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Browsing by Author "Verma, Arun"
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ADMIT1 : Automatic Differentiation and MATLAB Interface Toolbox
Coleman, Thomas F.; Verma, Arun (Cornell University, 199801)ADMIT1 enables you to compute {\em sparse} Jacobian and Hessian matrices, using automatic differentiation technology, from a MATLAB environment. You need only supply a function to be differentiated and ADMIT1 will exploit ... 
Dynamic Hedging in a Volatile Market
Coleman, Thomas F.; Kim, Yohan; Li, Yuying; Verma, Arun (Cornell University, 20030123)In financial markets, errors in option hedging can arise from two sources. First, the option value is a nonlinear function of the underlying; therefore, hedging is instantaneous and hedging with discrete rebalancing gives ... 
Dynamic Hedging with a Deterministic Local Volatility Function Model
Coleman, Thomas F.; Kim, Yohan; Li, Yuying; Verma, Arun (Cornell University, 20030123)We compare the dynamic hedging performance of the deterministic local volatility function approach with the implied/constant volatility method. Using an example in which the underlying price follows an absolute diffusion ... 
Efficient Calculation of Jacobian and Adjoint Vector Products in Wave Propagational Inverse Problems Using Automatic Differentiation
Coleman, Thomas F.; Santosa, Fadil; Verma, Arun (Cornell University, 20030123)Wave propagational inverse problems arise in several applications including medical imaging and geophysical exploration. In these problems, one is interested in obtaining the parameters describing the medium from its ... 
Efficient Calculation of Jacobian and Adjoint Vector Products in Wave Propagational Inverse Problems Using Automatic Differentiation
Coleman, Thomas F.; Santosa, Fadil; Verma, Arun (Cornell University, 20030122)Wave propagational inverse problems arise in several applications including medical imaging and geophysical exploration. In these problems, one is interested in obtaining the parameters describing the medium from its ... 
The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
Coleman, Thomas F.; Verma, Arun (Cornell University, 199512)This paper is concerned with the efficient computation of sparse Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of a graph coloring technique, bicoloring, ... 
The efficient computation of sparse Jacobian matrices using automaticdifferentiation
Coleman, Thomas F.; Verma, Arun (Cornell University, 199511)This paper is concerned with the efficient computation of sparse Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of a graph coloring technique, bicoloring, ... 
A Newton Method for American Option Pricing
Coleman, Thomas F.; Li, Yuying; Verma, Arun (Cornell University, 20030123)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, 199608)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, 20030128)We propose a new framework for the application of preconditioned conjugate gradients in the solution of largescale 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, 20030123)We propose a new framework for the application of preconditioned conjugate gradients in the solution of largescale 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, 20030123)Using market European option prices, a method for computing a smooth local volatility function in a 1factor 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, 199809)Using market European option prices, a method for computing a {\em smooth} local volatility function in a 1factor 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, 199608)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, 199603)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 ...