Application of Effective Markovian Projection to SABR and Heston Models

Bagraim, Jacques

Application of Effective Markovian Projection to SABR and Heston Models

Thesis / Dissertation

2023

Abstract

Model flexibility is often at odds with tractable pricing, and models with tractable pricing often lack flexibility. This poses an issue when calibrating a model to market data where tractability and flexibility are both required. We investigate an approach that allows one model to be projected onto another, potentially allowing for a flexible model to be represented by a tractable one. Here, Effective Markovian Projection is used to obtain equivalent Heston model parameters from a range of SABR models with different skew parameters using two distinct point-matching algorithms. The implied parameters are used to price European claims under a variety of schemes in order to outline the efficacy in this context. We see that this technique is accurate when the underlying probability densities of both models match closely, i.e., when the SABR skew parameter approaches unity, as is seen by comparing prices of claims using Classic Markovian Projection where the underlying SABR processes share the same density. PDE and perturbation SABR prices match closely while Heston characteristic function prices become unstable at lower skew parameters and far in-the-money and out-the-money values of the strike. Lastly, a potential improvement to this application involving error-correction terms is proposed for further application.

Keywords

Mathematical Finance

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