SABR symmetry

Typical implementations of the stochastic alpha beta rho model involve asymptotic expansion approximations, which can generate inaccurate prices for long-dated options. But directly solving a pricing partial differential equation incurs high computational costs. Hyukjae Park shows how the model’s symmetry can be harnessed to reduce the complexity of the calculation and improve accuracy over expansions

Pricing options using partial differential equations (PDEs) suffers from the so-called curse of dimensionality: as the number of variables involved increases, the complexity and the computational costs do so exponentially. So, if a multi-factor model is to be used, one that has analytic pricing formulas available is always preferred. This is one of the reasons why the stochastic alpha beta rho (SABR) model (Hagan et al, 2002, Hagan, Lesniewski & Woodward, 2005, Antonov & Spector, 2012) is