A Primer on Valuing Simple Risk-Free Bonds

Abstract

Options on stock indexes, currencies, and futures all have something in common: the holder of the option does not get the same thing that the holder of the underlying asset gets. This affects the value of the option. In this note, we cover the valuation implications of this for options on stock indexes, currencies, and futures.

Excerpt

UVA-F-1443

Rev. Sept. 27, 2012

A PRIMER ON VALUING SIMPLE RISK-FREE BONDS

For people ignorant of fine-art values, participation in the art market at an auction house such as Sotheby's is likely to be a dangerous affair. The inability to distinguish a $ 100 piece from a $ 100,000 piece creates a certain level of market peril for either the buyer or the seller. In the market for capital, buyers and sellers of money come together to trade financial contracts of every shape, sort, and size. As in the market for fine art, understanding the principles of capital-market-price determination is critical for effective market participation. In this note, we explore the first principles of financial-contract pricing.

Because the principles used to value simple contracts also apply to complicated contracts, we begin with the simplest of financial contracts—the one-period risk-free bond contract. Although debt contracts go by many names, to simplify the discussion in this note we will use the term “bond” to denote any market-traded debt contract. See Exhibit 1 for a review of common bond terminology.

Investment Decision 1

Suppose you are offered the following bond contract: your local government promises to pay $ 1,000 plus 7% interest in one year. If you believe the government to be creditworthy, what are you willing to pay today for a promise of $ 1,070 in one year?

One good place to start thinking about the value of such a contract is the discounted-cash-flow (DCF) model. The DCF model asserts that the economic value of a financial contract is equal to the sum of all future cash flows discounted at the appropriate discount rate. Applying the DCF model to debt contracts gives the pricing equation

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Keywords: futures, stock index, currency, valuation