Dynamic programming for optimal stopping via pseudo-regression

Abstract

We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the least-squares error functional. Coupled with new proposals for simulation of the underlying samples, we call the approach “pseudo regression”. A detailed convergence analysis is provided and it is shown that the approach asymptotically leads to lower computational cost for a pre-specified error tolerance, hence to lower complexity. The method is justified by numerical examples.

Keywords:

• Option pricing
• Bermudan options
• Basket options
• Linear regression
• Monte Carlo simulation

JEL Classification:

• C30
• C61
• G12
• G17

Acknowledgments

We are grateful to two anonymous referees for their valuable comments. Support by the German research foundation (DFG) through the research unit FOR 2402 is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).