Efficient valuation method for the SABR model

TL;DR

This paper introduces an efficient valuation method for the SABR model that leverages its scaling symmetry to reduce computational complexity, enabling faster pricing of European options and related payoffs.

Contribution

The paper presents a novel approach using symmetry to simplify SABR option pricing, reducing dimensionality and enabling the valuation of multiple related options efficiently.

Findings

Method reduces PDE complexity from 1+2 to N_V uncoupled 1+1 PDEs.

Prices of related options can be obtained from a single valuation.

Results compare favorably with Monte Carlo simulations.

Abstract

In this article, we show how the scaling symmetry of the SABR model can be utilized to efficiently price European options. For special kinds of payoffs, the complexity of the problem is reduced by one dimension. For more generic payoffs, instead of solving the 1+2 dimensional SABR PDE, it is sufficient to solve $N_V$ uncoupled 1+1 dimensional PDE's, where $N_V$ is the number of points used to discretize one dimension. Furthermore, the symmetry argument enables us to obtain prices of multiple options, whose payoffs are related to each other by convolutions, by valuing one of them. The results of the method are compared with the Monte Carlo simulation.