Efficient and accurate simulation of the stochastic-alpha-beta-rho model

TL;DR

This paper introduces a new simulation method for the SABR model that improves efficiency and accuracy by using novel approximations and exact sampling techniques, avoiding complex inversion algorithms.

Contribution

The paper presents a novel simulation scheme for the SABR model employing moment-matched approximations and exact sampling, enhancing efficiency and eliminating the need for Laplace inversion.

Findings

The proposed scheme is highly efficient and accurate.

It preserves the martingale condition and precludes arbitrage.

Numerical tests confirm reliability and improved performance.

Abstract

We propose an efficient, accurate and reliable simulation scheme for the stochastic-alpha-beta-rho (SABR) model. The two challenges of the SABR simulation lie in sampling (i) integrated variance conditional on terminal volatility and (ii) terminal forward price conditional on terminal volatility and integrated variance. For the first sampling procedure, we sample the conditional integrated variance using the moment-matched shifted lognormal approximation. For the second sampling procedure, we approximate the conditional terminal forward price as a constant-elasticity-of-variance (CEV) distribution. Our CEV approximation preserves the martingale condition and precludes arbitrage, which is a key advantage over Islah's approximation used in most SABR simulation schemes in the literature. We then adopt the exact sampling method of the CEV distribution based on the shifted-Poisson mixture Gamma random variable. Our enhanced procedures avoid the tedious Laplace inversion algorithm for sampling integrated variance and non-efficient inverse transform sampling of the forward price in some of the earlier simulation schemes. Numerical results demonstrate our simulation scheme to be highly efficient, accurate, and reliable.