Valuation of Swing Options Using an Extended Least Squares Monte Carlo Algorithm

2009 ◽  
Author(s):  
Rutang Thanawalla
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Monte Carlo Algorithm ◽  
Swing Options ◽  
Least Squares Monte Carlo

scholarly journals Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xisheng Yu ◽  
Qiang Liu
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Legendre Polynomials ◽  
American Options ◽  
Computational Cost ◽  
Monte Carlo Algorithm ◽  
Convergence Properties ◽  
Entropy Model ◽  
Least Squares Monte Carlo ◽  
Convergence Results

The paper by Liu (2010) introduces a method termed the canonical least-squares Monte Carlo (CLM) which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX) puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.

ESTIMATING RESIDUAL HEDGING RISK WITH LEAST-SQUARES MONTE CARLO

2014 ◽  
Vol 17 (07) ◽  
pp. 1450042
Author(s):  
STEFAN ANKIRCHNER ◽  
CHRISTIAN PIGORSCH ◽  
NIKOLAUS SCHWEIZER
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Error Variance ◽  
Monte Carlo Algorithm ◽  
Computationally Efficient ◽  
Basis Risk ◽  
Least Squares Monte Carlo ◽  
Hedging Strategies ◽  
Biased Estimators

Frequently, dynamic hedging strategies minimizing risk exposure are not given in closed form, but need to be approximated numerically. This makes it difficult to estimate residual hedging risk, also called basis risk, when only imperfect hedging instruments are at hand. We propose an easy to implement and computationally efficient least-squares Monte Carlo algorithm to estimate residual hedging risk. The algorithm approximates the variance minimal hedging strategy within general diffusion models. Moreover, the algorithm produces both high-biased and low-biased estimators for the residual hedging error variance, thus providing an intrinsic criterion for the quality of the approximation. In a number of examples we show that the algorithm delivers accurate hedging error characteristics within seconds.

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