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

2019 ◽  
Author(s):  
Lars Stentoft ◽  
Pascal Letourneau
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Least Squares ◽  
Least Squares Monte Carlo ◽  
Early Exercise ◽  
Exercise Boundary ◽  
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.

LEAST SQUARES MONTE CARLO CREDIT VALUE ADJUSTMENT WITH SMALL AND UNIDIRECTIONAL BIAS

2016 ◽  
Vol 19 (08) ◽  
pp. 1650048 ◽  
Author(s):  
MARK JOSHI ◽  
OH KANG KWON
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Global Financial Crisis ◽  
Regression Function ◽  
Cash Flows ◽  
Least Squares Monte Carlo ◽  
Early Exercise ◽  
Regression Functions ◽  
The Global Financial Crisis ◽  
Bermudan Swaptions

Credit value adjustment (CVA) and related charges have emerged as important risk factors following the Global Financial Crisis. These charges depend on uncertain future values of underlying products, and are usually computed by Monte Carlo simulation. For products that cannot be valued analytically at each simulation step, the standard market practice is to use the regression functions from least squares Monte Carlo method to approximate their values. However, these functions do not necessarily provide accurate approximations to product values over all simulated paths and can result in biases that are difficult to control. Motivated by a novel characterization of the CVA as the value of an option with an early exercise opportunity at a stochastic time, we provide an approximation for CVA and other credit charges that rely only on the sign of the regression functions. The values are determined, instead, by pathwise deflated cash flows. A comparison of CVA for Bermudan swaptions and cancellable swaps shows that the proposed approximation results in much smaller errors than the standard approach of using the regression function values.

scholarly journals Testing the Least-Squares Monte Carlo Method for the Evaluation of Capital Requirements in Life Insurance

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 48
Author(s):  
Massimo Costabile ◽  
Fabio Viviano
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Least Squares ◽  
Closed Form ◽  
Life Insurance ◽  
Numerical Experiments ◽  
Capital Requirements ◽  
Basis Functions ◽  
Evaluation Framework ◽  
Least Squares Monte Carlo

In this paper, we test the efficiency of least-squares Monte Carlo method to estimate capital requirements in life insurance. We choose a simplified Gaussian evaluation framework where closed-form formulas are available and allow us to obtain solid benchmarks. Extensive numerical experiments were conducted by considering different combinations of simulation runs and basis functions, and the corresponding results are illustrated.

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