Abstract
In this chapter, we discuss the classic SABR model. We review invariant forms of the backward and forward Kolmogorov equations, applying then the heat kernel asymptotic expansion to the SABR model. We improve the approximate results for SABR option pricing, combining asymptotic expansion close to ATM with mapping procedure (Antonov and Misirpashaev in Projection on a quadratic model by asymptotic expansion with an application to LMM swaption, SSRN paper, 2009 [7]) onto the exactly solvable zero correlation SABR.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We used the boundary properties of the density for \(v\rightarrow 0\) to zero the two last terms.
- 2.
The element of probability is defined as \(\mathrm{d}P=p(q, v)\,\mathrm{d}q\,\mathrm{d}v\).
- 3.
Presented here as O(t).
- 4.
Here, we explicitly set \(\tilde{\beta }=\beta \).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 The Author(s), under exclusive licence to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Antonov, A., Konikov, M., Spector, M. (2019). Classic SABR Model: Heat Kernel Expansion and Projection on Solvable Models. In: Modern SABR Analytics . SpringerBriefs in Quantitative Finance. Springer, Cham. https://doi.org/10.1007/978-3-030-10656-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-10656-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10655-3
Online ISBN: 978-3-030-10656-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)