Gavin wants to dig deep into pricing theory, so he decides to work out an application of

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Gavin wants to dig deep into pricing theory, so he decides to work out an application of Eq. (16.11). He suggests to himself that a simple model of interest rates in the risk-neutral world might be

\[\mathrm{d} r=\sigma \mathrm{d} \hat{z}\]

where \(\hat{z}\) is standard Brownian motion and where \(r(0)=r_{0}\). He is working out a formula for the value of a zero-coupon bond that pays \(\$ 1\) at time \(T\), based on Equation (16.11), without using the Black-Scholes equation. Can you? Compare with Example 16.11.


Equation

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Investment Science

ISBN: 9780199740086

2nd Edition

Authors: David G. Luenberger

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