Sixth-Order Compact Differencing with Staggered Boundary Schemes and 3(2) Bogacki-Shampine Pairs for Pricing Free-Boundary Options
We propose a stable sixth-order compact finite difference scheme with a dynamic fifth-order staggered boundary scheme and 3(2) R-K Bogacki and Shampine adaptive time stepping for pricing American style options. To locate, fix and compute the free-boundary simultaneously with option and delta sensitivity, we introduce a Landau transformation. Furthermore, we remove the convective term in the pricing model which could further introduce errors. Hence, an efficient sixth-order compact scheme can easily be implemented. The main challenge in coupling the sixth order compact scheme in discrete form is to efficiently account for the near-boundary scheme. In this work, we introduce novel fifth- and sixth-order Dirichlet near-boundary schemes suitable for solving our model. The optimal exercise boundary and other boundary values are approximated using a high-order analytical approximation obtained from a novel fifth-order staggered boundary scheme. Furthermore, we investigate the smoothness of the first and second derivatives of the optimal exercise boundary which is obtained from this high-order analytical approximation. Coupled with the 3(2) RK-Bogacki and Shampine time integration method, the interior values are then approximated using the sixth order compact operator. The expected convergence rate is obtained, and our present numerical scheme is very fast and gives highly accurate approximations with very coarse grids.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
An Adaptive and Explicit Fourth Order Runge-Kutta-Fehlberg Method Coupled with Compact Finite Differencing for Pricing American Put Options
We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, the free boundary problem is converted into a syst…
An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networks
We present an explicit second order staggered finite difference (FD) discretization scheme for forward simulation of natural gas transport in pipeline networks. By construction, this discretization approach guarantees th…
Compact and Infinite-Order Error Analysis for Null-Space SVD Estimation
We study null-space estimation from a noisy matrix. For a simple left null space, we first derive an exact compact expression for the error of the smallest left singular vector. We then give an all-order series for the S…
LDAC-Net: A Learnable Multi-Lag Differencing Attention-Convolution Network for Drift-Robust Recognition with Low-Cost MOX Gas Sensors
Portable electronic-nose systems based on low-cost metal-oxide (MOX) gas sensors offer a practical solution for gas and odour recognition, but their signals are affected by slow chemical transients, drifting sensor offse…
On the Efficiency of 5(4) RK-Embedded Pairs with High Order Compact Scheme and Robin Boundary Condition for Options Valuation
When solving the American options with or without dividends, numerical methods often obtain lower convergence rates if further treatment is not implemented even using high-order schemes. In this article, we present a fas…