B-Spline Based Monotone Multigrid Methods, with an Application to the Pricing of American Options
نویسندگان
چکیده
We propose a monotone multigrid method based on a B–spline basis of arbitrary smoothness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi–optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B–spline expansion coefficients. To illustrate the potential of the scheme, the method is applied to the pricing of American options in the Black–Scholes framework.
منابع مشابه
B–Spline Based Monotone Multigrid Methods, with an Application to the Prizing of American Options
We propose a monotone multigrid method based on a B–spline basis of arbitrary smoothness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi–optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B–spline expan...
متن کاملA new approach to using the cubic B-spline functions to solve the Black-Scholes equation
Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...
متن کاملThe Computation of American Option Price Sensitivities using a Monotone Multigrid Method for Higher Order B–Spline Discretizations
In this paper a fast solver for discrete free boundary value problems which is based on hierarchical higher order discretizations is presented. The numerical method consists of a finite element discretization with B–spline ansatz functions of arbitrary degree combined with a monotone multigrid method for the efficient solution of the resulting discrete system. In particular, the potential of th...
متن کاملB-Spline-Based Monotone Multigrid Methods
Abstract. For the efficient numerical solution of elliptic variational inequalities on closed convex sets, multigrid methods based on piecewise linear finite elements have been investigated over the past decades. Essential for their success is the appropriate approximation of the constraint set on coarser grids which is based on function values for piecewise linear finite elements. On the other...
متن کاملAmerican Option Pricing of Future Contracts in an Effort to Investigate Trading Strategies; Evidence from North Sea Oil Exchange
In this paper, Black Scholes’s pricing model was developed to study American option on future contracts of Brent oil. The practical tests of the model show that market priced option contracts as future contracts less than what model did, which mostly represent option contracts with price rather than without price. Moreover, it suggests call option rather than put option. Using t hypothesis test...
متن کامل