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Implied Dynamics in the SV-LMM Framework

In: Asymptotic Chaos Expansions in Finance

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  • David Nicolay

Abstract

In this chapter we apply the generic term structure framework defined in Chap. 5 to the particular case of interest rates options, within a universal Stochastic Volatility Libor Market Model (SV-LMM). As in Chap. 6 , our main focus is to solve the direct problem (generating the smile’s shape and dynamics from the model specification) up to the first layer (which includes the smile’s curvature and slope). We target some of the most liquid option types, namely caplets, swaptions and bond options. For technical reasons we exploit a model re-parametrisation via the rebased Zero Coupons, which allows us to recycle some of the SV-HJM results of Chap. 6 . Likewise, in order to manage swaptions we use the basket results of Sect. 3.5 . This enables us, in particular, to compute the systematic error of the usual frozen weights approximation.

Suggested Citation

  • David Nicolay, 2014. "Implied Dynamics in the SV-LMM Framework," Springer Finance, in: Asymptotic Chaos Expansions in Finance, edition 127, chapter 0, pages 367-419, Springer.
    • Handle: RePEc:spr:sprfcp:978-1-4471-6506-4_7
    DOI: 10.1007/978-1-4471-6506-4_7
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