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2018 | OriginalPaper | Buchkapitel

Hedging Asian Bond Options with Malliavin Calculus Under 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

In this chapter we use some recent hedging results for bond options, obtained with Malliavin calculus in the context of the stochastic string framework, to hedge different types of Asian options. In all the cases, we show that the hedging portfolio has no bank account part.

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Vorheriges Kapitel Sensitivity Analysis and Hedging in Stochastic String Models

Nächstes Kapitel Stochastic Recovery Rate: Impact of Pricing Measure’s Choice and Financial Consequences on Single-Name Products

As in the case of standard options, Asian options can be issued in American or European style. In this chapter we will focus on the European case.

For a description, valuation, and hedging of Australian options, see Moreno and Navas (2008).

We will not need any property of Z(t, x) in this chapter. For a detailed study of the stochastic string process and the probabilistic framework, we refer the reader to Bueno-Guerrero et al. (2015a).

We refer the reader to Nualart (2006) for the general theory of Malliavin Calculus and to Bueno-Guerrero et al. (2017) for the specific issues related to stochastic strings.

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Bueno-Guerrero, A., Moreno, M., & Navas, J. F. (2015a). Stochastic string models with continuous semimartingales. Physica A: Statistical Mechanics and its Applications, 433, 229–246.CrossRef

Bueno-Guerrero, A., Moreno, M., & Navas, J.F. (2015b). Bond market completeness under stochastic strings with distribution-valued strategies. Working paper available online at http://ssrn.com/abstract=2598403.

Bueno-Guerrero, A., Moreno, M., & Navas, J.F. (2017). Malliavin calculus for stochastic strings with applications to barrier options and optimal portfolios. Working paper available online at https://ssrn.com/abstract=2935579.

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Moreno, M., & Navas, J. F. (2008). Australian options. Australian Journal of Management, 33(1), 69–93.CrossRef

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Titel: Hedging Asian Bond Options with Malliavin Calculus Under 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_10