Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit

TL;DR

This paper develops semi-analytic methods for pricing double barrier options with time-dependent barriers and rebates, demonstrating improved efficiency over traditional numerical techniques.

Contribution

It extends semi-analytic pricing techniques to double barrier options with time-dependent parameters using two novel approaches.

Findings

Semi-analytic methods outperform finite-difference solvers in efficiency.

Two approaches: General Integral transform and Heat Potential method.

Validated for options with time-dependent barriers and rebates.

Abstract

We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as the barriers are time-dependent. We managed to show that these solutions are systematically more efficient for pricing and calibration than, eg., the corresponding finite-difference solvers. In this paper we extend this technique to pricing double barrier options and present two approaches to solving it: the General Integral transform method and the Heat Potential method. Our results confirm that for double barrier options these semi-analytic techniques are also more efficient than the traditional numerical methods used to solve this type of problems.