scholarly journals A product integration method for the approximation of the early exercise boundary in the American option pricing problem

2019 ◽  
Vol 42 (8) ◽  
pp. 2825-2841
Author(s):  
Khadijeh Nedaiasl ◽  
Ali Foroush Bastani ◽  
Aysan Rafiee
Keyword(s):  
Option Pricing ◽  
Integration Method ◽  
American Option ◽  
American Option Pricing ◽  
Product Integration ◽  
Early Exercise ◽  
Exercise Boundary ◽  
Product Integration Method ◽  
Early Exercise Boundary

scholarly journals Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method

2019 ◽  
Vol 12 (4) ◽  
pp. 190 ◽  
Author(s):  
Pascal Létourneau ◽  
Lars Stentoft
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
American Option Pricing ◽  
Cross Sectional ◽  
Early Exercise ◽  
Backwards Induction ◽  
Simulation Based ◽  
Multiple Cross ◽  
Exercise Boundary ◽  
Early Exercise Boundary

This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross-sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method, less errors are accumulated, and as a result of this, the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method.

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