Howard’s algorithm for high-order approximations of American options under jump-diffusion models

Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning tech...
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Autor*in:	Thakoor, Nawdha [verfasserIn] Behera, Dhiren Kumar [verfasserIn] Tangman, Désiré Yannick [verfasserIn] Bhuruth, Muddun [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	American options Partial integro-differential equations Jump-diffusion models Policy iteration Learning networks

Übergeordnetes Werk:	Enthalten in: International journal of data science and analytics - Cham, Switzerland : Springer International Publishing, 2016, 10(2019), 2 vom: 09. Jan., Seite 193-203
Übergeordnetes Werk:	volume:10 ; year:2019 ; number:2 ; day:09 ; month:01 ; pages:193-203

Links:	Volltext

DOI / URN:	10.1007/s41060-018-00173-x

Katalog-ID:	SPR040377784

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520			\|a Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples.
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700	1		\|a Bhuruth, Muddun \|e verfasserin \|4 aut
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allfields	10.1007/s41060-018-00173-x doi (DE-627)SPR040377784 (SPR)s41060-018-00173-x-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Thakoor, Nawdha verfasserin aut Howard’s algorithm for high-order approximations of American options under jump-diffusion models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples. American options (dpeaa)DE-He213 Partial integro-differential equations (dpeaa)DE-He213 Jump-diffusion models (dpeaa)DE-He213 Policy iteration (dpeaa)DE-He213 Learning networks (dpeaa)DE-He213 Behera, Dhiren Kumar verfasserin aut Tangman, Désiré Yannick verfasserin aut Bhuruth, Muddun verfasserin aut Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 09. Jan., Seite 193-203 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:09 month:01 pages:193-203 https://dx.doi.org/10.1007/s41060-018-00173-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 09 01 193-203
spelling	10.1007/s41060-018-00173-x doi (DE-627)SPR040377784 (SPR)s41060-018-00173-x-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Thakoor, Nawdha verfasserin aut Howard’s algorithm for high-order approximations of American options under jump-diffusion models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples. American options (dpeaa)DE-He213 Partial integro-differential equations (dpeaa)DE-He213 Jump-diffusion models (dpeaa)DE-He213 Policy iteration (dpeaa)DE-He213 Learning networks (dpeaa)DE-He213 Behera, Dhiren Kumar verfasserin aut Tangman, Désiré Yannick verfasserin aut Bhuruth, Muddun verfasserin aut Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 09. Jan., Seite 193-203 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:09 month:01 pages:193-203 https://dx.doi.org/10.1007/s41060-018-00173-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 09 01 193-203
allfields_unstemmed	10.1007/s41060-018-00173-x doi (DE-627)SPR040377784 (SPR)s41060-018-00173-x-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Thakoor, Nawdha verfasserin aut Howard’s algorithm for high-order approximations of American options under jump-diffusion models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples. American options (dpeaa)DE-He213 Partial integro-differential equations (dpeaa)DE-He213 Jump-diffusion models (dpeaa)DE-He213 Policy iteration (dpeaa)DE-He213 Learning networks (dpeaa)DE-He213 Behera, Dhiren Kumar verfasserin aut Tangman, Désiré Yannick verfasserin aut Bhuruth, Muddun verfasserin aut Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 09. Jan., Seite 193-203 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:09 month:01 pages:193-203 https://dx.doi.org/10.1007/s41060-018-00173-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 09 01 193-203
allfieldsGer	10.1007/s41060-018-00173-x doi (DE-627)SPR040377784 (SPR)s41060-018-00173-x-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Thakoor, Nawdha verfasserin aut Howard’s algorithm for high-order approximations of American options under jump-diffusion models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples. American options (dpeaa)DE-He213 Partial integro-differential equations (dpeaa)DE-He213 Jump-diffusion models (dpeaa)DE-He213 Policy iteration (dpeaa)DE-He213 Learning networks (dpeaa)DE-He213 Behera, Dhiren Kumar verfasserin aut Tangman, Désiré Yannick verfasserin aut Bhuruth, Muddun verfasserin aut Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 09. Jan., Seite 193-203 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:09 month:01 pages:193-203 https://dx.doi.org/10.1007/s41060-018-00173-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 09 01 193-203
allfieldsSound	10.1007/s41060-018-00173-x doi (DE-627)SPR040377784 (SPR)s41060-018-00173-x-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE Thakoor, Nawdha verfasserin aut Howard’s algorithm for high-order approximations of American options under jump-diffusion models 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples. American options (dpeaa)DE-He213 Partial integro-differential equations (dpeaa)DE-He213 Jump-diffusion models (dpeaa)DE-He213 Policy iteration (dpeaa)DE-He213 Learning networks (dpeaa)DE-He213 Behera, Dhiren Kumar verfasserin aut Tangman, Désiré Yannick verfasserin aut Bhuruth, Muddun verfasserin aut Enthalten in International journal of data science and analytics Cham, Switzerland : Springer International Publishing, 2016 10(2019), 2 vom: 09. Jan., Seite 193-203 (DE-627)84425083X (DE-600)2843078-5 2364-4168 nnns volume:10 year:2019 number:2 day:09 month:01 pages:193-203 https://dx.doi.org/10.1007/s41060-018-00173-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 10 2019 2 09 01 193-203
language	English
source	Enthalten in International journal of data science and analytics 10(2019), 2 vom: 09. Jan., Seite 193-203 volume:10 year:2019 number:2 day:09 month:01 pages:193-203
sourceStr	Enthalten in International journal of data science and analytics 10(2019), 2 vom: 09. Jan., Seite 193-203 volume:10 year:2019 number:2 day:09 month:01 pages:193-203
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	American options Partial integro-differential equations Jump-diffusion models Policy iteration Learning networks
dewey-raw	004
isfreeaccess_bool	false
container_title	International journal of data science and analytics
authorswithroles_txt_mv	Thakoor, Nawdha @@aut@@ Behera, Dhiren Kumar @@aut@@ Tangman, Désiré Yannick @@aut@@ Bhuruth, Muddun @@aut@@
publishDateDaySort_date	2019-01-09T00:00:00Z
hierarchy_top_id	84425083X
dewey-sort	14
id	SPR040377784
language_de	englisch
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author	Thakoor, Nawdha
spellingShingle	Thakoor, Nawdha ddc 004 misc American options misc Partial integro-differential equations misc Jump-diffusion models misc Policy iteration misc Learning networks Howard’s algorithm for high-order approximations of American options under jump-diffusion models
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topic_title	004 ASE Howard’s algorithm for high-order approximations of American options under jump-diffusion models American options (dpeaa)DE-He213 Partial integro-differential equations (dpeaa)DE-He213 Jump-diffusion models (dpeaa)DE-He213 Policy iteration (dpeaa)DE-He213 Learning networks (dpeaa)DE-He213
topic	ddc 004 misc American options misc Partial integro-differential equations misc Jump-diffusion models misc Policy iteration misc Learning networks
topic_unstemmed	ddc 004 misc American options misc Partial integro-differential equations misc Jump-diffusion models misc Policy iteration misc Learning networks
topic_browse	ddc 004 misc American options misc Partial integro-differential equations misc Jump-diffusion models misc Policy iteration misc Learning networks
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title	Howard’s algorithm for high-order approximations of American options under jump-diffusion models
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title_full	Howard’s algorithm for high-order approximations of American options under jump-diffusion models
author_sort	Thakoor, Nawdha
journal	International journal of data science and analytics
journalStr	International journal of data science and analytics
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author_browse	Thakoor, Nawdha Behera, Dhiren Kumar Tangman, Désiré Yannick Bhuruth, Muddun
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title_sort	howard’s algorithm for high-order approximations of american options under jump-diffusion models
title_auth	Howard’s algorithm for high-order approximations of American options under jump-diffusion models
abstract	Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples.
abstractGer	Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples.
abstract_unstemmed	Abstract Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples.
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title_short	Howard’s algorithm for high-order approximations of American options under jump-diffusion models
url	https://dx.doi.org/10.1007/s41060-018-00173-x
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author2	Behera, Dhiren Kumar Tangman, Désiré Yannick Bhuruth, Muddun
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doi_str	10.1007/s41060-018-00173-x
up_date	2024-07-03T15:35:59.656Z
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Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. 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Howard’s algorithm for high-order approximations of American options under jump-diffusion models

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