Libor Market Model with Stochastic Volatilities

Jianwei Zhu ()
Additional contact information
Jianwei Zhu: Lucht Probst Associates

Chapter Chapter 11 in Applications of Fourier Transform to Smile Modeling, 2010, pp 273-317 from Springer

Abstract: Abstract In this chapter we address the smile modeling with stochastic volatility within the setup of Libor Market Model (LMM). Meanwhile, LMM is a standard pricing model for interest rate derivatives. Since LMM is based on a series of lognormal dynamics, the methods for building up the smile models, particularly with stochastic volatilities, can be adopted from the previous chapters. After a brief introduction to interest derivative markets in Section 11.1, we review in Section 11.2 a standard LMM with which we may gain the first impression of the high dimensionality and the large dependence structure of LMM. Next in Section 11.3, swaption valuation and Swap Market Model (SMM) are explained. The consistent valuation of swaptions and swap-rate linked products (CMS products) with LMM remains a challenge in quantitative finance. The key section in this chapter is Section 11.4 where five stochastic volatility LMMs are discussed. All of these five models apply characteristic functions or moment-generating functions for pricing caps and swaptions to different extent. While CFs do not find significant applications in the models of Andersen and Brotherton-Ratcliffe (2001), and Piterbarg (2003), the models of Zhang and Wu (2006), Zhu (2007) as well as Belomestny, Matthew and Schoenmakers (2007) have used CFs extensively and consequently to arrive at the closed-form pricing formulas for caplets and swaptions. The last section provides some conclusive remarks.

Keywords: Stochastic Volatility; Implied Volatility; Stochastic Volatility Model; Price Formula; Local Volatility (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-642-01808-4_11

Ordering information: This item can be ordered from
http://www.springer.com/9783642018084

DOI: 10.1007/978-3-642-01808-4_11

Access Statistics for this chapter

More chapters in Springer Finance from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().