Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
A Posteriori Finite Element Error Estimation for Diffusion Problems
SIAM Journal on Scientific Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
On the Approximation of Optimal Stopping Problems with Application to Financial Mathematics
SIAM Journal on Scientific Computing
Far Field Boundary Conditions for Black--Scholes Equations
SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Pricing Multi-Asset American Options: A Finite Element Method-of-Lines with Smooth Penalty
Journal of Scientific Computing
Journal of Scientific Computing
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
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We consider the valuation of interest rate products with effected cash flow under a multifactor Heath-Jarrow-Morton (HJM) model of the term-structure of interest rates by hierarchical approximation. At the higher-level, we apply a stochastic spectral approximation of the forward rates and exhaust an indexed family of regularized Hamilton-Jacobi characterizations of the value function. At the lower-level, we utilize penalization and an extrapolation method-of-lines finite element method. Application to interest rate caps and an American discount bond option are considered in order to demonstrate the applicability of the method.