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CHAPTER 2:  Bond Prices and Interest Rates

2.1 Introduction

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any of the principles for valuing fixed-income securities depend on arbitrage arguments. For there to be no arbitrage, it must be the case that no investor can receive a positive (risk-free) return without investing any money. In this chapter, we will identify the arbitrage-free value of bonds. The argument is first developed in Topic 2.2, Arbitrage-Free Prices: Single-Period Cases. In Topic 2.3, this is extended to Arbitrage-Free Prices: Multi-Period Case.

Generally, when fixed-income securities are traded in the marketplace, the buyer pays the price in cash and receives a legal claim to the future cash flows from the security. However, it is possible to trade fixed-income securities where this is not the case. That is, no cash is exchanged at the time of the trade. In this type of trade, a forward contract is entered into where both parties are obligated to settle at some time in the future for a price agreed upon now. Therefore, in the case of forward contracts, investors are concerned not only with the arbitrage-free value of securities today, but also with the arbitrage-free value of the position at some time in the future. In Topic 2.4, Future Value, we consider develop this concept further.