Now showing items 8-15 of 15

    • A Newton Method for American Option Pricing 

      Coleman, Thomas F.; Li, Yuying; Verma, Arun (Cornell University, 2003-01-23)
      The variational inequality formulation provides a mechanism to determine both the option value and the early exercise curve implicitly [17]. Standard finite difference approximation typically leads to linear complementarity ...
    • On the Efficient Methods to Solve ODEs and BVPs Using Automatic Differentiation 

      Verma, Arun (Cornell University, 1996-08)
      A large number of physical phenomena are modeled by a system of ODEs or a system of implicit ODEs. We demonstrate applicability of automatic differentiation (AD) for solving: (1) Boundary value problems in ODEs and implicit ...
    • A Preconditioned Conjugate Gradient Approach to Linear Equality 

      Coleman, Thomas F.; Verma, Arun (Cornell University, 2003-01-28)
      We propose a new framework for the application of preconditioned conjugate gradients in the solution of large-scale linear equality constrained minimization problems. This framework allows for the exploitation of ...
    • A Preconditioned Conjugate Gradient Approach to Linear Equality Constrained Minimization 

      Coleman, Thomas F.; Verma, Arun (Cornell University, 2003-01-23)
      We propose a new framework for the application of preconditioned conjugate gradients in the solution of large-scale linear equality constrained minimization problems. This framework allows for the exploitation of structure ...
    • Reconstructing the Unknown Local Volatility Function 

      Coleman, Thomas F.; Li, Yuying; Verma, Arun (Cornell University, 2003-01-23)
      Using market European option prices, a method for computing a smooth local volatility function in a 1-factor continuous diffusion model is proposed. Smoothness is introduced to facilitate accurate approximation of the ...
    • Reconstructing the unknown volatility function 

      Coleman, Thomas F; Li, Yuying; Verma, Arun (Cornell University, 1998-09)
      Using market European option prices, a method for computing a {\em smooth} local volatility function in a 1-factor continuous diffusion model is proposed. Smoothness is introduced to facilitate accurate approximation of ...
    • Structure and Efficient Hessian Calculation 

      Coleman, Thomas F.; Verma, Arun (Cornell University, 1996-08)
      Modern methods for numerical optimization calculate (or approximate) the matrix of second derivatives, the Hessian matrix, at each iteration. The recent arrival of robust software for automatic differentiation allows for ...
    • Structure and Efficient Jacobian Calculation 

      Coleman, Thomas F.; Verma, Arun (Cornell University, 1996-03)
      Many computational tasks require the determination of the Jacobian matrix, at a given argument, for a large nonlinear system of equations. Calculation or approximation of a Newton step is a related task. The development ...