Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints
Abstract We propose an efficient method for the construction of an arbitrage-free call option price function from observed call price quotes. The no-arbitrage theory of option pricing places various shape constraints on the option price function. For each available maturity on a given trading day, t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1097-x |
| _version_ | 1818618104582766592 |
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| author | Arindam Kundu Sumit Kumar Nutan Kumar Tomar Shiv Kumar Gupta |
| author_facet | Arindam Kundu Sumit Kumar Nutan Kumar Tomar Shiv Kumar Gupta |
| author_sort | Arindam Kundu |
| collection | DOAJ |
| description | Abstract We propose an efficient method for the construction of an arbitrage-free call option price function from observed call price quotes. The no-arbitrage theory of option pricing places various shape constraints on the option price function. For each available maturity on a given trading day, the proposed method estimates an option price function of strike price using a Bernstein polynomial basis. Using the properties of this basis, we transform the constrained functional regression problem to the least-squares problem of finite dimension and derive the sufficiency conditions of no-arbitrage pricing to a set of linear constraints. The resultant linearly constrained least square minimization problem can easily be solved using an efficient quadratic programming algorithm. The proposed method is easy to use and constructs a smooth call price function which is arbitrage-free in the entire domain of the strike price with any finite number of observed call price quotes. We empirically test the proposed method on S&P 500 option price data and compare the results with the cubic spline smoothing method to see the applicability. |
| first_indexed | 2024-12-16T17:16:17Z |
| format | Article |
| id | doaj.art-a503db4a8e2f4688a8ae81adfde358e9 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-16T17:16:17Z |
| publishDate | 2016-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-a503db4a8e2f4688a8ae81adfde358e92022-12-21T22:23:17ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-06-012016111610.1186/s13660-016-1097-xCall option price function in Bernstein polynomial basis with no-arbitrage inequality constraintsArindam Kundu0Sumit Kumar1Nutan Kumar Tomar2Shiv Kumar Gupta3Department of Mathematics, Indian Institute of Technology PatnaFaculty, Operations Management Quantitative Methods & Information System, Indian Institute of Management UdaipurDepartment of Mathematics, Indian Institute of Technology PatnaDepartment of Mathematics, Indian Institute of Technology RoorkeeAbstract We propose an efficient method for the construction of an arbitrage-free call option price function from observed call price quotes. The no-arbitrage theory of option pricing places various shape constraints on the option price function. For each available maturity on a given trading day, the proposed method estimates an option price function of strike price using a Bernstein polynomial basis. Using the properties of this basis, we transform the constrained functional regression problem to the least-squares problem of finite dimension and derive the sufficiency conditions of no-arbitrage pricing to a set of linear constraints. The resultant linearly constrained least square minimization problem can easily be solved using an efficient quadratic programming algorithm. The proposed method is easy to use and constructs a smooth call price function which is arbitrage-free in the entire domain of the strike price with any finite number of observed call price quotes. We empirically test the proposed method on S&P 500 option price data and compare the results with the cubic spline smoothing method to see the applicability.http://link.springer.com/article/10.1186/s13660-016-1097-xcall price functionno-arbitrage inequality constraintsconstrained functional regressionBernstein polynomial basisquadratic programming |
| spellingShingle | Arindam Kundu Sumit Kumar Nutan Kumar Tomar Shiv Kumar Gupta Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints Journal of Inequalities and Applications call price function no-arbitrage inequality constraints constrained functional regression Bernstein polynomial basis quadratic programming |
| title | Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints |
| title_full | Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints |
| title_fullStr | Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints |
| title_full_unstemmed | Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints |
| title_short | Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints |
| title_sort | call option price function in bernstein polynomial basis with no arbitrage inequality constraints |
| topic | call price function no-arbitrage inequality constraints constrained functional regression Bernstein polynomial basis quadratic programming |
| url | http://link.springer.com/article/10.1186/s13660-016-1097-x |
| work_keys_str_mv | AT arindamkundu calloptionpricefunctioninbernsteinpolynomialbasiswithnoarbitrageinequalityconstraints AT sumitkumar calloptionpricefunctioninbernsteinpolynomialbasiswithnoarbitrageinequalityconstraints AT nutankumartomar calloptionpricefunctioninbernsteinpolynomialbasiswithnoarbitrageinequalityconstraints AT shivkumargupta calloptionpricefunctioninbernsteinpolynomialbasiswithnoarbitrageinequalityconstraints |