SABR/LIBOR market models: pricing and calibration for some interest rate derivatives

TL;DR

This paper presents a method for efficiently calibrating advanced SABR/LIBOR market models with stochastic volatility to real market data using a parallelized multi-GPU simulated annealing algorithm, improving practical applicability.

Contribution

It introduces a parallelized multi-GPU calibration technique for SABR/LIBOR models, enhancing efficiency in fitting complex models to market data.

Findings

Demonstrates the effectiveness of multi-GPU calibration on real market data.

Shows improved calibration speed and accuracy over traditional methods.

Validates the approach with real market prices of caplets and swaptions.

Abstract

In order to overcome the drawbacks of assuming deterministic volatility coefficients in the standard LIBOR market models to capture volatility smiles and skews in real markets, several extensions of LIBOR models to incorporate stochastic volatilities have been proposed. The efficient calibration to market data of these more complex models becomes a relevant target in practice. The main objective of the present work is to efficiently calibrate some recent SABR/LIBOR market models to real market prices of caplets and swaptions. For the calibration we propose a parallelized version of the simulated annealing algorithm for multi-GPUs. The numerical results clearly illustrate the advantages of using the proposed multi-GPUs tools when applied to real market data and popular SABR/LIBOR models.