Variance Reduction for Multivariate Monte Carlo Simulation

Wang, Jr‐Yan

doi:10.3905/jod.2008.710895

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…To improve the computational efficiency and arithmetic stability of MCMC simulations, we employed a non-centered parameterization of the random effects based on a Cholesky factorization of the correlation matrix. This decomposition represents the Hermitian positive-definite correlation matrix as a product of a lower triangular matrix and its conjugate transpose 62 , 63 . We set a Cholesky factorized prior with shape equal to 2 for the parameterized correlation matrix.…”

Section: Methodsmentioning

confidence: 99%

Modeling children’s moral development in postwar Taiwan through naturalistic observations preserved in historical texts

Sui,

Wang,

2024

Sci Rep

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A core issue in the interdisciplinary study of human morality is its ontogeny in diverse cultures, but systematic, naturalistic data in specific cultural contexts are rare to find. This study conducts a novel analysis of 213 children’s socio-moral behavior in a historical, non-Western, rural setting, based on a unique dataset of naturalistic observations from the first field research on Han Chinese children. Using multilevel multinomial modeling, we examined a range of proactive behaviors in 0-to-12-year-old children’s peer cooperation and conflict in an entire community in postwar Taiwan. We modeled the effects of age, sex, kinship, and behavioral roles, and revealed complex interactions between these four variables in shaping children’s moral development. We discovered linkages between coercive and non-coercive behaviors as children strategically negotiated leadership dynamics. We identified connections between prosocial and aggressive behaviors, illuminating the nuances of morality in real life. Our analysis also revealed gendered patterns and age-related trends that deviated from cultural norms and contradicted popular assumptions about Chinese family values. These findings highlight the importance of naturalistic observations in cultural contexts for understanding how we become moral persons. This re-analysis of historically significant fieldnotes also enriches the interdisciplinary study of child development across societies.

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Section: Methodsmentioning

confidence: 99%

Modeling children’s moral development in postwar Taiwan through naturalistic observations preserved in historical texts

Sui,

Wang,

2024

Sci Rep

View full text Add to dashboard Cite

show abstract

“…To improve the computational efficiency and arithmetic stability of MCMC simulations, we employed a non-centered parameterization of the random effects based on a Cholesky factorization of the correlation matrix. This decomposition represents the Hermitian positive-definite correlation matrix as a product of a lower triangular matrix and its conjugate transpose 60,61 . We set a Cholesky factorized prior with shape equal to 2 for the parameterized correlation matrix.…”

Section: Model Mfit_i -Individual-level Random Effects Onlymentioning

confidence: 99%

Demographic factors impact children’s moral development in postwar Taiwan: Modeling naturalistic observations from historical texts

Sui,

Wang,

2023

Preprint

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A core issue in the interdisciplinary study of human morality is its ontogeny in diverse cultures, but systematic, naturalistic data in specific cultural contexts are rare to find. This study conducts a novel analysis of 213 children’s socio-moral behavior in a historical, non-Western, rural setting, based on a unique dataset of naturalistic observations from the first field research on Han Chinese children. Using multilevel multinomial modeling, we examined a range of proactive behaviors in 0-to-12-year-old children’s peer cooperation and conflict in an entire community in postwar Taiwan. We modeled the effects of age, sex, kinship and behavioral roles, and revealed complex interactions between these four variables in shaping children’s moral development. We discovered linkages between coercive and non-coercive behaviors as children strategically negotiated leadership dynamics. We identified connections between prosocial and aggressive behaviors, illuminating the nuances of morality in real life. Our analysis also revealed gendered patterns and age-related trends that deviated from cultural norms and contradicted popular assumptions about Chinese family values. These findings highlight the importance of naturalistic observations in cultural contexts for understanding how we become moral persons. This re-analysis of historically significant fieldnotes also enriches the interdisciplinary study of child development across societies.

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“…Both the LSM and FM use the moment matching (see, e.g., Glasserman, ) and inverse Cholesky (see, e.g., Wang, ) methods to improve the pricing efficiency in all simulation processes. The option is exercisable 50 times per year.…”

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confidence: 99%

A Forward Monte Carlo Method for American Options Pricing

Miao

Lee

2012

Journal of Futures Markets

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This study proposes a forward Monte Carlo method for the pricing of American options. The main advantage of this method is that it does not use backward induction as required by other methods. Instead, the proposed approach relies on a wise determination about whether a simulated stock price has entered the exercise region. The validity of the proposed method is supported by the mathematical proofs for the vanilla cases. With some adaption, it is shown that this forward method can be extended to price other American style options such as chooser and exchange options. This study demonstrates the effectiveness of the proposed approach using a series of numerical examples, revealing significant improvements in numerical efficiency and accuracy in contrast with the standard regressionbased method of Longstaff and Schwartz (2001). C 2012 Wiley Periodicals, Inc. Jrl Fut MarkWe are grateful for the helpful comments and suggestions from Bob Webb (Editor) and an anonymous referee.Due to the lack of analytic solutions to American options prices, researchers have developed a number of methods for these pricing problems. Broadie and Detemple (2004) provided an excellent review summarizing the existing methods for the pricing of American options. Roughly speaking, these approaches can be separated into two main categories: the analytical approximation and the numerical methods. The former is dated back to Barone-Adesi and Whaley's (1987) quadratic approximation, which is regarded as the most representative work of its kind. Many subsequent studies extended their work to consider more complicated options or models, such as the recent examples of Chang, Kang, Kim, and Kim (2007) and Guo, Hung, and So (2009). On the other hand, Monte Carlo simulation is considered to be the most powerful numerical techniques for the valuation of American options. Unlike other methods (e.g., finite difference), the Monte Carlo method has higher flexibility, wider applicability to various products, and is convergent to the true values. Moreover, it is also less sensitive to the problem dimension and therefore better suited to pricing problems involving multiple assets.Using Monte Carlo methods for option pricing dates back to Boyle (1977) for European options. Earlier applications of the Monte Carlo to American option pricing include Tilley's (1993) bundling algorithm, Barraquant and Martineau's (1995) stratified state aggregation algorithm, Broadie and Glasserman's (1997) stochastic tree based algorithm, Longstaff and Schwartz's (2001) regression-based algorithm. Boyle, Broadie, and Glasserman (1997) and Areal, Rodrigues, and Armada (2008) provide a comprehensive review of these methods. The Longstaff and Schwartz's method (also known as the least squares method [LSM]) is perhaps the most popular and promising one of these methods. Many researchers have adopted, modified, and extended this method over the years, including Liu (2010). The main idea of LSM is to estimate the continuation value through a least square regression on future simulated s...

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Variance Reduction for Multivariate Monte Carlo Simulation

Cited by 3 publications

References 14 publications

Modeling children’s moral development in postwar Taiwan through naturalistic observations preserved in historical texts

Modeling children’s moral development in postwar Taiwan through naturalistic observations preserved in historical texts

Demographic factors impact children’s moral development in postwar Taiwan: Modeling naturalistic observations from historical texts

A Forward Monte Carlo Method for American Options Pricing

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