Abstract
The HJM framework is well-established in academia and practise to price and hedge interest rate derivatives. Imposing a special time dependent structure on the forward rate volatility function leads directly to the class of Cheyette models. In contrast to the general HJM model, the dynamics are Markovian, which allows the application of standard econometric valuation concepts. Finally, we distinguish this approach from alternative settings discussed in literature.
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Notes
- 1.
The Radon-Nikodym derivative is given by
$$\frac{\mathrm{d}\widetilde{\mathbb{Q}}} {\mathrm{d}\mathbb{Q}} =\exp \Big{(} -\displaystyle\int \limits _{0}^{t}\frac{1} {2}{q}^{2}(s)\mathrm{d}s -\displaystyle\int \limits _{ 0}^{t}q(s)\mathrm{d}W(s)\Big{)}.$$We assume \({\mathbb{E}}^{\mathbb{Q}}\Big{[}\exp \Big{(} -\int \limits _{0}^{t}\frac{1} {2}{q}^{2}(s)\mathrm{d}s -\int \limits _{0}^{t}q(s)\mathrm{d}W(s)\Big{)}\Big{]} = 1\) to ensure that the Radon-Nikodyn derivative is a martingale.
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Beyna, I. (2013). The Cheyette Model Class. In: Interest Rate Derivatives. Lecture Notes in Economics and Mathematical Systems, vol 666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34925-6_2
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DOI: https://doi.org/10.1007/978-3-642-34925-6_2
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