The time-discrete method of lines for options and bonds :: a PDE approach /
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 theor...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey :
World Scientific,
[2015]
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9789814619684 981461968X |
Internformat
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| 245 | 1 | 4 | |a The time-discrete method of lines for options and bonds : |b a PDE approach / |c Gunter H. Meyer, Georgia Institute of Technology, USA. |
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| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Derivative securities |x Mathematical models. |0 http://id.loc.gov/authorities/subjects/sh2009123216 | |
| 650 | 0 | |a Options (Finance) |x Mathematical models. | |
| 650 | 0 | |a Bonds |x Mathematical models. | |
| 650 | 0 | |a Discrete-time systems. |0 http://id.loc.gov/authorities/subjects/sh85038370 | |
| 650 | 0 | |a Differential equations, Partial. |0 http://id.loc.gov/authorities/subjects/sh85037912 | |
| 650 | 6 | |a Instruments dérivés (Finances) |x Modèles mathématiques. | |
| 650 | 6 | |a Options (Finances) |x Modèles mathématiques. | |
| 650 | 6 | |a Obligations (Valeurs) |x Modèles mathématiques. | |
| 650 | 6 | |a Systèmes échantillonnés. | |
| 650 | 6 | |a Équations aux dérivées partielles. | |
| 650 | 7 | |a BUSINESS & ECONOMICS |x Finance. |2 bisacsh | |
| 650 | 7 | |a Bonds |x Mathematical models |2 fast | |
| 650 | 7 | |a Derivative securities |x Mathematical models |2 fast | |
| 650 | 7 | |a Differential equations, Partial |2 fast | |
| 650 | 7 | |a Discrete-time systems |2 fast | |
| 650 | 7 | |a Options (Finance) |x Mathematical models |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Meyer, Gunter H. |t Time-discrete method of lines for options and bonds |z 9789814619677 |w (DLC) 2014029166 |w (OCoLC)895500602 |
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| adam_text | |
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| author | Meyer, Gunter H. |
| author_facet | Meyer, Gunter H. |
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| 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. |
| ctrlnum | (OCoLC)900633244 |
| dewey-full | 332.64/5701183 |
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| dewey-ones | 332 - Financial economics |
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| spelling | Meyer, Gunter H. The time-discrete method of lines for options and bonds : a PDE approach / Gunter H. Meyer, Georgia Institute of Technology, USA. New Jersey : World Scientific, [2015] 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references. Print version record. 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. 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. Derivative securities Mathematical models. http://id.loc.gov/authorities/subjects/sh2009123216 Options (Finance) Mathematical models. Bonds Mathematical models. Discrete-time systems. http://id.loc.gov/authorities/subjects/sh85038370 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Instruments dérivés (Finances) Modèles mathématiques. Options (Finances) Modèles mathématiques. Obligations (Valeurs) Modèles mathématiques. Systèmes échantillonnés. Équations aux dérivées partielles. BUSINESS & ECONOMICS Finance. bisacsh Bonds Mathematical models fast Derivative securities Mathematical models fast Differential equations, Partial fast Discrete-time systems fast Options (Finance) Mathematical models fast Print version: Meyer, Gunter H. Time-discrete method of lines for options and bonds 9789814619677 (DLC) 2014029166 (OCoLC)895500602 FWS01 ZDB-4-EBU FWS_PDA_EBU https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=942158 Volltext |
| spellingShingle | Meyer, Gunter H. The time-discrete method of lines for options and bonds : a PDE approach / 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. Derivative securities Mathematical models. http://id.loc.gov/authorities/subjects/sh2009123216 Options (Finance) Mathematical models. Bonds Mathematical models. Discrete-time systems. http://id.loc.gov/authorities/subjects/sh85038370 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Instruments dérivés (Finances) Modèles mathématiques. Options (Finances) Modèles mathématiques. Obligations (Valeurs) Modèles mathématiques. Systèmes échantillonnés. Équations aux dérivées partielles. BUSINESS & ECONOMICS Finance. bisacsh Bonds Mathematical models fast Derivative securities Mathematical models fast Differential equations, Partial fast Discrete-time systems fast Options (Finance) Mathematical models fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh2009123216 http://id.loc.gov/authorities/subjects/sh85038370 http://id.loc.gov/authorities/subjects/sh85037912 |
| title | The time-discrete method of lines for options and bonds : a PDE approach / |
| title_auth | The time-discrete method of lines for options and bonds : a PDE approach / |
| title_exact_search | The time-discrete method of lines for options and bonds : a PDE approach / |
| title_full | The time-discrete method of lines for options and bonds : a PDE approach / Gunter H. Meyer, Georgia Institute of Technology, USA. |
| title_fullStr | The time-discrete method of lines for options and bonds : a PDE approach / Gunter H. Meyer, Georgia Institute of Technology, USA. |
| title_full_unstemmed | The time-discrete method of lines for options and bonds : a PDE approach / Gunter H. Meyer, Georgia Institute of Technology, USA. |
| title_short | The time-discrete method of lines for options and bonds : |
| title_sort | time discrete method of lines for options and bonds a pde approach |
| title_sub | a PDE approach / |
| topic | Derivative securities Mathematical models. http://id.loc.gov/authorities/subjects/sh2009123216 Options (Finance) Mathematical models. Bonds Mathematical models. Discrete-time systems. http://id.loc.gov/authorities/subjects/sh85038370 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Instruments dérivés (Finances) Modèles mathématiques. Options (Finances) Modèles mathématiques. Obligations (Valeurs) Modèles mathématiques. Systèmes échantillonnés. Équations aux dérivées partielles. BUSINESS & ECONOMICS Finance. bisacsh Bonds Mathematical models fast Derivative securities Mathematical models fast Differential equations, Partial fast Discrete-time systems fast Options (Finance) Mathematical models fast |
| topic_facet | Derivative securities Mathematical models. Options (Finance) Mathematical models. Bonds Mathematical models. Discrete-time systems. Differential equations, Partial. Instruments dérivés (Finances) Modèles mathématiques. Options (Finances) Modèles mathématiques. Obligations (Valeurs) Modèles mathématiques. Systèmes échantillonnés. Équations aux dérivées partielles. BUSINESS & ECONOMICS Finance. Bonds Mathematical models Derivative securities Mathematical models Differential equations, Partial Discrete-time systems Options (Finance) Mathematical models |
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