Classic SABR Model: Heat Kernel Expansion and Projection on Solvable Models
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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 ) onto the exactly solvable zero correlation SABR.