The time-discrete method of lines for options and bonds : a PDE approach / Gunter H. Meyer, Georgia Institute of Technology, USA.

Format:

Book

Author/Creator:

Meyer, Gunter H., author.

Language:

English

Subjects (All):

Derivative securities--Mathematical models.

Derivative securities.

Options (Finance)--Mathematical models.

Options (Finance).

Bonds--Mathematical models.

Bonds.

Discrete-time systems.

Differential equations, Partial.

Physical Description:

1 online resource (286 p.)

Place of Publication:

New Jersey : World Scientific, [2015]

Language Note:

English

Summary:

Few financial mathematical books have discussed mathematically acceptable boundary conditions for the degenerate diffusion equations in finance. In The Time-Discrete Method of Lines for Options and Bonds, Gunter H. Meyer examines PDE models for financial derivatives and shows where the Fichera theory requires the pricing equation at degenerate boundary points, and what modifications of it lead to acceptable tangential boundary conditions at non-degenerate points on computational boundaries when no financial data are available. Extensive numerical simulations are carried out with the method of lines to examine the influence of the finite computational domain and of the chosen boundary conditions on option and bond prices in one and two dimensions, reflecting multiple assets, stochastic volatility, jump diffusion and uncertain parameters. Special emphasis is given to early exercise boundaries, prices and their derivatives near expiration. Detailed graphs and tables are included which may serve as benchmark data for solutions found with competing numerical methods.

Contents:

1. Comments on the pricing equations in finance. 1.1. Solutions and their properties. 1.2. Boundary conditions for the pricing equations

2. The method of lines (MOL) for the diffusion equation. 2.1. The method of lines with continuous time (the vertical MOL). 2.2. The method of lines with continuous x (the horizontal MOL). 2.3. The method of lines with continuous x for multidimensional problems. 2.4. Free boundaries and the MOL in two dimensions

3. The Riccati transformation method for linear two point boundary value problems. 3.1. The Riccati transformation on a fixed interval. 3.2. The Riccati transformation for a free boundary problem. 3.3. The numerical solution of the sweep equations

4. European options

5. American puts and calls

6. Bonds and options for one-factor interest rate models

7. Two-dimensional diffusion problems in finance. 7.1. Front tracking in Cartesian coordinates. 7.2. American calls and puts in polar coordinates. 7.3. A three-dimensional problem.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on print version record.

ISBN:

981-4619-68-X

OCLC:

900633244