Semi-Analytical Pricing of Barrier Options in the Time-Dependent λ-SABR Model: Uncorrelated Case

We consider semi-analytical pricing of barrier options for the time-dependent SABR stochastic volatility model (with drift in the instantaneous volatility) with zero correlation between spot and stochastic volatility. In doing so, we modify the general integral transform method (see Itkin et al. 2021) and deliver solution of this problem in the form of Fourier-Bessel series. The weights of this series solve a linear mixed Volterra-Fredholm equation (LMVF) of the second kind also derived in the article. Numerical examples illustrate the speed and accuracy of our method, which are comparable with those of the finite-difference approach at small maturities and outperform them at high maturities even by using a simplistic implementation of the RBF method for solving the LMVF.