# CHAPTER 3

# Vanilla Instruments

## 3.1 DEFINITIONS

Financial assets may be roughly classified, according to the payoff, into three categories:

- Fixed income
- Derivatives
- Variable income.

The financial instruments presented in this book relate to assets with:

- predetermined cash flow payment dates
- revenues that can be modelized.

This excludes variable-income instruments, such as equities that bear random coupons: stocks will solely be accounted for as underlying assets involved in equity-related derivatives.

## 3.2 FIXED INCOME

For this class of assets, the calculation of the fair value is straightforward. Since cash flows and payment dates are predetermined at inception, the **present value** of the future flows is easily obtained, provided that a **relevant yield curve** is available for the calculation of the **discount factors**.

Let us denote by *df*_{i} these discount factors: the theoretical value of an asset paying *n* coupons *c*_{i}, i = 1…*n* writes:

It is common to figure payments on a cash flow chart: each flow is represented by an arrow pointing either to a time line (inflows) or out of it (outflows). Practically, it implies that this kind of chart is drawn *from the point of view of one counterparty*. As an example, the *n* coupons received by an investor in a bond can be figured as below:

In a fair ...