One dollar today is better than one dollar tomorrow and one dollar tomorrow is certainly better than one dollar in one year. In other words, time is money. But what should be paid today or tomorrow or, more generally at time t, for a guaranteed cash payment of one dollar at a time T, T ≥ t, in the far future? This is one of the questions which will be answered in the interest-rate market. Up to today this market is one of the most important financial markets trading instruments such as coupon bonds, forward-rate agreements on coupon bonds, interest-rate futures and swaps as well as standard or exotic interest-rate options. Because the interest-rate market is a specific financial market, we will apply the results of Chapter 3 to embed it in the general framework of Section 3.1. We start by defining the general interest-rate market model in Section 4.1. No-arbitrage and completeness conditions in the interest-rate market model are given in Section 4.2, while Section 4.3 deals with the pricing of interest-rate-related contingent claims. Because there are infinitely many possible maturity times when we could get an invested amount of money back from a bank or the market, there are also infinitely many interest rates representing the possible investment horizons and changing their values over time. It has therefore been and still is a specific challenge to find factors which sufficiently well describe the behaviour of all interest rates over time. In Section 4.4 we discuss one of the most general platforms for pricing interest-rate derivatives, the Heath-Jarrow-Morton framework. It deals with an infinite number of so-called forward short rates, specified today for an infinitely short time-period at some future point in time, to describe the movement of interest rates.
KeywordsFiltration Hull Radon Dition Volatility
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