{"title":"Analytical conversion between implied volatilities based on different dividend models","authors":"V. Lucic, V. Jovanovic","doi":"10.21314/jcf.2022.026","DOIUrl":"https://doi.org/10.21314/jcf.2022.026","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67703072","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":"A general firm value model under partial information","authors":"Cheikh Mbaye, Abass Sagna, Frédéric Vrins","doi":"10.21314/jcf.2022.020","DOIUrl":"https://doi.org/10.21314/jcf.2022.020","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67702934","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":"Simulating the Cox–Ingersoll–Ross and Heston processes: matching the first four moments","authors":"Ostap Okhrin, M. Rockinger, M. Schmid","doi":"10.21314/jcf.2022.022","DOIUrl":"https://doi.org/10.21314/jcf.2022.022","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67702956","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":"Automatic differentiation for diffusion operator integral variance reduction","authors":"Johan Auster","doi":"10.21314/jcf.2021.013","DOIUrl":"https://doi.org/10.21314/jcf.2021.013","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"23 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138537391","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 consider the pricing of VIX options in the rough Bergomi model. In this setting, the VIX random variable is defined by the one-dimensional integral of the exponential of a Gaussian process with correlated increments, hence approximate samples of the VIX can be constructed via discretization of the integral and simulation of a correlated Gaussian vector. A Monte-Carlo estimator of VIX options based on a rectangle discretization scheme and exact Gaussian sampling via the Cholesky method has a computational complexity of order $mathcal{O}(varepsilon^{-4})$ when the mean-squared error is set to $varepsilon^2$. We demonstrate that this cost can be reduced to $mathcal{O}(varepsilon^{-2} log^2(varepsilon))$ combining the scheme above with the multilevel method, and further reduced to the asymptotically optimal cost $mathcal{O}(varepsilon^{-2})$ when using a trapezoidal discretization. We provide numerical experiments highlighting the efficiency of the multilevel approach in the pricing of VIX options in such a rough forward variance setting.
{"title":"Multilevel Monte Carlo simulation for VIX options in the rough Bergomi model","authors":"Florian Bourgey, S. Marco","doi":"10.21314/jcf.2022.023","DOIUrl":"https://doi.org/10.21314/jcf.2022.023","url":null,"abstract":"We consider the pricing of VIX options in the rough Bergomi model. In this setting, the VIX random variable is defined by the one-dimensional integral of the exponential of a Gaussian process with correlated increments, hence approximate samples of the VIX can be constructed via discretization of the integral and simulation of a correlated Gaussian vector. A Monte-Carlo estimator of VIX options based on a rectangle discretization scheme and exact Gaussian sampling via the Cholesky method has a computational complexity of order $mathcal{O}(varepsilon^{-4})$ when the mean-squared error is set to $varepsilon^2$. We demonstrate that this cost can be reduced to $mathcal{O}(varepsilon^{-2} log^2(varepsilon))$ combining the scheme above with the multilevel method, and further reduced to the asymptotically optimal cost $mathcal{O}(varepsilon^{-2})$ when using a trapezoidal discretization. We provide numerical experiments highlighting the efficiency of the multilevel approach in the pricing of VIX options in such a rough forward variance setting.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43819467","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 stochastic Volterra rough volatility models, the volatility follows a truncated Brownian semi-stationary process with stochastic vol-of-vol. Recently, efficient VIX pricing Monte Carlo methods have been proposed for the case where the vol-of-vol is Markovian and independent of the volatility. Following recent empirical data, we discuss the VIX option pricing problem for a generalized framework of these models, where the vol-of-vol may depend on the volatility and/or not be Markovian. In such a setting, the aforementioned Monte Carlo methods are not valid. Moreover, the classical least squares Monte Carlo faces exponentially increasing complexity with the number of grid time steps, whilst the nested Monte Carlo method requires a prohibitive number of simulations. By exploring the infinite dimensional Markovian representation of these models, we device a scalable least squares Monte Carlo for VIX option pricing. We apply our method firstly under the independence assumption for benchmarks, and then to the generalized framework. We also discuss the rough vol-of-vol setting, where Markovianity of the vol-of-vol is not present. We present simulations and benchmarks to establish the efficiency of our method. Keywords— VIX, rough volatility, stochastic Volterra models, least squares Monte Carlo, volatility of volatility ∗Supported by FCT Grant SFRH/BD/147161/2019. †Partially supported by the project CEMAPRE/REM-UiDB/05069/2020 financed by FCT/MCTES through national funds. 1 ar X iv :2 10 5. 04 51 1v 1 [ qfi n. PR ] 1 0 M ay 2 02 1
在随机Volterra粗糙波动率模型中，波动率遵循具有随机vol-of-vol的截断布朗半平稳过程。最近，针对体积为马尔可夫且与波动率无关的情况，提出了有效的VIX定价蒙特卡罗方法。根据最近的经验数据，我们讨论了这些模型的广义框架的波动率指数期权定价问题，其中波动率的波动率可能取决于波动率和/或不是马尔可夫的。在这种情况下，上述蒙特卡罗方法是无效的。此外，经典的最小二乘蒙特卡罗方法面临着随着网格时间步长的增加而呈指数级增加的复杂性，而嵌套蒙特卡罗方法需要大量的模拟。通过探索这些模型的无限维马尔可夫表示，我们为VIX期权定价提供了一个可扩展的最小二乘蒙特卡罗方法。我们首先将我们的方法应用于基准的独立性假设下，然后应用于广义框架。我们还讨论了体积设置的粗略体积，其中体积的马尔可夫性不存在。我们提供了模拟和基准来确定我们的方法的效率。关键词——波动率指数，粗略波动率，随机Volterra模型，最小二乘蒙特卡罗，波动率波动率*由FCT Grant SFRH/BD/147161/2019支持。†部分由FCT/MCTES通过国家基金资助的CEMAPRE/REM UiDB/05069/2020项目支持。1 ar X iv：2 10 5。04 51 1v 1[qfi.PR]1 0 May 2 1
{"title":"Least squares Monte Carlo methods in stochastic Volterra rough volatility models","authors":"H. Guerreiro, João Guerra","doi":"10.21314/jcf.2022.027","DOIUrl":"https://doi.org/10.21314/jcf.2022.027","url":null,"abstract":"In stochastic Volterra rough volatility models, the volatility follows a truncated Brownian semi-stationary process with stochastic vol-of-vol. Recently, efficient VIX pricing Monte Carlo methods have been proposed for the case where the vol-of-vol is Markovian and independent of the volatility. Following recent empirical data, we discuss the VIX option pricing problem for a generalized framework of these models, where the vol-of-vol may depend on the volatility and/or not be Markovian. In such a setting, the aforementioned Monte Carlo methods are not valid. Moreover, the classical least squares Monte Carlo faces exponentially increasing complexity with the number of grid time steps, whilst the nested Monte Carlo method requires a prohibitive number of simulations. By exploring the infinite dimensional Markovian representation of these models, we device a scalable least squares Monte Carlo for VIX option pricing. We apply our method firstly under the independence assumption for benchmarks, and then to the generalized framework. We also discuss the rough vol-of-vol setting, where Markovianity of the vol-of-vol is not present. We present simulations and benchmarks to establish the efficiency of our method. Keywords— VIX, rough volatility, stochastic Volterra models, least squares Monte Carlo, volatility of volatility ∗Supported by FCT Grant SFRH/BD/147161/2019. †Partially supported by the project CEMAPRE/REM-UiDB/05069/2020 financed by FCT/MCTES through national funds. 1 ar X iv :2 10 5. 04 51 1v 1 [ qfi n. PR ] 1 0 M ay 2 02 1","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46636320","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":"The CTMC–Heston model: calibration and exotic option pricing with SWIFT","authors":"Álvaro Leitao, J. Kirkby, L. Ortiz-Gracia","doi":"10.21314/JCF.2020.398","DOIUrl":"https://doi.org/10.21314/JCF.2020.398","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43328770","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":"Penalty methods for bilateral XVA pricing in European and American contingent claims by a partial differential equation model","authors":"Yuwei Chen, C. Christara","doi":"10.21314/JCF.2020.402","DOIUrl":"https://doi.org/10.21314/JCF.2020.402","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47783360","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}
Jesse Davis, Laurens Devos, S. Reyners, W. Schoutens
In this paper, we discuss how tree-based machine learning techniques can be used in the context of derivatives pricing. Gradient boosted regression trees are employed to learn the pricing map for a couple of classical, time-consuming problems in quantitative finance. In particular, we illustrate this methodology by reducing computation times for pricing exotic derivative products and American options. Once the gradient boosting model is trained, it is used to make fast predictions of new prices. We show that this approach leads to speed-ups of several orders of magnitude, while the loss of accuracy is very acceptable from a practical point of view. Besides the predictive performance of machine learning methods, financial regulators attach more and more importance to the interpretability of pricing models. For both applications, we therefore look under the hood of the gradient boosting model and try to reveal how the price is constructed and interpreted.
{"title":"Gradient boosting for quantitative finance","authors":"Jesse Davis, Laurens Devos, S. Reyners, W. Schoutens","doi":"10.21314/JCF.2020.403","DOIUrl":"https://doi.org/10.21314/JCF.2020.403","url":null,"abstract":"In this paper, we discuss how tree-based machine learning techniques can be used in the context of derivatives pricing. Gradient boosted regression trees are employed to learn the pricing map for a couple of classical, time-consuming problems in quantitative finance. In particular, we illustrate this methodology by reducing computation times for pricing exotic derivative products and American options. Once the gradient boosting model is trained, it is used to make fast predictions of new prices. We show that this approach leads to speed-ups of several orders of magnitude, while the loss of accuracy is very acceptable from a practical point of view. Besides the predictive performance of machine learning methods, financial regulators attach more and more importance to the interpretability of pricing models. For both applications, we therefore look under the hood of the gradient boosting model and try to reveal how the price is constructed and interpreted.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49231821","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 propose deep neural network algorithms to calculate efficient frontier in some Mean-Variance and Mean-CVaR portfolio optimization problems. We show that we are able to deal with such problems when both the dimension of the state and the dimension of the control are high. Adding some additional constraints, we compare different formulations and show that a new projected feedforward network is able to deal with some global constraints on the weights of the portfolio while outperforming classical penalization methods. All developed formulations are compared in between. Depending on the problem and its dimension, some formulations may be preferred.
{"title":"Deep learning for efficient frontier calculation in finance","authors":"X. Warin","doi":"10.21314/jcf.2021.017","DOIUrl":"https://doi.org/10.21314/jcf.2021.017","url":null,"abstract":"We propose deep neural network algorithms to calculate efficient frontier in some Mean-Variance and Mean-CVaR portfolio optimization problems. We show that we are able to deal with such problems when both the dimension of the state and the dimension of the control are high. Adding some additional constraints, we compare different formulations and show that a new projected feedforward network is able to deal with some global constraints on the weights of the portfolio while outperforming classical penalization methods. All developed formulations are compared in between. Depending on the problem and its dimension, some formulations may be preferred.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45017909","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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