Modern Computational Finance

Scripting for Derivatives and xVA

Antoine Savine, Jesper Andreasen

• Éditeur: Wiley
• Année: 2021
• ISBN:
  9781119540793
• Édition: 1
• Sujet: Matemáticas
• Sous-sujet: Matemática aplicada

An incisive and essentialguide to building a complete system for derivative scripting

InVolume 2 of Modern Computational Finance Scripting for Derivatives and xVA, quantitative finance expertsand practitioners Drs. Antoine Savine and Jesper Andreasen deliver an indispensable and insightfulroadmap to the interrogation, aggregation, and manipulation of cash-flows in a variety of ways. The book demonstrates how to facilitate portfolio-wide risk assessment andregulatory calculations (like xVA).

Complete with a professional scripting library written in modern C++, this stand-alone volumewalks readers through the construction of a comprehensiverisk and valuationtool.Thisessentialbook also offers:

• Effective strategies for improving scripting libraries, from basic examples—likesupport for dates and vectors—to advanced improvements, including American Monte Carlo techniques
• Exploration of the concepts of fuzzy logic and risk sensitivities, including support for smoothing and condition domains
• Discussion of the application of scripting to xVA, complete with a full treatment of branching

Perfect for quantitative analysts, risk professionals, system developers, derivatives traders, and financial analysts, Modern Computational Finance Scripting for Derivatives and xVA: Volume 2is also amust-read resourcefor students and teachers inmaster'sand PhD finance programs.

PART I
A Scripting Library in C++

Introduction

This part leads readers through the development steps of the scripting library provided in our source repository.

A transaction consists of a number of events occurring on given dates in the future. This is where a payment or coupon is fixed, a discrete barrier is monitored, or an exercise takes place. This is also where a path‐dependency is updated with reference to the simulated variables on that future date.¹ Future dates when such events take place are called event dates.

As an illustration, we consider a simplified version of the popular autocallable transaction. It pays a high coupon (say 10%) if some index (say S&P500) increased during the first year of its life. In this case, it pays the notional redemption together with the coupon of 10% and terminates at the end of year 1. Otherwise, it may still deliver a 20% coupon (10% per annum) at the end of year 2 provided the index overall increased over the two years. In this case, it repays the notional together with the 20% coupon and terminates at the end of year 2. If not, it is given a last chance on year 3, provided the underlying index increased over the three years. If this is the case, the investor receives the redemption + 30% at the end of year 3. If not, only 50% of the notional is repaid. It is easy to see that the investor implicitly sells a (somewhat exotic) option on what may appear as a low probability event (index decreasing over one, two, and three years) in exchange for a high coupon in a low‐yield environment, which explains the success of this structure.² This product may be scripted as follows (say today is 1 June 2020)³:

---

01Jun2020	vRef=spot() vAlive=1
01Jun2021	if spot() > vRef then prd=110 vAlive=0 endIf
01Jun2022	if spot() > vRef then if vAlive=1 then prd=120 endIf vAlive=0 endIf
01Jun2023	if vAlive=1 then if spot() > vRef then prd=130 else prd=50 endIf endIf

---

We have four events on four event dates:

1. Today, we set the reference to the current spot level and initialize the alive status to 1.
2. Year 1, we check whether the spot increased, in which case we pay redemption + 10% and die.
3. Year 2, we check that the spot overall increased over two years. In this case, provided we survived year 1, we pay redemption + 20% and die.
4. Year 3, provided we survived the first two, we check if the spot overall increased. In this case we pay redemption + 30%. If not, we repay 50% of the notional.

We see that our language must at the very minimum support numbers, arithmetic operations, and conditional statements. We know we also need some mathematical functions like

or

and some financial functions such as a multi‐argument

and

. Critically, we must be able to read, write, and compare variables and access the simulated market with a spot() keyword that references the fixing of the underlying asset on the corresponding event date. This is a simple language, similar to Python, that supports only the constructs necessary for the description of financial cash‐flows, for which it provides some specific keywords.

The language considers as a variable anything that starts with a letter and is not otherwise a keyword. We used the variables

,

, and

in our example. Evidently, ancillary variable names don't have to start with the letter V; this is only for clarity.

Products are variables. The language makes no difference between products and ancilla...