Real Valued Affine Diffusions

  • Aurélien Alfonsi
Part of the Bocconi & Springer Series book series (BS, volume 6)


This chapter gives a first contact with general affine diffusions by presenting the ones that take real values. We will see that these diffusions are basically of two types, and are either a Ornstein-Uhlenbeck process or a Cox-Ingersoll-Ross process. Thus, the two first sections of this chapter study these processes and present their main properties. The third section defines what are affine diffusions and characterize them by the mean of the infinitesimal generator. The last section is devoted to the application of these processes for the interest rate modelling. A quick introduction is given on the financial framework, and we present the main pricing formulas that have made the use of these processes popular.


Interest Rate Stochastic Differential Equation Arbitrage Opportunity Zero Coupon Bond Coupon Bond 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Aurélien Alfonsi
    • 1
  1. 1.CERMICSEcole Nationale des Ponts et ChausséesChamps-sur-MarneFrance

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