Neural networks have been used as a nonparametric method for option pricing and hedging since the early 1990s. Far over a hundred papers have been published on this topic. This note intends to provide a comprehensive review. Papers are compared in terms of input features, output variables, benchmark models, performance measures, data partition methods, and underlying assets. Furthermore, related work and regularisation techniques are discussed.
{"title":"Neural networks for option pricing and hedging: a literature review","authors":"Johannes Ruf,Weiguan Wang","doi":"10.21314/jcf.2020.390","DOIUrl":"https://doi.org/10.21314/jcf.2020.390","url":null,"abstract":"Neural networks have been used as a nonparametric method for option pricing and hedging since the early 1990s. Far over a hundred papers have been published on this topic. This note intends to provide a comprehensive review. Papers are compared in terms of input features, output variables, benchmark models, performance measures, data partition methods, and underlying assets. Furthermore, related work and regularisation techniques are discussed.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"85 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537394","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}
We present a methodology to generate future scenarios of interest rates for different credit ratings under a real-world probability measure. More precisely, we explain how to perform simulations of the real-world forward rates for different rating classes by generalizing the multidimensional shifted lognormal London Interbank Offered Rate market model to account for credit ratings and a specification of the market prices of risk vector processes. The proposed methodology allows for the presence of negative interest rates, as currently observed in the markets, and guarantees the monotonicity of forward rates with respect to credit ratings.
{"title":"A Libor Market Model Including Credit Risk Under the Real-World Measure","authors":"S. Lopes, Carlos Vázquez Cendón","doi":"10.21314/jcf.2020.399","DOIUrl":"https://doi.org/10.21314/jcf.2020.399","url":null,"abstract":"We present a methodology to generate future scenarios of interest rates for different credit ratings under a real-world probability measure. More precisely, we explain how to perform simulations of the real-world forward rates for different rating classes by generalizing the multidimensional shifted lognormal London Interbank Offered Rate market model to account for credit ratings and a specification of the market prices of risk vector processes. The proposed methodology allows for the presence of negative interest rates, as currently observed in the markets, and guarantees the monotonicity of forward rates with respect to credit ratings.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48428289","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}
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process that is constructed by replacing the calendar time with the gamma time in a Brownian motion with drift, resulting in a time-changed Brownian motion. In the case of the Black–Merton–Scholes model, there exist fast approximation methods for pricing American options. However, these methods cannot be used for the variance gamma model. We develop a new fast and accurate approximation method – inspired by the quadratic approximation – to get rid of the time steps required in finite-difference and simulation methods, while reducing error by making use of a machine learning technique on precalculated quantities. We compare the performance of our method with those of the existing methods and show that our method is efficient and accurate in the context of practical use.
{"title":"Fast Pricing of American Options Under Variance Gamma","authors":"Weilong Fu, Ali Hirsa","doi":"10.21314/jcf.2021.002","DOIUrl":"https://doi.org/10.21314/jcf.2021.002","url":null,"abstract":"We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process that is constructed by replacing the calendar time with the gamma time in a Brownian motion with drift, resulting in a time-changed Brownian motion. In the case of the Black–Merton–Scholes model, there exist fast approximation methods for pricing American options. However, these methods cannot be used for the variance gamma model. We develop a new fast and accurate approximation method – inspired by the quadratic approximation – to get rid of the time steps required in finite-difference and simulation methods, while reducing error by making use of a machine learning technique on precalculated quantities. We compare the performance of our method with those of the existing methods and show that our method is efficient and accurate in the context of practical use.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"31 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67703232","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}
The yield curve is a fundamental input parameter of valuation theories in capital markets. Information about yields can be observed in a discrete form, either directly through traded yield instruments (eg., interest rate swaps) or indirectly through the prices of bonds (eg., government bonds). Capital markets usually create benchmark yield curves for specific and very liquid market instruments, or for issuers where many different quotes of individual yield information for specific maturities are observable. The standard methods to construct a continuous yield curve from discrete observable yield data quotes are the fit of a mathematical model function, interpolation or regression algorithms. This paper expands these standard methods to include artificial intelligence algorithms, which have the advantage of avoiding any assumptions with regard to the mathematical model functions of the yield curve, and which can conceptually adapt easily to any market changes. Nowadays, the most widely used risk-free yield curve in capital markets is the overnight index swap (OIS) curve, which is derived from observable OISs and is used in this paper as the benchmark curve to derive and compare different yield curve fits.
{"title":"Yield Curve Fitting with Artificial Intelligence: A Comparison of Standard Fitting Methods with Artificial Intelligence Algorithms","authors":"Dr. Achim Posthaus","doi":"10.21314/JCF.2019.362","DOIUrl":"https://doi.org/10.21314/JCF.2019.362","url":null,"abstract":"The yield curve is a fundamental input parameter of valuation theories in capital markets. Information about yields can be observed in a discrete form, either directly through traded yield instruments (eg., interest rate swaps) or indirectly through the prices of bonds (eg., government bonds). Capital markets usually create benchmark yield curves for specific and very liquid market instruments, or for issuers where many different quotes of individual yield information for specific maturities are observable. The standard methods to construct a continuous yield curve from discrete observable yield data quotes are the fit of a mathematical model function, interpolation or regression algorithms. This paper expands these standard methods to include artificial intelligence algorithms, which have the advantage of avoiding any assumptions with regard to the mathematical model functions of the yield curve, and which can conceptually adapt easily to any market changes. Nowadays, the most widely used risk-free yield curve in capital markets is the overnight index swap (OIS) curve, which is derived from observable OISs and is used in this paper as the benchmark curve to derive and compare different yield curve fits.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49392632","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}
The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes the quadratic approximation scheme of Barone-Adesi & Whaley (1987) and several of its extensions. Using perturbative arguments, we decompose the early exercise pricing problem into sub-problems of different orders and solve these sub-problems successively. The obtained solutions are combined to recover approximations to the original pricing problem of multiple orders, with the 0-th order version matching the general Barone-Adesi & Whaley ansatz. We test the accuracy and efficiency of the approximations via numerical simulations. The results show a clear dominance of higher order approximations over their respective 0-th order version and reveal that significantly more pricing accuracy can be obtained by relying on approximations of the first few orders. Additionally, they suggest that increasing the order of any approximation by one generally refines the pricing precision, however that this happens at the expense of greater computational costs.
{"title":"On Extensions of the Barone-Adesi & Whaley Method to Price American-Type Options","authors":"Ludovic Mathys","doi":"10.2139/ssrn.3482064","DOIUrl":"https://doi.org/10.2139/ssrn.3482064","url":null,"abstract":"The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes the quadratic approximation scheme of Barone-Adesi & Whaley (1987) and several of its extensions. Using perturbative arguments, we decompose the early exercise pricing problem into sub-problems of different orders and solve these sub-problems successively. The obtained solutions are combined to recover approximations to the original pricing problem of multiple orders, with the 0-th order version matching the general Barone-Adesi & Whaley ansatz. We test the accuracy and efficiency of the approximations via numerical simulations. The results show a clear dominance of higher order approximations over their respective 0-th order version and reveal that significantly more pricing accuracy can be obtained by relying on approximations of the first few orders. Additionally, they suggest that increasing the order of any approximation by one generally refines the pricing precision, however that this happens at the expense of greater computational costs.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43616879","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":"Fast stochastic forward sensitivities in Monte Carlo simulations using stochastic automatic differentiation (with applications to initial margin valuation adjustments)","authors":"Christian Fries","doi":"10.21314/jcf.2018.359","DOIUrl":"https://doi.org/10.21314/jcf.2018.359","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"28 1","pages":"103-125"},"PeriodicalIF":0.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543429","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 describes an adaptive Filon quadrature for the computation of option prices under the Heston stochastic volatility model. A comparison against popular alternatives in terms of accuracy and performance is then presented, ending with the concrete case of model calibration on different market data.
{"title":"An adaptive Filon quadrature for stochastic volatility models","authors":"Fabien Le Floc’h","doi":"10.21314/JCF.2018.356","DOIUrl":"https://doi.org/10.21314/JCF.2018.356","url":null,"abstract":"This paper describes an adaptive Filon quadrature for the computation of option prices under the Heston stochastic volatility model. A comparison against popular alternatives in terms of accuracy and performance is then presented, ending with the concrete case of model calibration on different market data.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"22 1","pages":"65-88"},"PeriodicalIF":0.9,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47218971","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 analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies, minimizing the variance of the final wealth. These strategies are based on first- and second-order approximations of option prices. The hedging instrument is either the underlying asset or another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor’s 500.
{"title":"Hedging of Options in the Presence of Jump Clustering","authors":"Donatien Hainaut, Franck Moraux","doi":"10.21314/JCF.2018.354","DOIUrl":"https://doi.org/10.21314/JCF.2018.354","url":null,"abstract":"This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies, minimizing the variance of the final wealth. These strategies are based on first- and second-order approximations of option prices. The hedging instrument is either the underlying asset or another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor’s 500.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49222048","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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