The Heston-Dupire model is a well-established stochastic local volatility model that offers a non-parametric representation. This model is known to closely match the implied volatility surface of options observed in the market. However, due to its non-parametric local component, Monte Carlo simulation is the only viable numerical method for derivative pricing under this model. This article proposes a novel willow tree method to replace Monte Carlo simulation for pricing exotic options and VIX options under the Heston-Dupire model. We provide the convergence rate of this method and conduct several numerical experiments to demonstrate its accuracy and efficiency. Our proposed method offers an alternative numerical technique that can enhance the computational efficiency of pricing derivatives under the Heston-Dupire model.
{"title":"VIX Option Pricing for Non-Parameter Heston Stochastic Local Volatility Model","authors":"Junmei Ma, Jiaxing Gong, Wei Xu","doi":"10.3905/jod.2023.1.195","DOIUrl":"https://doi.org/10.3905/jod.2023.1.195","url":null,"abstract":"The Heston-Dupire model is a well-established stochastic local volatility model that offers a non-parametric representation. This model is known to closely match the implied volatility surface of options observed in the market. However, due to its non-parametric local component, Monte Carlo simulation is the only viable numerical method for derivative pricing under this model. This article proposes a novel willow tree method to replace Monte Carlo simulation for pricing exotic options and VIX options under the Heston-Dupire model. We provide the convergence rate of this method and conduct several numerical experiments to demonstrate its accuracy and efficiency. Our proposed method offers an alternative numerical technique that can enhance the computational efficiency of pricing derivatives under the Heston-Dupire model.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"12 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135873803","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}
Over-the-counter (OTC) derivatives are subject to counterparty credit risk (CCR), in that a counterparty could jump to default or its credit spread could vary over time. In Basel 3 and 4, OTC market risk, CCR risk, and credit valuation adjustment (CVA) risk capital requirements are designed on a standalone basis, against Basel’s own wishes of integrated market and credit risks. This global regulatory framework—whilst an honest attempt to treat a subject as complex as OTC counterparty risk—is severely fragmented and burdensome, because of its astronomical implementation, operational and regulatory costs, and inability to accommodate newly emerged valuation adjustments. This article presents a holistic OTC-derivatives risk capital framework, based on an integrated pricing model of market risk and CCR. The proposed framework drops CVA capital and CCR in the hope of pulling OTC derivatives closer to their real economic risk, streamlining Basel capital requirements rules, cutting costs, and revitalizing the limited uncollateralized OTC customer businesses.
{"title":"Beyond Basel 4: Integrating Over-the-Counter Derivatives Risk Capital Requirements","authors":"Wujiang Lou, Gavin Xu","doi":"10.3905/jod.2023.1.194","DOIUrl":"https://doi.org/10.3905/jod.2023.1.194","url":null,"abstract":"Over-the-counter (OTC) derivatives are subject to counterparty credit risk (CCR), in that a counterparty could jump to default or its credit spread could vary over time. In Basel 3 and 4, OTC market risk, CCR risk, and credit valuation adjustment (CVA) risk capital requirements are designed on a standalone basis, against Basel’s own wishes of integrated market and credit risks. This global regulatory framework—whilst an honest attempt to treat a subject as complex as OTC counterparty risk—is severely fragmented and burdensome, because of its astronomical implementation, operational and regulatory costs, and inability to accommodate newly emerged valuation adjustments. This article presents a holistic OTC-derivatives risk capital framework, based on an integrated pricing model of market risk and CCR. The proposed framework drops CVA capital and CCR in the hope of pulling OTC derivatives closer to their real economic risk, streamlining Basel capital requirements rules, cutting costs, and revitalizing the limited uncollateralized OTC customer businesses.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312601","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 commodity ETF market has reached an equilibrium where most precious-metal ETFs are backed with physical assets, while other commodity ETFs tend to be backed with futures contracts. In this study, we consider the impact that these two different approaches have on the built-in arbitrage mechanism for ETFs, and find that the arbitrage mechanism for physical-backed ETFs works better. Futures-backed ETFs are smaller and less liquid, which we find contributes to the decreased arbitrage activity. We speculate that the significantly higher fees for futures-backed ETFs contribute to the lack of scale necessary to maintain close tracking of the ETF net asset value through arbitrage.
{"title":"Commodity ETF Arbitrage: Futures-Backed versus Physical-Backed ETFs","authors":"Denver H. Travis, Jon A. Fulkerson","doi":"10.3905/jod.2023.1.193","DOIUrl":"https://doi.org/10.3905/jod.2023.1.193","url":null,"abstract":"The commodity ETF market has reached an equilibrium where most precious-metal ETFs are backed with physical assets, while other commodity ETFs tend to be backed with futures contracts. In this study, we consider the impact that these two different approaches have on the built-in arbitrage mechanism for ETFs, and find that the arbitrage mechanism for physical-backed ETFs works better. Futures-backed ETFs are smaller and less liquid, which we find contributes to the decreased arbitrage activity. We speculate that the significantly higher fees for futures-backed ETFs contribute to the lack of scale necessary to maintain close tracking of the ETF net asset value through arbitrage.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135315972","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 article explores the use of lattice-based approximation schemes for pricing and hedging financial derivatives under GARCH models. The explosion problem and the computational cost associated with the implementation of GARCH-based trees have been well documented in the literature. To address these shortcomings, we propose a truncated mean-tracking tree that limits the number of nodes generated within the tree, focusing only on the relevant state space of the GARCH model. We assess the efficiency and accuracy of our approach by computing European style option prices and optimal quadratic hedges derived based on the local-risk minimization criteria under the physical measure. We test the effectiveness of our approach relative to the standard mean-tracking tree benchmark using different sets of GARCH parameters. Overall, we find that our truncation strategy significantly reduces the computational cost of implementing the tree, without sacrificing its accuracy, the largest gains being noticed for longer-term maturity contracts.
{"title":"Efficient Implementation of Tree-Based Option Pricing and Hedging Algorithms under GARCH Models","authors":"Zhiyu Guo, Maciej Augustyniak, Alexandru Badescu","doi":"10.3905/jod.2023.1.192","DOIUrl":"https://doi.org/10.3905/jod.2023.1.192","url":null,"abstract":"This article explores the use of lattice-based approximation schemes for pricing and hedging financial derivatives under GARCH models. The explosion problem and the computational cost associated with the implementation of GARCH-based trees have been well documented in the literature. To address these shortcomings, we propose a truncated mean-tracking tree that limits the number of nodes generated within the tree, focusing only on the relevant state space of the GARCH model. We assess the efficiency and accuracy of our approach by computing European style option prices and optimal quadratic hedges derived based on the local-risk minimization criteria under the physical measure. We test the effectiveness of our approach relative to the standard mean-tracking tree benchmark using different sets of GARCH parameters. Overall, we find that our truncation strategy significantly reduces the computational cost of implementing the tree, without sacrificing its accuracy, the largest gains being noticed for longer-term maturity contracts.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135759271","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, we propose a methodology for measuring the information flows that underpin option price movements and for analyzing the distribution of these flows. We develop a framework in which information flows can be measured in terms of the relative entropy between the risk-neutral distributions obtained from implied volatility data at different dates. We set up a numerical methodology to compute such quantities using an empirical market dataset that corresponds to options written on the S&P 500 index. This methodology uses Normal Inverse Gaussian distributions for the log-return of the index. We apply our method to six years of daily data, from 2015 to 2021, and find that options with short maturities capture a greater share of new information. We also use a mixture of two exponential distributions to analyze the distribution of the information flows obtained. In this mixture, one component corresponds to frequent small values and the other to less frequent high values.
{"title":"Measuring Information Flows in Option Markets: A Relative Entropy Approach","authors":"Eric André, Lorenz Schneider, Bertrand Tavin","doi":"10.3905/jod.2023.1.191","DOIUrl":"https://doi.org/10.3905/jod.2023.1.191","url":null,"abstract":"In this article, we propose a methodology for measuring the information flows that underpin option price movements and for analyzing the distribution of these flows. We develop a framework in which information flows can be measured in terms of the relative entropy between the risk-neutral distributions obtained from implied volatility data at different dates. We set up a numerical methodology to compute such quantities using an empirical market dataset that corresponds to options written on the S&P 500 index. This methodology uses Normal Inverse Gaussian distributions for the log-return of the index. We apply our method to six years of daily data, from 2015 to 2021, and find that options with short maturities capture a greater share of new information. We also use a mixture of two exponential distributions to analyze the distribution of the information flows obtained. In this mixture, one component corresponds to frequent small values and the other to less frequent high values.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135959868","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}
Pub Date : 2023-08-31DOI: 10.3905/jod.2023.31.1.001
Joseph M. Pimbley
{"title":"Editor’s Letter","authors":"Joseph M. Pimbley","doi":"10.3905/jod.2023.31.1.001","DOIUrl":"https://doi.org/10.3905/jod.2023.31.1.001","url":null,"abstract":"","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135891144","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 Two-Factor Contingent Convertible Bond Pricing Model with Calibrated Option-Adjusted Spread","authors":"Matthew Hyatt, Tom P. Davis, Figo Liu","doi":"10.3905/jod.2023.1.188","DOIUrl":"https://doi.org/10.3905/jod.2023.1.188","url":null,"abstract":"","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"248 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135049440","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 document that a theoretically founded, real-time, and easy-to-implement option-based measure, termed synthetic-stock difference (SSD), accurately estimates the part of stock’s expected return arising from stock’s transaction costs. We calculate SSD for US optionable stocks. SSD can be more than 10% per annum, it can fluctuate significantly over time and its cross-sectional dispersion widens over market crises periods. We confirm the accuracy of SSD by empirically verifying the predictions of a standard asset pricing setting with transaction costs. First, we document its predicted type of connection with various proxies of stocks’ transaction costs. Second, we conduct simple asset pricing tests which render further support. Our setting allows explaining the size of alphas reported by previous literature on the predictive ability of deviations from put-call parity.
{"title":"The Contribution of Transaction Costs to Expected Stock Returns: A Novel Measure","authors":"Kazuhiro Hiraki, George Skiadopoulos","doi":"10.3905/jod.2023.1.187","DOIUrl":"https://doi.org/10.3905/jod.2023.1.187","url":null,"abstract":"We document that a theoretically founded, real-time, and easy-to-implement option-based measure, termed <italic>synthetic-stock difference</italic> (SSD), accurately estimates the part of stock’s expected return arising from stock’s transaction costs. We calculate SSD for US optionable stocks. SSD can be more than 10% per annum, it can fluctuate significantly over time and its cross-sectional dispersion widens over market crises periods. We confirm the accuracy of SSD by empirically verifying the predictions of a standard asset pricing setting with transaction costs. First, we document its predicted type of connection with various proxies of stocks’ transaction costs. Second, we conduct simple asset pricing tests which render further support. Our setting allows explaining the size of alphas reported by previous literature on the predictive ability of deviations from put-call parity.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135903040","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 article derives explicit expressions to simulate theta and gamma for American options using the pathwise derivative method. Although the pathwise derivative formulas for delta, rho, and vega of American options have been studied in the literature, no correct explicit results for theta and gamma exist. In addition, we propose a simulation-based least-square method to compute the optimal stopping boundary for American options. The optimal stopping boundary is needed to evaluate our pathwise derivative expression for gamma and can be used in the integral method to calculate the price and Greeks of American options. Our proposed least-square approach to compute the optimal stopping boundary provides an alternative to the traditional recursive method of solving a system of equations. We also incorporate a Brownian bridge in the computation of the Greeks and extend the application of our results to American basket options.
{"title":"Simulating Theta and Gamma of American Options","authors":"P.A. Nguyen, Daniel Mitchell","doi":"10.3905/jod.2023.1.177","DOIUrl":"https://doi.org/10.3905/jod.2023.1.177","url":null,"abstract":"This article derives explicit expressions to simulate theta and gamma for American options using the pathwise derivative method. Although the pathwise derivative formulas for delta, rho, and vega of American options have been studied in the literature, no correct explicit results for theta and gamma exist. In addition, we propose a simulation-based least-square method to compute the optimal stopping boundary for American options. The optimal stopping boundary is needed to evaluate our pathwise derivative expression for gamma and can be used in the integral method to calculate the price and Greeks of American options. Our proposed least-square approach to compute the optimal stopping boundary provides an alternative to the traditional recursive method of solving a system of equations. We also incorporate a Brownian bridge in the computation of the Greeks and extend the application of our results to American basket options.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135383842","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 market for Adverse Development Covers and Loss Portfolio Transfer has been growing in the past few years. Despite this growth, reinsurers are still struggling to define a standard method for pricing such covers. In this context, this article aims at providing an innovative method for pricing such contracts. The proposed method is based on the famous Mack model and fits a Constant Elasticity of Variance (CEV) model to the Mack results (expected value and standard deviation) on each future development year of each accident/underwriting year. Having fitted the CEV model, it is possible to estimate the value of the Adverse Development Covers for each accident/underwriting year using standard European option pricing techniques and to compare this valuation with usual Non-Life Insurance valuation techniques. TOPICS:Derivatives, options, quantitative methods, statistical methods, risk management Key Findings ▪ It is possible to replicate the Mack model estimating the ultimate non–life insurance reserves with a CEV model and to find a good fit for the CEV model. ▪ The proposed CEV model seem to provide better results than models based solely on the ultimate view of the non–life insurance reserves. ▪ It is important to take into account not only the ultimate volatility of the insurance reserves but also the way in which the volatility develops. Such conclusion matches the usual question of the volatility smile for option pricing techniques.
{"title":"Pricing of Adverse Development Covers Using Option Pricing Methods","authors":"Eric Dal Moro","doi":"10.3905/JOD.2021.1.136","DOIUrl":"https://doi.org/10.3905/JOD.2021.1.136","url":null,"abstract":"The market for Adverse Development Covers and Loss Portfolio Transfer has been growing in the past few years. Despite this growth, reinsurers are still struggling to define a standard method for pricing such covers. In this context, this article aims at providing an innovative method for pricing such contracts. The proposed method is based on the famous Mack model and fits a Constant Elasticity of Variance (CEV) model to the Mack results (expected value and standard deviation) on each future development year of each accident/underwriting year. Having fitted the CEV model, it is possible to estimate the value of the Adverse Development Covers for each accident/underwriting year using standard European option pricing techniques and to compare this valuation with usual Non-Life Insurance valuation techniques. TOPICS:Derivatives, options, quantitative methods, statistical methods, risk management Key Findings ▪ It is possible to replicate the Mack model estimating the ultimate non–life insurance reserves with a CEV model and to find a good fit for the CEV model. ▪ The proposed CEV model seem to provide better results than models based solely on the ultimate view of the non–life insurance reserves. ▪ It is important to take into account not only the ultimate volatility of the insurance reserves but also the way in which the volatility develops. Such conclusion matches the usual question of the volatility smile for option pricing techniques.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"25 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80872573","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：