This article presents a new variance reduction technique for diffusion processes where a control variate is constructed using a quantization of the coefficients of the Karhunen-Loeve decomposition of the underlying Brownian motion. This method may be indeed used for other Gaussian processes.
{"title":"A VARIANCE REDUCTION TECHNIQUE USING A QUANTIZED BROWNIAN MOTION AS A CONTROL VARIATE","authors":"A. Lejay, Victor Reutenauer","doi":"10.21314/JCF.2012.242","DOIUrl":"https://doi.org/10.21314/JCF.2012.242","url":null,"abstract":"This article presents a new variance reduction technique for diffusion processes where a control variate is constructed using a quantization of the coefficients of the Karhunen-Loeve decomposition of the underlying Brownian motion. This method may be indeed used for other Gaussian processes.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"16 1","pages":"61-84"},"PeriodicalIF":0.9,"publicationDate":"2012-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701219","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 a paper that appeared in volume 2 (2011) of SIAM Financial Mathematics by R. Cont, N. Lantos and the author, it was shown that by writing the solution of the Black-Scholes partial dierential equation on a small set of basis functions the computing time can be dramatically reduced. In this study we show that it is in fact a P.O.D. method and in some other variable it is also a spectral method. It allows us to nd a good preconditioning matrix to minimize the ill conditioned linear system, and even have explicit solutions.
R. Cont, N. Lantos和作者在SIAM金融数学第2卷(2011)中发表的一篇论文表明，通过在一小组基函数上写出Black-Scholes偏微分方程的解可以大大减少计算时间。在这项研究中，我们表明它实际上是一种P.O.D.方法，在某些其他变量中，它也是一种谱方法。它允许我们找到一个好的预处理矩阵来最小化病态线性系统，甚至有显式解。
{"title":"Proper Orthogonal Decomposition for Pricing Options","authors":"O. Pironneau","doi":"10.21314/JCF.2012.246","DOIUrl":"https://doi.org/10.21314/JCF.2012.246","url":null,"abstract":"In a paper that appeared in volume 2 (2011) of SIAM Financial Mathematics by R. Cont, N. Lantos and the author, it was shown that by writing the solution of the Black-Scholes partial dierential equation on a small set of basis functions the computing time can be dramatically reduced. In this study we show that it is in fact a P.O.D. method and in some other variable it is also a spectral method. It allows us to nd a good preconditioning matrix to minimize the ill conditioned linear system, and even have explicit solutions.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"16 1","pages":"33-46"},"PeriodicalIF":0.9,"publicationDate":"2012-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701603","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 pension plans based on average salary without early retirement: partial differential equation modeling and numerical solution","authors":"M. Calvo-Garrido","doi":"10.21314/JCF.2012.243","DOIUrl":"https://doi.org/10.21314/JCF.2012.243","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"16 1","pages":"111-140"},"PeriodicalIF":0.9,"publicationDate":"2012-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701258","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":"Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation","authors":"T. Haentjens, K. I. Hout","doi":"10.21314/JCF.2012.244","DOIUrl":"https://doi.org/10.21314/JCF.2012.244","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"16 1","pages":"83-110"},"PeriodicalIF":0.9,"publicationDate":"2012-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701275","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}
Diffusion processes play a major role in continuous-time modeling in economics, particularly in continuous-time finance. In most cases, however, the transition density function of a diffusion process is not available in closed form. Using Feynman-Kac integration, we construct a recursive scheme for the Laplace transform (in time) of the transition density function. This provides a semianalytic and highly accurate solution to a wide range of asset pricing problems. Generalizations of our technique to functionals of non-Gaussian processes are also briefly discussed.
{"title":"Transform analysis and asset pricing for diffusion processes: a recursive approach","authors":"M. Goovaerts, R. Laeven, Zhaoning Shang","doi":"10.21314/JCF.2012.245","DOIUrl":"https://doi.org/10.21314/JCF.2012.245","url":null,"abstract":"Diffusion processes play a major role in continuous-time modeling in economics, particularly in continuous-time finance. In most cases, however, the transition density function of a diffusion process is not available in closed form. Using Feynman-Kac integration, we construct a recursive scheme for the Laplace transform (in time) of the transition density function. This provides a semianalytic and highly accurate solution to a wide range of asset pricing problems. Generalizations of our technique to functionals of non-Gaussian processes are also briefly discussed.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"16 1","pages":"47-81"},"PeriodicalIF":0.9,"publicationDate":"2012-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701567","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":"Applications of periodic and quasiperiodic decompositions to options pricing","authors":"Dominique R. A. Bang","doi":"10.21314/JCF.2012.247","DOIUrl":"https://doi.org/10.21314/JCF.2012.247","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"16 1","pages":"3-31"},"PeriodicalIF":0.9,"publicationDate":"2012-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701675","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 a model where each company’s asset value follows a jump-diusion process, and is connected with other companies via global factors. Motivated by ideas in Bush et al. (2011), where the joint density of asset values is evolved in a large basket approximation, we develop an algorithm for the ecient estimation of CDO index and tranche spreads consistent with underlying CDSs, through a nite dierence simulation of the resulting SPDE. We verify the validity of this approximation numerically by comparison to results obtained by direct Monte Carlo simulation of the basket constituents. A calibration exercise assesses the exibility of the model and its extensions to match CDO spreads from pre-crisis and crisis periods.
{"title":"Numerical valuation of basket credit derivatives in structural jump-diffusion models","authors":"K. Bujok, C. Reisinger","doi":"10.21314/JCF.2012.249","DOIUrl":"https://doi.org/10.21314/JCF.2012.249","url":null,"abstract":"We consider a model where each company’s asset value follows a jump-diusion process, and is connected with other companies via global factors. Motivated by ideas in Bush et al. (2011), where the joint density of asset values is evolved in a large basket approximation, we develop an algorithm for the ecient estimation of CDO index and tranche spreads consistent with underlying CDSs, through a nite dierence simulation of the resulting SPDE. We verify the validity of this approximation numerically by comparison to results obtained by direct Monte Carlo simulation of the basket constituents. A calibration exercise assesses the exibility of the model and its extensions to match CDO spreads from pre-crisis and crisis periods.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"15 1","pages":"115-158"},"PeriodicalIF":0.9,"publicationDate":"2012-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701368","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 discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Foellmer-Schweizer decomposition for solving the mean-variance hedging problem. In particular, we establish that decomposition explicitely, for a large class of vanilla contingent claims. Interest is devoted in the choice of rebalancing dates and its impact on the hedging error, regarding the payoff regularity and the non stationarity of the log-price process.
{"title":"Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets","authors":"Stéphane Goutte, N. Oudjane, F. Russo","doi":"10.21314/JCF.2013.261","DOIUrl":"https://doi.org/10.21314/JCF.2013.261","url":null,"abstract":"We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Foellmer-Schweizer decomposition for solving the mean-variance hedging problem. In particular, we establish that decomposition explicitely, for a large class of vanilla contingent claims. Interest is devoted in the choice of rebalancing dates and its impact on the hedging error, regarding the payoff regularity and the non stationarity of the log-price process.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"17 1","pages":"71-111"},"PeriodicalIF":0.9,"publicationDate":"2012-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67702279","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 credit derivatives using an asymptotic expansion approach","authors":"Yoshifumi Muroi","doi":"10.21314/JCF.2012.251","DOIUrl":"https://doi.org/10.21314/JCF.2012.251","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"15 1","pages":"135-171"},"PeriodicalIF":0.9,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67701338","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 pricing and calculation of sensitivities of out-of-the-money European options under Lévy processes","authors":"S. Levendorskii, Jiayao Xie","doi":"10.21314/JCF.2012.252","DOIUrl":"https://doi.org/10.21314/JCF.2012.252","url":null,"abstract":"","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"15 1","pages":"71-133"},"PeriodicalIF":0.9,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67702041","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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