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Classic SABR Model: Heat Kernel Expansion and Projection on Solvable Models

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Part of the SpringerBriefs in Quantitative Finance book series (BRIEFFINANCE)

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.

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© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Standard Chartered BankLondonUK
  2. 2.Numerix LLCNew YorkUSA

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