Kernel-based Monte Carlo simulation for American option pricing

Han, Gyu-Sik; Kim, Bo‐Hyun; Lee, Jae‐Wook

doi:10.1016/j.eswa.2008.05.004

Cited by 8 publications

(8 citation statements)

References 18 publications

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“…One of the drawbacks of regression-based methods is that there is not an objective way of choosing the basis functions for regression, especially for the high-dimensional options. As a result, nonparametric regression, kernel-based regression (Han et al (2009)), robust regression (Jonen (2011)) and so on have been proposed to overcome or alleviate this issue. Among these approaches, the kernel method is appealing.…”

Section: Introductionmentioning

confidence: 99%

Pricing high-dimensional American options by kernel ridge regression

Wen-bin

Zastawniak

2020

Quantitative Finance

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In this paper, we propose using kernel ridge regression (KRR) to avoid the step of selecting basis functions for regression-based approaches in pricing high-dimensional American options by simulation. Our contribution is threefold. Firstly, we systematically introduce the main idea and theory of KRR and apply it to American option pricing for the first time. Secondly, we show how to use KRR with the Gaussian kernel in the regression-later method and give the computationally efficient formulas for estimating the continuation values and the Greeks. Thirdly, we propose to accelerate and improve the accuracy of KRR by performing local regression based on the bundling technique. The numerical test results show that our method is robust and has both higher accuracy and efficiency than the Least Squares Monte Carlo method in pricing high-dimensional American options.

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Section: Introductionmentioning

confidence: 99%

Pricing high-dimensional American options by kernel ridge regression

Wen-bin

Zastawniak

2020

Quantitative Finance

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“…Newton iterative method is applied to deal with the nonlinear difference scheme. Following from the last section, (13) can be compacted to…”

Section: Numerical Experiments and Discussionmentioning

confidence: 99%

“…Zhu applied the Laplace transform to find the optimal exercise boundary. Regression approaches have been widely used to price an American‐style option approximately with Monte Carlo simulation, such as the works of Han et al, Fu et al, etc. Fourier transform approach has been applied to pricing American options under stochastic volatility model but many literature works assume that the trajectories of the underlying asset prices are continuous and do not consider the jumps in the prices.…”

Section: Introductionmentioning

confidence: 99%

American option pricing under financial crisis

Luo

Xiang

Ding

2018

Appl Stoch Models Bus & Ind

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In this paper, we take financial crisis into consideration for American call options and put options pricing problems by using a jump diffusion model. Under no‐arbitrage pricing principle, we obtain a PDE (partial differential equation), which is different from the PDE derived from the classical Black‐Scholes model, it adds a postcrash market index to the primary equation. Then, we introduce the penalty method for solving the nonlinear PDE. Numerical results suggest that the option value will be affected by the crash.

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“…However, a drawback of the LSM method in the standard form is the low efficiency. Several authors argued that it is possible to improve the performance of the LSM method by substituting the least-squares regression with other regression methods (Areal et al, 2008;Han et al, 2009). However, this makes it an expensive cost to improve the valuation accuracy by taking more complex regression methods.…”

Section: Introductionmentioning

confidence: 98%

Valuing American options by least-squares randomized quasi-Monte Carlo methods

Zhou

Wang

2014

J. Finan. Eng.

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Valuation of American options is a difficult and challenging problem encountered in financial engineering. Longstaff and Schwartz [Longstaff, FA and ES Schwartz (2001). Valuing American Options by Simulation: A Simple Least-squares Approach, Review of Financial Studies, 14(1), 113-147.] Proposed the least-squares Monte Carlo (LSM) method for valuing American options. As this approach is intuitive and easy to apply, it has received much attention in the finance literature. However, a drawback of the LSM method is the low efficiency. In order to overcome this problem, we propose the least-squares randomized quasi-Monte Carlo (LSRQM) methods which can be viewed as a use low-discrepancy sequences as a variance reduction technique in the LSM method for valuing American options in this paper. Numerical results demonstrate that our proposed LSRQM methods are more efficient than the LSM method in terms of the valuation accuracy, the computation time and the convergence rate.

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Kernel-based Monte Carlo simulation for American option pricing

Cited by 8 publications

References 18 publications

Pricing high-dimensional American options by kernel ridge regression

Pricing high-dimensional American options by kernel ridge regression

American option pricing under financial crisis

Valuing American options by least-squares randomized quasi-Monte Carlo methods

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