Introduction

Welcome to the module on “Pricing Conventions, Discounting, and Arbitrage”. In this module, we will delve into essential concepts that form the foundation of fixed income securities’ pricing. Understanding these principles is crucial for anyone involved in finance, as it lays the groundwork for pricing various financial instruments, especially bonds. Let’s start by providing an overview of the key topics we will cover in this module.

Module Objectives

In this module, we will explore pricing conventions, discounting, and the role of arbitrage in financial markets. These concepts are fundamental to the accurate valuation of fixed income securities, such as bonds. Here are the main objectives we aim to achieve in this module:

1) Defining Discount Factors: We will begin by understanding the concept of discount factors. Discount factors play a critical role in computing present and future values of cash flows. We will explore how to calculate them and their significance in bond pricing.

2) The Law of One Price: The “Law of One Price” is a fundamental principle in finance. It states that identical assets should have the same price. We’ll explain this law using arbitrage arguments and demonstrate how it applies to bond pricing.

3) Arbitrage Opportunities: Arbitrage is the process of taking advantage of price discrepancies in financial markets. We will identify situations in fixed income securities where arbitrage opportunities exist due to certain cash flows.

4) Components of US Treasury Bonds: Understanding the components of US Treasury bonds is essential for bond pricing. We’ll break down the structure of a typical US Treasury coupon bond and compare it to Treasury STRIPS (Separate Trading of Registered Interest and Principal of Securities).

5) Constructing Replicating Portfolios: To match the cash flows of a given fixed-income security, we need to construct replicating portfolios. We’ll explore how to create portfolios using multiple fixed income securities and their role in risk management.

6) Clean and Dirty Bond Pricing: Bond pricing involves two crucial terms: “clean” and “dirty” pricing. We’ll differentiate between these two pricing methods and explain the implications of accrued interest when pricing bonds.

7) Day-Count Conventions: Different markets and regions use various day-count conventions when calculating interest and accrued interest. We’ll describe some common conventions and discuss their importance in bond pricing.

By the end of this module, you’ll have a solid understanding of the core principles that underpin the pricing of fixed income securities. These concepts are invaluable for financial analysts, risk managers, and anyone involved in investment decision-making.