Introduction

The Law of One Price is a cornerstone concept in finance, emphasizing the idea that identical assets should have the same price in a competitive and efficient market. In this chapter, we will delve into this principle, understand how it is explained through arbitrage arguments, and see how it plays a vital role in bond pricing.

Law of One Price

The Law of One Price asserts that identical goods or assets, when freely traded and devoid of transaction costs, should have the same price. If two assets with identical characteristics are priced differently, an arbitrage opportunity arises. An arbitrageur can profit by buying the underpriced asset and simultaneously selling the overpriced one. This process continues until prices equalize.

Example: Let’s illustrate the Law of One Price with a simple example. Suppose we have a bond issued by Company A, and an identical bond issued by Company B. Both bonds have the same face value of USD 1,000, the same maturity date, and the same coupon rate of 5%. However, Company A’s bond is priced at $950, while Company B’s bond is priced at $980.

According to the Law of One Price, these bonds should be priced the same. An arbitrageur could buy the cheaper bond from Company A for USD 950 and simultaneously sell the more expensive bond from Company B for USD 980. By doing so, they make an instant profit of USD 30 (980 - 950).

Application to Bond Pricing

In the context of bond pricing, the Law of One Price means that two bonds with the same cash flows should have the same price. Cash flows from a bond include coupon payments and the face value payment at maturity.

For example, if we have two bonds with identical characteristics - the same face value, coupon rate, and maturity date- they should be priced the same. If they are not, investors would exploit the price difference through arbitrage, quickly equalizing the prices.