrates that our framework, based on visitors, can resolve many other problems.
Part IV shows how our framework can accommodate a systematic smoothing of discontinuities to resolve the problem of unstable risk sensitivities for products like digitals or barriers with Monte‐Carlo simulations. Smoothing consists of the approximation of the discontinuous payoffs by close continuous ones, like the approximation of digitals by tight call spreads. Bergomi discusses and optimizes smoothing in [4]. Our purpose is different. We demonstrate that smoothing can be abstracted as a particular application of fuzzy logic. This realization leads to an algorithm to systematically smooth not only digitals and barriers but also any payoff, automatically. The practical implementation of the algorithm is facilitated by the design of our scripting library. For clarity, the source code is not provided in the body of the text, but it is provided in our online repository.
Part V introduces the application to xVA, which is further covered in our upcoming dedicated publication. The code for xVA calculations is not provided.
1.1 SCRIPTING IS NOT ONLY FOR EXOTICS
While scripted payoffs are now part of the standard toolkit for the structuring of derivatives, it does not appear to be widely used yet in the wider context of xVA, CCR, VAR, FRTB, capital charges, or other related calculations. This is an unfortunate oversight. Market risk, value adjustments, and capital calculations over large heterogeneous portfolios of transactions are best conducted when all cash‐flows from all transactions are represented in a consistent manner, which the software can understand, analyze, and otherwise manipulate. This is exactly what scripting offers, for a small performance cost if implemented correctly.
Further, a CVA (similarly to other xVAs and other regulatory calculations) is a real option that a bank gives away any time it trades with a defaultable counterparty. That option is a put
