Backward Deep BSDE Methods and Applications to Nonlinear Problems

Yajie Yu, Narayan Ganesan and Bernhard Hientzsch ()
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Yajie Yu: Corporate Model Risk, Wells Fargo, New York, NY 10017, USA
Narayan Ganesan: Corporate Model Risk, Wells Fargo, New York, NY 10017, USA
Bernhard Hientzsch: Corporate Model Risk, Wells Fargo, New York, NY 10017, USA

Risks, 2023, vol. 11, issue 3, 1-16

Abstract: We present a pathwise deep Backward Stochastic Differential Equation (BSDE) method for Forward Backward Stochastic Differential Equations with terminal conditions that time-steps the BSDE backwards and apply it to the differential rates problem as a prototypical nonlinear problem of independent financial interest. The nonlinear equation for the backward time-step is solved exactly or by a Taylor-based approximation. This is the first application of such a pathwise backward time-stepping deep BSDE approach for problems with nonlinear generators. We extend the method to the case when the initial value of the forward components X can be a parameter rather than fixed and similarly to also learn values at intermediate times. We present numerical results for a call combination and for a straddle, the latter comparing well to those obtained by Forsyth and Labahn with a specialized PDE solver.

Keywords: differential rates; FBSDEs; nonlinear pricing; deep learning for pricing (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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