Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2019 | OriginalPaper | Chapter

5. Extending SABR Model to Negative Rates

Authors : Alexandre Antonov, Michael Konikov, Michael Spector

Published in: Modern SABR Analytics

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In the low or negative interest rates environment, extending option models to negative rates becomes important. This chapter describes two such extensions of the SABR model: free SABR and mixture SABR. For free SABR, an exact formula is derived for option prices in the case of zero correlation between the rate and its volatility. For nonzero correlation, a mapping procedure onto a mimicking zero-correlation model is applied. Mixture SABR always has a closed-form solution for option prices, and has additional degrees of freedom allowing it to calibrate to a broader set of trades, e.g a set of swaptions and a CMS payment. Analytical results for free and mixture SABR models are compared with the Monte Carlo simulation ones.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Classic SABR Model: Heat Kernel Expansion and Projection on Solvable Models
next chapter Conclusion
Footnotes
1
Note that the SABR approximation [39] based on the Heat-Kernel expansion cannot be applied to the free SABR because it does not take into account the boundary conditions.
 
2
To avoid potential problems related with a non-smooth behavior around \(F_0=10\, K\) we suggest \( \max (K, 0.1F) \approx 0.1F + \frac{1}{2}\left( K - 0.1F + \sqrt{(K-0.1F)^2+\varepsilon ^2} \right) \) for small parameter \(\varepsilon \) around 1bp.
 
3
We will write here \(\alpha \) instead of \(v_0\).
 
4
The normal model component can be obviously written via zero beta Free SABR form, \(\mathscr {O}_{N}(T,\, K;\,\alpha _2,\rho _2, \gamma _2)= \mathscr {O}_{F}(T,\, K;\,\alpha _2, 0, \rho _2, \gamma _2)\).
 
5
As far as the SABR is mainly the strike interpolation (not a term-structure model) its process-level dynamic properties, i.e. conditional expectation \(\mathbb {E}{[(F_T-K)^+\;|\;F_t=f]}\), are irrelevant.
 
Metadata
Title
Extending SABR Model to Negative Rates
Authors
Alexandre Antonov
Michael Konikov
Michael Spector
Copyright Year
2019
Book
Modern SABR Analytics

Print ISBN: 978-3-030-10655-3

Electronic ISBN: 978-3-030-10656-0

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-10656-0_5