Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

3

Spot instruments

This chapter deals with spot instruments other than stocks: given the large amount of quantitative material about stocks they are treated separately, in the next chapter.

3.1 SHORT-TERM RATES

With respect to quantitative aspects and calculations, there is almost nothing to add for short-term rates instruments beyond what we considered in Chapter 1 (among others, the calculations relative to present and future values). But we should mention that some of the short-term instruments are generally traded in prices, on a “discount basis”, namely in PV prices (e.g., Treasury bills, banker's acceptances and commercial paper), while others are traded in rates, “on a yield basis”, that is, in interest percentage (i.e., repo rates, certificates of deposits, bank deposits, interbank rates, etc.).

Short-Term Rates Traded on a Discount Basis

For US T-bills, quoted in PV prices corresponding to a FV as par value of 100 at maturity, to compute the corresponding yield z the US Treasury uses a formula slightly different from the conventional Eq. 1.2 of Chapter 1, as follows:

on an ACT/360 basis. Let us take, for example, the 180-days US T-bill as traded on 01/04/08, @ 98.39: for t = 180/360 = 0.5, it corresponds to a yield of

Using Eq. 1.2,

we would have obtained

Short-Term Rates ...