By Jeroen F. J. De Munnik
The elevated volatility of rates of interest in the course of contemporary years and the corresponding advent of various rate of interest by-product securities like bond concepts, futures and embedded ideas in mortgages, tension the necessity for a entire monetary idea to figure out values of mounted source of revenue tools and spinoff securities regularly.
This ebook offers: an in depth review and category of the several techniques to price rate of interest based securities; a comparability of the numerical methods to worth advanced securities; and an empirical exam for the Dutch mounted source of revenue marketplace of a few famous rate of interest types which demonstrates fresh advancements to explain rate of interest activities with regards to contingent declare valuation.
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Extra resources for The valuation of interest rate derivative securities, 1st Edition
Referring to the abovementioned volatility of the yield-to-maturity implied by their bond price process, this result is hardly surprising. This chapter develops a model incorporating both the volatility specification of the Schaefer and Schwartz model and the “drift-to-face-value” effect of the model of Ball and Torous. Starting with a specification of the stochastic process of the yield-to-maturity of a bond with constant coefficients, the corresponding stochastic process of the bond prices is easily obtained.
Because the underlying assets of the contingent claim are in fact derivative securities, too, the unique arbitrage-free prices of these securities must also be derived. Without a detailed description of the probability space, it will be assumed for the moment that sufficient conditions are fulfilled to ensure that these unique prices exist. 2) It is obvious that , again, denotes the expectation operator under the measure . The last step is the actual calculation of the value of the contingent claim.
14 In Ball and Torous (1983, Section V), the volatility parameters are estimated using logarithmic bond returns. In addition, it is assumed that the mean logarithmic bond return at some time ti, i=1, …, N is equal to the expected return at time t0. Although the proposed estimators are unbiased if the time interval between different observations approaches zero, the estimation procedure derived above is preferable, as no additional assumptions about the observed sample of bond prices are necessary.