Abstract
In this chapter we apply the techniques developed in the previous chapters to the fast-growing fixed-income securities market. We mainly focus on the continuous-time model (since the available tools from stochastic calculus allow an elegant presentation) and comment of the discrete-time analogue ([132] gives a splendid account of discrete-time models). As we want to develop a relative pricing theory, based on the no-arbitrage assumption, we will assume prices of some underlying objects as given. In the present context we take zero-coupon bonds as the building blocks of our theory. In doing so we face the additional modelling restriction that the value of a zero-coupon bond at time of maturity is predetermined (= 1). Furthermore, since the entirety of fixed-income securities gives rise to the term-structure of interest rates (sometimes called the yield curve), which describes the relationship between the yield-to-maturity and the maturity of a given fixed-income security, we face the further task of calibrating our model to a whole continuum of initial values (and not just to a vector of prices). A first attempt at explaining the behaviour of the yield curve is in terms of a continuum of spot rates of maturities between τ and T, where τ is the shortest (instantaneous) lending/borrowing period, and T the longest maturity of interest. We model these rates as correlated stochastic variables with the degree of correlation decreasing in terms of the difference in maturity.
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© 1998 Springer-Verlag London
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Bingham, N.H., Kiesel, R. (1998). Interest Rate Theory. In: Risk-Neutral Valuation. Springer Finance. Springer, London. https://doi.org/10.1007/978-1-4471-3619-4_8
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DOI: https://doi.org/10.1007/978-1-4471-3619-4_8
Publisher Name: Springer, London
Print ISBN: 978-1-4471-3621-7
Online ISBN: 978-1-4471-3619-4
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