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2018 | OriginalPaper | Buchkapitel

Sensitivity Analysis and Hedging in Stochastic String Models

verfasst von : Alberto Bueno-Guerrero, Manuel Moreno, Javier F. Navas

Erschienen in: New Methods in Fixed Income Modeling

Verlag: Springer International Publishing

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Abstract

We analyze certain results on the stochastic string modeling of the term structure of interest rates and we apply them to study the sensitivities and the hedging of options with payoff functions homogeneous of degree one. Under the same framework, we use an exact multi-factor extension of Jamshidian (1989) to find the sensitivities for swaptions and we prove that it cannot be applied to captions. We present a new approximate result for pricing options on coupon bonds based on the Fenton-Wilkinson method and we show that it generalizes the fast coupon bond option pricing proposed in Munk (1999). This result can be easily applied to the approximate valuation of swaptions and captions.

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For the probabilistic setting and assumptions of the stochastic string framework, we refer the reader to Bueno-Guerrero et al. (2015a).

We will return to this problem in the next section.

Usually this assumption is satisfied with constant \( \varPhi_{i} ,\quad i = 0, 1, \ldots , n. \)

We state the result for calls as the put case can be obtained in a similar way.

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Titel: Sensitivity Analysis and Hedging in Stochastic String Models
verfasst von: Alberto Bueno-Guerrero
Manuel Moreno
Javier F. Navas
Verlag: Springer International Publishing
Buch: New Methods in Fixed Income Modeling
Print ISBN: 978-3-319-95284-0

Electronic ISBN: 978-3-319-95285-7

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-95285-7_9