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Risk Neutral Pricing and Financial Mathematics: A Primer by John L. Teall, Peter M. Knopf

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Chapter 4

Continuous Time and State Models

This chapter is primarily concerned with financial instruments in continuous time under certainty. Fixed income instruments are valued in continuous time and forward contracts are introduced. The pricing of a zero-coupon bond, subject to a continuous deterministic short-term interest rate, is obtained. This relatively simple derivation captures some of the important elements in more sophisticated stochastic bond pricing techniques presented later in the book. Discussions of ordinary differential equations and how to solve separable differential equations are applied under scenarios of certainty. There are a number of illustrations involving annuities and interest bearing securities, showing how to construct ...

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