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Term Structure, Market Expectations of the Short Rate, and Expected Inflation Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Hedging Asian Bond Options with Malliavin Calculus Under Stochastic String Models

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

Published in: New Methods in Fixed Income Modeling

Publisher: 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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previous chapter Sensitivity Analysis and Hedging in Stochastic String Models
next chapter Stochastic Recovery Rate: Impact of Pricing Measure’s Choice and Financial Consequences on Single-Name Products
Footnotes
1
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.
 
2
For a description, valuation, and hedging of Australian options, see Moreno and Navas (2008).
 
3
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).
 
4
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.
 
Literature
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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
Curran, M. (1994). Valuing Asian and Portfolio options by conditioning on the geometric mean price. Management Science, 40(12), 1705–1711.CrossRef
Dufresne, D. (2005). Bessel Processes and Asian Options. In Breton, M., & Ben-Ameur, H. (Eds.) Numerical methods in finance (pp. 35–57). Springer, Berlin.
Geman, H., & Yor, M. (1993). Bessel processes, Asian options and perpetuities. Mathematical Finance, 3(4), 349–375.CrossRef
Jacques, M. (1996). On the hedging Portfolio of Asian options. Astin Bulletin, 26(2), 165–183.CrossRef
Kemna, A. G. Z., & Vorst, A. C. F. (1990). A pricing method for options based on an average asset value. Journal of Banking & Finance, 14, 113–129.CrossRef
Landa-Fernández, M., & Moreno, M. (2017). Pricing and hedging of fixed income Asian and Australian options: An approach based on seasonal models. Working paper available upon request.
Moreno, M., & Navas, J. F. (2008). Australian options. Australian Journal of Management, 33(1), 69–93.CrossRef
Moreno, M., Novales, A., & Platania, F. (2018). A term structure representation with cyclical mean reversion. Economic Modelling, 72, 140–150.
Moreno, M., & Platania, F. (2015). A cyclical square-root model for the term structure of interest rates. European Journal of Operational Research, 241, 109–121.CrossRef
Nualart, D. (2006). The Malliavin calculus and related topics (2nd ed.). Springer, Berlin.
Roman, J.R.M. (2010). Curran model for pricing asian options. New York City: Mimeo.
Santa-Clara, P., & Sornette, D. (2001). The dynamics of the forward interest rate curve with stochastic string shocks. Review of Financial Studies, 14, 149–185.CrossRef
Metadata
Title
Hedging Asian Bond Options with Malliavin Calculus Under Stochastic String Models
Authors
Alberto Bueno-Guerrero
Manuel Moreno
Javier F. Navas
Copyright Year
2018
Book
New Methods in Fixed Income Modeling

Print ISBN: 978-3-319-95284-0

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

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-95285-7_10