TL;DR
This paper introduces a new deep learning-based method to price barrier options by directly solving the associated forward-backward stochastic differential equations, effectively handling boundary conditions in high-dimensional settings.
Contribution
It extends forward deep BSDE methods to explicitly incorporate barrier boundary conditions, enabling accurate pricing of barrier options in complex, high-dimensional models.
Findings
Handles any barrier condition in FBSDE framework
Applicable to high-dimensional problems
Accurately captures boundary conditions in pricing
Abstract
This paper presents a novel and direct approach to price boundary and final-value problems, corresponding to barrier options, using forward deep learning to solve forward-backward stochastic differential equations (FBSDEs). Barrier instruments are instruments that expire or transform into another instrument if a barrier condition is satisfied before maturity; otherwise they perform like the instrument without the barrier condition. In the PDE formulation, this corresponds to adding boundary conditions to the final value problem. The deep BSDE methods developed so far have not addressed barrier/boundary conditions directly. We extend the forward deep BSDE to the barrier condition case by adding nodes to the computational graph to explicitly monitor the barrier conditions for each realization of the dynamics as well as nodes that preserve the time, state variables, and trading strategy…
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