Volatility Dynamics in a Term Structure

  • David NicolayEmail author
Part of the Springer Finance book series (FINANCE)


In this chapter we start by considering a generalised framework, encompassing in particular the Caplets and Swaptions markets, but potentially applicable to other products. This is made possible because these payoffs, as well as the martingale method used to price them, are very similar. Hence the main requirement is to find the correct numeraire and pricing measure. The difference with the single underlying setting of Part I is that we are now dealing with a collection of underlyings, for instance the forward Libor or forward par swap rates. Each of these underlying has its own numeraire, is martingale under the associated measure, and defines a specific strike-continuum of vanilla options. Hence we end up with associated collections of numeraires, measures and options. All these families are parametrised by their own list of maturities, which we will naturally extend to a common maturity continuum. We end up naturally with a term structure (TS) framework, and in solving the direct and indirect problems we will point to the structural difference simpler single-underlying environment of Part I.


Risk Premia Term Structure Implied Volatility Forward Rate Stochastic Volatility Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    El Karoui, N., Geman, H., Rochet, J.-C.: Changes of numéraire, changes of probability measure and option pricing. J. Appl. Probab. 32(2), 443–458 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Brigo, D., Mercurio, F.: Interest Rate Models: Theory and Practice, 2nd edn. Springer Finance, Heidelberg (2006)Google Scholar
  3. 3.
    Hagan, P.S., Kumar, D., Lesniewski, A.S., Woodward, D.E.: Managing smile risk. Wilmott Mag. 1, 84–108 (2002)Google Scholar
  4. 4.
    Schoenmakers, J.: Robust libor modelling and pricing of derivative products. In: Financial Mathematics. Chapman & Hall, London (2005)Google Scholar
  5. 5.
    Piterbarg, V.V.: Stochastic volatility model with time-dependent skew. Appl. Math. Financ. 12, 147–185 (2005)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.LondonUK

Personalised recommendations