Antoine Savine - Modern Computational Finance

Templates are typically used for vanilla swaps, European options or first‐generation exotics (short‐term forex barrier options). They combine the practicality of hard‐coded transactions with the benefits of scripting. Many transactions are also regarded as “almost” vanilla swaps, “almost” European, or “almost” standard barriers. In these cases, it is most practical to start with a template and modify the auto‐generated script by hand. Templates are also useful when some transactions are booked in a separate system, which is often the case for, say, vanilla swaps. To aggregate these transactions with the rest of a netting set for the calculation of an xVA, for example, those transactions can be scripted on the fly with template code.

This logic may be pushed a step higher, with the design of GUIs, programmed in a language like C#, so that finance professionals without programming expertise, or customers, may build transactions by assembling blocks on a graphical representation of the transaction. This graphical representation is then automatically turned into the corresponding script.

Writing templates is trivial and a template can be implemented directly in a spreadsheet without code. To write a GUI platform for the design of transactions and translate that graphical representation into a script is perhaps more advanced. It certainly requires an expertise in GUI design, something out of the scope of this publication but covered in many recent C# or Python textbooks.

1 1Depending on scripting grammar, that barrier could also be written in functional form:STRIKE100BARRIER12001Jun2020append ( vFixings, spot())Start: 01Jun2020End: 01Jun2021append ( vFixings, spot())Freq: weekly01Jun2021opt pays (max( vFixings) < BARRIER) * max( 0, spot() ‐ STRIKE)We develop a classic, procedural scripting language in what follows, although readers can easily apply the logic and code of this book to design a functional scripting language like in the script above, or implement the grammar of their choice.

2 2We develop a scripting language similar to a high‐level language like Python, not a programming language like C++. Classic constructs like variables, loops, and conditions are part of the language, as well as special keywords for the description of cash‐flows, such as spot(), which references simulated market prices. Of course, this is one particular choice and different rules are implemented with minor modifications, for example, a C/C++ inspired syntax or a functional grammar without conditionals or variables.

3 3All transactions against a counterparty.

4 4Stochastic volatility models are covered in many textbooks, including [21] [13], [3], or our lecture notes [26].

5 5It is indeed relevant for calibration.

6 6We can accommodate step‐wise MC in a trivial, if memory‐inefficient manner: store the paths generated step‐wise and deliver them path‐wise to the script evaluator.

7 7The model also generates a value for the numeraire under which it performs the simulation, although that numeraire is a scalar value (per event date) that must be simulated and communicated in all circumstances.

8 8Any condition can be evidently expressed under one of these forms; for example, is obviously the same as with . We built a pre‐processor to transform all conditions under these canonical forms.

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