Ken Jackson | University of Toronto (original) (raw)

Papers by Ken Jackson

Research paper thumbnail of An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs

ACM Transactions on Mathematical Software, 1980

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Research paper thumbnail of Comparative test results for two ODE solvers: EPISODE and GEAR

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Research paper thumbnail of User's guide for dverk--a subroutine for solving nonstiff ode's

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Research paper thumbnail of Remarks on the optimal convolution kernel for CSOR waveform relaxation

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Research paper thumbnail of Dynamic Factor Copula Model

The Gaussian factor copula model is the market standard model for multi-name credit derivatives. ... more The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. We introduce a multi-period factor copula model to overcome the calibration deficiency of factor copula models by allowing the factor loadings to be time-dependent. Usually, multi-period factor copula models require multi-dimensional integration, typically computed by Monte Carlo simulation, which makes calibration extremely time consuming. In our model, the portfolio loss of a completely homogeneous pool possesses the Markov property, thus we can compute the portfolio loss distribution analytically without multi-dimensional integration. Numerical results demonstrate the efficiency and flexibility of our model to match market quotes.

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Research paper thumbnail of A neural network approach to efficient valuation of large portfolios of variable annuities

Insurance: Mathematics and Economics, 2016

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Research paper thumbnail of Pricing synthetic collateralized debt obligations based on exponential approximations to the payoff function

The Journal of Computational Finance, 2013

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Research paper thumbnail of 4. Application of the Yale Sparse Technique to Solve the Three-Dimensional Parabolic Equation

and Application of the Parabolic …, 1984

... The second type is the three-dimensional wide angle partial differential equation, developed ... more ... The second type is the three-dimensional wide angle partial differential equation, developed by Siegmann, Lee, and Kriegsmarin. ... expressed in a short expression using the above definitions, ie, -u 1ik+ iko+ plx+(8) ar(i 0 o TK 0 1 qjx+ q2Y) Write ki+ ik1+ P~ x+ 2Y(9) (-•' iko 0 i++ ...

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Research paper thumbnail of Valuation of forward-starting CDOs

International Journal of Computer Mathematics, 2009

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Research paper thumbnail of Quadratic spline Galerkin method for the shallow water equations on the sphere

... BibTeX. @MISC{Layton02quadraticspline, author = {Anita T. Layton and Christina C. Christara a... more ... BibTeX. @MISC{Layton02quadraticspline, author = {Anita T. Layton and Christina C. Christara and Kenneth R. Jackson}, title = {Quadratic Spline Galerkin ... 14, Climate simulations with a semi-Lagrangian version of the NCAR Community Climate - Williamson, Olson - 1994. ...

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Research paper thumbnail of Pricing correlation-dependent derivatives based on exponential approximations to the hockey stick function

preparation, January, 2007

Canada; krj@cs.utoronto.ca §Algorithmics Inc., 185 Spadina Avenue, Toronto, ON, M5T 2C6, Canada; ... more Canada; krj@cs.utoronto.ca §Algorithmics Inc., 185 Spadina Avenue, Toronto, ON, M5T 2C6, Canada; Alex.Kreinin@algorithmics.com ¶Department of Computer Science, University of Toronto, 10 King's College Rd, Toronto, ON, M5S 3G4, ... Correlation-dependent ...

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Research paper thumbnail of The Order of Monotone Piecewise Cubic Interpolation

SIAM Journal on Numerical Analysis, 1985

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Research paper thumbnail of Analytic Dynamic Factor Copula Model

The Gaussian factor copula model is the market standard model for multi-name credit derivatives. ... more The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. To overcome the calibration deficiency, ...

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Research paper thumbnail of Numerical solution of stochastic models of biochemical kinetics

Canadian Applied …, 2009

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Research paper thumbnail of Fast Valuation of Forward-Starting Basket Default Swaps

International Journal of Theoretical and Applied Finance, 2010

A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by... more A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by a combination of default events of the reference entities. A forward-starting basket default swap (FBDS) is a BDS starting at a specified future time. Existing analytic or semi-analytic methods for pricing FBDS are time consuming due to the large number of possible default combinations before the BDS starts. This paper develops a fast approximation method for FBDS based on the conditional independence framework. The method converts the pricing of a FBDS to an equivalent BDS pricing problem and combines Monte Carlo simulation with an analytic approach to achieve an effective method. This hybrid method is a novel technique which can be viewed either as a means to accelerate the convergence of Monte Carlo simulation or as a way to estimate parameters in an analytic method that are difficult to compute directly. Numerical results demonstrate the accuracy and efficiency of the proposed hybri...

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Research paper thumbnail of Modeling and Simulation of Skeletal Muscle for Computer Graphics: A Survey

Foundations and Trends® in Computer Graphics and Vision, 2011

ABSTRACT Muscles provide physiological functions to drive body movement and anatomically characte... more ABSTRACT Muscles provide physiological functions to drive body movement and anatomically characterize body shape, making them a crucial component of modeling animated human figures. Substantial effort has been devoted to developing computational models of muscles for the purpose of increasing realism and accuracy in computer graphics and biomechanics. We survey various approaches to model and simulate muscles both morphologically and functionally. Modeling the realistic morphology of muscle requires that muscle deformation be accurately depicted. To this end, several methodologies are presented, including geometrically-based, physically-based, and data-driven approaches. On the other hand, the simulation of physiological muscle functions aims to identify the biomechanical controls responsible for realistic human motion. Estimating these muscle controls has been pursued through static and dynamic simulations. We review and discuss all these approaches, and conclude with suggestions for future research.

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Research paper thumbnail of Dynamic Factor Copula Model

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Research paper thumbnail of Loss Distribution Evaluation for Synthetic CDOs

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Research paper thumbnail of FAST VALUATION OF FORWARD-STARTING BASKET DEFAULT SWAPS

International Journal of Theoretical and Applied Finance, 2010

∗This research was supported in parted by the Natural Sciences and Engineering Research Council (... more ∗This research was supported in parted by the Natural Sciences and Engineering Research Council (NSERC) of Canada. †Department of Computer Science, University of Toronto, 10 King's College Road, Toronto, ON, M5S 3G4, Canada; krj@cs.toronto.edu ‡Algorithmics Inc., ...

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Research paper thumbnail of A Neural Network Approach to Efficient Valuation of Large Portfolios of Variable Annuities

Managing and hedging the risks associated with Variable Annuity (VA) products require intraday va... more Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to value their large portfolios of VA products. Because the MC simulations are computationally demanding, especially for in-traday valuations, insurance companies need more efficient valuation techniques. Recently, a framework based on traditional spatial interpolation techniques has been proposed that can significantly decrease the computational complexity of MC simulation (Gan and Lin, 2015). However, traditional interpolation techniques require the definition of a distance function that can significantly impact their accuracy. Moreover, none of the traditional spatial interpolation techniques provide all of the key properties of accuracy, efficiency, and granularity (Hejazi et al., 2015). In this paper, we present a neural network approach for the spatial interpolation framework that affords an efficient way to find an effective distance function. The proposed approach is accurate, efficient, and provides an accurate granular view of the input portfolio. Our numerical experiments illustrate the superiority of the performance of the proposed neural network approach compared to the traditional spatial interpolation schemes.

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Research paper thumbnail of An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs

ACM Transactions on Mathematical Software, 1980

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Research paper thumbnail of Comparative test results for two ODE solvers: EPISODE and GEAR

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Research paper thumbnail of User's guide for dverk--a subroutine for solving nonstiff ode's

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Research paper thumbnail of Remarks on the optimal convolution kernel for CSOR waveform relaxation

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Research paper thumbnail of Dynamic Factor Copula Model

The Gaussian factor copula model is the market standard model for multi-name credit derivatives. ... more The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. We introduce a multi-period factor copula model to overcome the calibration deficiency of factor copula models by allowing the factor loadings to be time-dependent. Usually, multi-period factor copula models require multi-dimensional integration, typically computed by Monte Carlo simulation, which makes calibration extremely time consuming. In our model, the portfolio loss of a completely homogeneous pool possesses the Markov property, thus we can compute the portfolio loss distribution analytically without multi-dimensional integration. Numerical results demonstrate the efficiency and flexibility of our model to match market quotes.

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Research paper thumbnail of A neural network approach to efficient valuation of large portfolios of variable annuities

Insurance: Mathematics and Economics, 2016

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Research paper thumbnail of Pricing synthetic collateralized debt obligations based on exponential approximations to the payoff function

The Journal of Computational Finance, 2013

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Research paper thumbnail of 4. Application of the Yale Sparse Technique to Solve the Three-Dimensional Parabolic Equation

and Application of the Parabolic …, 1984

... The second type is the three-dimensional wide angle partial differential equation, developed ... more ... The second type is the three-dimensional wide angle partial differential equation, developed by Siegmann, Lee, and Kriegsmarin. ... expressed in a short expression using the above definitions, ie, -u 1ik+ iko+ plx+(8) ar(i 0 o TK 0 1 qjx+ q2Y) Write ki+ ik1+ P~ x+ 2Y(9) (-•' iko 0 i++ ...

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Research paper thumbnail of Valuation of forward-starting CDOs

International Journal of Computer Mathematics, 2009

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Research paper thumbnail of Quadratic spline Galerkin method for the shallow water equations on the sphere

... BibTeX. @MISC{Layton02quadraticspline, author = {Anita T. Layton and Christina C. Christara a... more ... BibTeX. @MISC{Layton02quadraticspline, author = {Anita T. Layton and Christina C. Christara and Kenneth R. Jackson}, title = {Quadratic Spline Galerkin ... 14, Climate simulations with a semi-Lagrangian version of the NCAR Community Climate - Williamson, Olson - 1994. ...

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Research paper thumbnail of Pricing correlation-dependent derivatives based on exponential approximations to the hockey stick function

preparation, January, 2007

Canada; krj@cs.utoronto.ca §Algorithmics Inc., 185 Spadina Avenue, Toronto, ON, M5T 2C6, Canada; ... more Canada; krj@cs.utoronto.ca §Algorithmics Inc., 185 Spadina Avenue, Toronto, ON, M5T 2C6, Canada; Alex.Kreinin@algorithmics.com ¶Department of Computer Science, University of Toronto, 10 King's College Rd, Toronto, ON, M5S 3G4, ... Correlation-dependent ...

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Research paper thumbnail of The Order of Monotone Piecewise Cubic Interpolation

SIAM Journal on Numerical Analysis, 1985

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Research paper thumbnail of Analytic Dynamic Factor Copula Model

The Gaussian factor copula model is the market standard model for multi-name credit derivatives. ... more The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. To overcome the calibration deficiency, ...

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Research paper thumbnail of Numerical solution of stochastic models of biochemical kinetics

Canadian Applied …, 2009

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Research paper thumbnail of Fast Valuation of Forward-Starting Basket Default Swaps

International Journal of Theoretical and Applied Finance, 2010

A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by... more A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by a combination of default events of the reference entities. A forward-starting basket default swap (FBDS) is a BDS starting at a specified future time. Existing analytic or semi-analytic methods for pricing FBDS are time consuming due to the large number of possible default combinations before the BDS starts. This paper develops a fast approximation method for FBDS based on the conditional independence framework. The method converts the pricing of a FBDS to an equivalent BDS pricing problem and combines Monte Carlo simulation with an analytic approach to achieve an effective method. This hybrid method is a novel technique which can be viewed either as a means to accelerate the convergence of Monte Carlo simulation or as a way to estimate parameters in an analytic method that are difficult to compute directly. Numerical results demonstrate the accuracy and efficiency of the proposed hybri...

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Research paper thumbnail of Modeling and Simulation of Skeletal Muscle for Computer Graphics: A Survey

Foundations and Trends® in Computer Graphics and Vision, 2011

ABSTRACT Muscles provide physiological functions to drive body movement and anatomically characte... more ABSTRACT Muscles provide physiological functions to drive body movement and anatomically characterize body shape, making them a crucial component of modeling animated human figures. Substantial effort has been devoted to developing computational models of muscles for the purpose of increasing realism and accuracy in computer graphics and biomechanics. We survey various approaches to model and simulate muscles both morphologically and functionally. Modeling the realistic morphology of muscle requires that muscle deformation be accurately depicted. To this end, several methodologies are presented, including geometrically-based, physically-based, and data-driven approaches. On the other hand, the simulation of physiological muscle functions aims to identify the biomechanical controls responsible for realistic human motion. Estimating these muscle controls has been pursued through static and dynamic simulations. We review and discuss all these approaches, and conclude with suggestions for future research.

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Research paper thumbnail of Dynamic Factor Copula Model

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Research paper thumbnail of Loss Distribution Evaluation for Synthetic CDOs

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Research paper thumbnail of FAST VALUATION OF FORWARD-STARTING BASKET DEFAULT SWAPS

International Journal of Theoretical and Applied Finance, 2010

∗This research was supported in parted by the Natural Sciences and Engineering Research Council (... more ∗This research was supported in parted by the Natural Sciences and Engineering Research Council (NSERC) of Canada. †Department of Computer Science, University of Toronto, 10 King's College Road, Toronto, ON, M5S 3G4, Canada; krj@cs.toronto.edu ‡Algorithmics Inc., ...

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Research paper thumbnail of A Neural Network Approach to Efficient Valuation of Large Portfolios of Variable Annuities

Managing and hedging the risks associated with Variable Annuity (VA) products require intraday va... more Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to value their large portfolios of VA products. Because the MC simulations are computationally demanding, especially for in-traday valuations, insurance companies need more efficient valuation techniques. Recently, a framework based on traditional spatial interpolation techniques has been proposed that can significantly decrease the computational complexity of MC simulation (Gan and Lin, 2015). However, traditional interpolation techniques require the definition of a distance function that can significantly impact their accuracy. Moreover, none of the traditional spatial interpolation techniques provide all of the key properties of accuracy, efficiency, and granularity (Hejazi et al., 2015). In this paper, we present a neural network approach for the spatial interpolation framework that affords an efficient way to find an effective distance function. The proposed approach is accurate, efficient, and provides an accurate granular view of the input portfolio. Our numerical experiments illustrate the superiority of the performance of the proposed neural network approach compared to the traditional spatial interpolation schemes.

Bookmarks Related papers MentionsView impact