{"title":"Expansion method for pricing foreign exchange options under stochastic volatility and interest rates","authors":"Kenji Nagami","doi":"10.21314/jcf.2021.005","DOIUrl":"https://doi.org/10.21314/jcf.2021.005","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"18 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate integration scheme of McGhee [2011] as well as a two factor finite difference scheme. The resulting ANN calculates 10,000 times faster than the finite difference scheme whilst maintaining a high degree of accuracy. As a result, the ANN dispenses with the need for the commonly used SABR Approximation.
{"title":"An artificial neural network representation of the SABR stochastic volatility model","authors":"William McGhee","doi":"10.21314/jcf.2021.007","DOIUrl":"https://doi.org/10.21314/jcf.2021.007","url":null,"abstract":"In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate integration scheme of McGhee [2011] as well as a two factor finite difference scheme. The resulting ANN calculates 10,000 times faster than the finite difference scheme whilst maintaining a high degree of accuracy. As a result, the ANN dispenses with the need for the commonly used SABR Approximation.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"5 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression tree-based methods to solve the resulting conditional expectations. Several numerical experiments including high-dimensional problems are provided to demonstrate the accuracy and performance of the tree-based approach. For the applicability of FBSDEs in financial problems, we apply our tree-based approach to the Heston stochastic volatility model, the high-dimensional pricing problems of a Rainbow option and an European financial derivative with different interest rates for borrowing and lending.
{"title":"A review of tree-based approaches to solving forward–backward stochastic differential equations","authors":"Long Teng","doi":"10.21314/jcf.2021.010","DOIUrl":"https://doi.org/10.21314/jcf.2021.010","url":null,"abstract":"In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression tree-based methods to solve the resulting conditional expectations. Several numerical experiments including high-dimensional problems are provided to demonstrate the accuracy and performance of the tree-based approach. For the applicability of FBSDEs in financial problems, we apply our tree-based approach to the Heston stochastic volatility model, the high-dimensional pricing problems of a Rainbow option and an European financial derivative with different interest rates for borrowing and lending.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"173 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pricing of derivatives with an underlying security","authors":"Francesco Cesarone","doi":"10.4324/9781003045588-9","DOIUrl":"https://doi.org/10.4324/9781003045588-9","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"52 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73383959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An introduction to MATLAB® with applications","authors":"Francesco Cesarone","doi":"10.4324/9781003045588-2","DOIUrl":"https://doi.org/10.4324/9781003045588-2","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"31 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85442760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Further elements on Probability Theory and Statistics","authors":"Francesco Cesarone","doi":"10.4324/9781003045588-8","DOIUrl":"https://doi.org/10.4324/9781003045588-8","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"12 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74415769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of convection–diffusion–reaction type. These are known as the radial-basis-function generated finite-difference method and the Hermite finite-difference method. The convergence and stability of these schemes are investigated numerically using some examples in two and three dimensions with regularly and irregularly shaped domains. Then we consider the numerical pricing of European and American options under the Heston stochastic volatility model. The European option leads to the solution of a two-dimensional parabolic PDE, and the price of the American option is given by a linear complementarity problem with a two-dimensional parabolic PDE of convection–diffusion–reaction type. Then we use the operator splitting method to perform time-stepping after space discretization. The resulting linear systems of equations are well conditioned and sparse, and by numerical experiments we show that our numerical technique is fast and stable with respect to the change in the shape parameter of the radial basis function. Finally, numerical results are provided to illustrate the quality of approximation and to show how well our approach converges with the results presented in the literature.
{"title":"Numerical Simulation and Applications of the Convection–Diffusion–Reaction Equation with the Radial Basis Function in a Finite-Difference Mode","authors":"R. Mollapourasl, M. Haghi, A. Heryudono","doi":"10.21314/jcf.2020.382","DOIUrl":"https://doi.org/10.21314/jcf.2020.382","url":null,"abstract":"This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of convection–diffusion–reaction type. These are known as the radial-basis-function generated finite-difference method and the Hermite finite-difference method. The convergence and stability of these schemes are investigated numerically using some examples in two and three dimensions with regularly and irregularly shaped domains. Then we consider the numerical pricing of European and American options under the Heston stochastic volatility model. The European option leads to the solution of a two-dimensional parabolic PDE, and the price of the American option is given by a linear complementarity problem with a two-dimensional parabolic PDE of convection–diffusion–reaction type. Then we use the operator splitting method to perform time-stepping after space discretization. The resulting linear systems of equations are well conditioned and sparse, and by numerical experiments we show that our numerical technique is fast and stable with respect to the change in the shape parameter of the radial basis function. Finally, numerical results are provided to illustrate the quality of approximation and to show how well our approach converges with the results presented in the literature.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48742228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On extensions of the Barone-Adesi and Whaley method to price American-type options","authors":"Ludovic Mathys","doi":"10.21314/jcf.2020.397","DOIUrl":"https://doi.org/10.21314/jcf.2020.397","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"42 4 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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