The authors propose the first closed-form price formulas for VIX futures under the widely used discrete-time symmetric GARCH(1, 1) and asymmetric Glosten–Jagannathan–Runkle (GJR) GARCH(1, 1) models. For VIX futures expired before July 21, 2017, the proposed methods, which are truly simple, perform reasonably well in out-of-sample pricing. In regard to pricing errors and efficiency, the new methods significantly outperform a continuous-time benchmark based on the Heston volatility model and a discrete-time benchmark based on the Heston–Nandi GARCH(1, 1). Empirically, GJR is the most “potent”—a term the authors apply to the ability of the model to successfully price VIX futures in the data set. The GJR potency in this study is as high as 96.6%. The novel GARCH approaches are unique with the implication of applicability in real time. Finally, an insight is gained into the research of pricing, namely, that potency is an important gauge of a pricing method. TOPICS: Futures and forward contracts, derivatives, factor-based models Key Findings • Closed-form price formulas for VIX futures under GARCH(1,1) and GJR GARCH(1,1) models are proposed. • The novel approaches are shown to be really competitive for out-of-sample, and more importantly imply applicability in real time, pricing of VIX futures. • Potency, as a gauge of the success rate of pricing, is proposed.
{"title":"Efficient Out-of-Sample Pricing of VIX Futures","authors":"Shuxin Guo, Qiang Liu","doi":"10.3905/jod.2019.1.089","DOIUrl":"https://doi.org/10.3905/jod.2019.1.089","url":null,"abstract":"The authors propose the first closed-form price formulas for VIX futures under the widely used discrete-time symmetric GARCH(1, 1) and asymmetric Glosten–Jagannathan–Runkle (GJR) GARCH(1, 1) models. For VIX futures expired before July 21, 2017, the proposed methods, which are truly simple, perform reasonably well in out-of-sample pricing. In regard to pricing errors and efficiency, the new methods significantly outperform a continuous-time benchmark based on the Heston volatility model and a discrete-time benchmark based on the Heston–Nandi GARCH(1, 1). Empirically, GJR is the most “potent”—a term the authors apply to the ability of the model to successfully price VIX futures in the data set. The GJR potency in this study is as high as 96.6%. The novel GARCH approaches are unique with the implication of applicability in real time. Finally, an insight is gained into the research of pricing, namely, that potency is an important gauge of a pricing method. TOPICS: Futures and forward contracts, derivatives, factor-based models Key Findings • Closed-form price formulas for VIX futures under GARCH(1,1) and GJR GARCH(1,1) models are proposed. • The novel approaches are shown to be really competitive for out-of-sample, and more importantly imply applicability in real time, pricing of VIX futures. • Potency, as a gauge of the success rate of pricing, is proposed.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"27 1","pages":"126 - 139"},"PeriodicalIF":0.0,"publicationDate":"2020-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47686094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Previous estimation results of risk-neutral densities explain in rather general terms that the tails of the resulting distribution “look fat,” and a way has to be found to model the tails of the estimated distribution. The author uses deep out-of-the-money S&P 500 index options to examine model mispricing of the tails of daily estimated risk-neutral densities. Out-of-sample tests show that model mispricing increases as one moves farther into the tails of the distribution. Across most moneyness groups, model mispricing increases as the option reaches maturity. The author compares two curve-fitting methods that have been proposed in the literature to estimate risk-neutral densities. The first method interpolates with a fourth-order spline and attaches tails from the general extreme value distribution (Figlewski 2010). The second method extends the available implied volatility space by balancing smoothness and fit of the estimated risk-neutral density (Jackwerth 2004). Fitting a fourth-order spline produces a closer fit to the observed implied volatilities. Examining the ability to replicate the implied volatility with the complete estimated option-implied risk-neutral density by looking at mean root-mean-square error, the method by Jackwerth (2004) resulted in lower in- and out-of-sample model mispricing, except for the deepest out-of-the-money put options. TOPICS: Tail risks, options Key Findings • This article compares two methods from the curve-fitting literature to estimate option-implied risk-neutral densities and looks at the accuracy to recover implied volatilities. • Model mispricing, measured by the root-mean-square error, increases for deeper out-of-the-money options. • Model mispricing increases as the option reaches its maturity across most out-of-sample moneyness groups.
{"title":"Risk-Neutral Density Estimation: Looking at the Tails","authors":"Martin Reinke","doi":"10.3905/jod.2019.1.090","DOIUrl":"https://doi.org/10.3905/jod.2019.1.090","url":null,"abstract":"Previous estimation results of risk-neutral densities explain in rather general terms that the tails of the resulting distribution “look fat,” and a way has to be found to model the tails of the estimated distribution. The author uses deep out-of-the-money S&P 500 index options to examine model mispricing of the tails of daily estimated risk-neutral densities. Out-of-sample tests show that model mispricing increases as one moves farther into the tails of the distribution. Across most moneyness groups, model mispricing increases as the option reaches maturity. The author compares two curve-fitting methods that have been proposed in the literature to estimate risk-neutral densities. The first method interpolates with a fourth-order spline and attaches tails from the general extreme value distribution (Figlewski 2010). The second method extends the available implied volatility space by balancing smoothness and fit of the estimated risk-neutral density (Jackwerth 2004). Fitting a fourth-order spline produces a closer fit to the observed implied volatilities. Examining the ability to replicate the implied volatility with the complete estimated option-implied risk-neutral density by looking at mean root-mean-square error, the method by Jackwerth (2004) resulted in lower in- and out-of-sample model mispricing, except for the deepest out-of-the-money put options. TOPICS: Tail risks, options Key Findings • This article compares two methods from the curve-fitting literature to estimate option-implied risk-neutral densities and looks at the accuracy to recover implied volatilities. • Model mispricing, measured by the root-mean-square error, increases for deeper out-of-the-money options. • Model mispricing increases as the option reaches its maturity across most out-of-sample moneyness groups.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"27 1","pages":"125 - 99"},"PeriodicalIF":0.0,"publicationDate":"2020-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41335113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider derivatives that maximize an investor’s expected utility in the stochastic volatility model. We show that the optimal derivative that depends on the stock and its variance significantly outperforms the optimal derivative that depends on the stock only. Such derivatives yield a much higher certainty equivalent return. This result implies that investors could benefit from structured financial products constructed along these ideas. TOPICS: Derivatives, fixed income and structured finance Key Findings ▪ A derivative is optimal if it maximizes an investor’s expected utility. In the stochastic volatility model, the optimal buy-and-hold derivative with the payoff that depends on the stock price and its volatility incorporates both the market risk premium and the variance risk premium. ▪ The optimal buy-and-hold derivative with the payoff that depends on the stock price and its volatility usually outperforms significantly both the optimal buy-and-hold derivative with the payoff that depends on the stock price only and the optimal buy-and-hold portfolio made up of the stock and the risk-free bond. ▪ Investors could benefit from derivatives with payoffs that depend on the stock price and its volatility.
{"title":"Optimal Volatility Dependent Derivatives in the Stochastic Volatility Model","authors":"Artem Dyachenko, M. Rieger","doi":"10.2139/ssrn.3508670","DOIUrl":"https://doi.org/10.2139/ssrn.3508670","url":null,"abstract":"We consider derivatives that maximize an investor’s expected utility in the stochastic volatility model. We show that the optimal derivative that depends on the stock and its variance significantly outperforms the optimal derivative that depends on the stock only. Such derivatives yield a much higher certainty equivalent return. This result implies that investors could benefit from structured financial products constructed along these ideas. TOPICS: Derivatives, fixed income and structured finance Key Findings ▪ A derivative is optimal if it maximizes an investor’s expected utility. In the stochastic volatility model, the optimal buy-and-hold derivative with the payoff that depends on the stock price and its volatility incorporates both the market risk premium and the variance risk premium. ▪ The optimal buy-and-hold derivative with the payoff that depends on the stock price and its volatility usually outperforms significantly both the optimal buy-and-hold derivative with the payoff that depends on the stock price only and the optimal buy-and-hold portfolio made up of the stock and the risk-free bond. ▪ Investors could benefit from derivatives with payoffs that depend on the stock price and its volatility.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"28 1","pages":"24 - 44"},"PeriodicalIF":0.0,"publicationDate":"2019-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45019819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article barrier options are analytically evaluated under the regime-switching model, with the volatility of the underlying price being allowed to jump between different states following a Markov chain. The target barrier option prices are expressed in a Fourier cosine series after a particular approximation formula is obtained. The accuracy and efficiency of the newly derived formula are demonstrated through numerical experiments, demonstrating the formula’s potential for practical applications. TOPICS: Analysis of individual factors/risk premia, factor-based models, options Key Findings • Barrier options are analytically evaluated under the regime-switching model. • This approximation formula is written in the form of a converged Fourier cosine series. • The formula is shown to be very accurate and efficient, and has a great potential to be applied in practice.
{"title":"Analytical Approximation Formula for Barrier Option Prices under the Regime-Switching Model","authors":"Xin‐Jiang He, Song‐Ping Zhu","doi":"10.3905/jod.2019.1.088","DOIUrl":"https://doi.org/10.3905/jod.2019.1.088","url":null,"abstract":"In this article barrier options are analytically evaluated under the regime-switching model, with the volatility of the underlying price being allowed to jump between different states following a Markov chain. The target barrier option prices are expressed in a Fourier cosine series after a particular approximation formula is obtained. The accuracy and efficiency of the newly derived formula are demonstrated through numerical experiments, demonstrating the formula’s potential for practical applications. TOPICS: Analysis of individual factors/risk premia, factor-based models, options Key Findings • Barrier options are analytically evaluated under the regime-switching model. • This approximation formula is written in the form of a converged Fourier cosine series. • The formula is shown to be very accurate and efficient, and has a great potential to be applied in practice.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"27 1","pages":"108 - 119"},"PeriodicalIF":0.0,"publicationDate":"2019-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41671495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abootaleb Shirvani, Yuan Hu, S. Rachev, F. Fabozzi
It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this article, the authors reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, they employ the method of subordination that has been proposed in the literature by including business (intrinsic, market) time. They define a mixed Lévy subordinated model by adding a single subordinated Lévy process to the well-known log-normal model, resulting in a new log-price process. They apply the proposed models to study the behavioral finance notion of “greed and fear” disposition from the perspective of rational dynamic asset pricing theory. The greedy or fearful disposition of option traders is studied using the shape of the probability weighting function. They then derive the implied probability weighting function for the fear and greed deposition of option traders in comparison to spot traders. Their result shows the diminishing sensitivity of option traders. Diminishing sensitivity results in option traders overweighting the probability of big losses in comparison to spot traders. TOPICS: Derivatives, options Key Findings • Behavioral finance and rational finance are reconciled by using a mixed Lévy subordinated process. • The mixed Lévy subordinated process develops a more realistic asset pricing model by incorporating the behavior and sentiment of investors in the log-return pricing model. • The implied probability weighting function under the mixed Lévy subordinated process model indicates the diminishing sensitivity of option traders.
{"title":"Option Pricing with Mixed Lévy Subordinated Price Process and Implied Probability Weighting Function","authors":"Abootaleb Shirvani, Yuan Hu, S. Rachev, F. Fabozzi","doi":"10.3905/jod.2020.1.102","DOIUrl":"https://doi.org/10.3905/jod.2020.1.102","url":null,"abstract":"It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this article, the authors reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, they employ the method of subordination that has been proposed in the literature by including business (intrinsic, market) time. They define a mixed Lévy subordinated model by adding a single subordinated Lévy process to the well-known log-normal model, resulting in a new log-price process. They apply the proposed models to study the behavioral finance notion of “greed and fear” disposition from the perspective of rational dynamic asset pricing theory. The greedy or fearful disposition of option traders is studied using the shape of the probability weighting function. They then derive the implied probability weighting function for the fear and greed deposition of option traders in comparison to spot traders. Their result shows the diminishing sensitivity of option traders. Diminishing sensitivity results in option traders overweighting the probability of big losses in comparison to spot traders. TOPICS: Derivatives, options Key Findings • Behavioral finance and rational finance are reconciled by using a mixed Lévy subordinated process. • The mixed Lévy subordinated process develops a more realistic asset pricing model by incorporating the behavior and sentiment of investors in the log-return pricing model. • The implied probability weighting function under the mixed Lévy subordinated process model indicates the diminishing sensitivity of option traders.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"28 1","pages":"47 - 58"},"PeriodicalIF":0.0,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42939603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Traditional plain vanilla options may be regarded as contingent claims whose value depends upon the simple returns of an underlying asset. These options have convex payoffs, and as a consequence of Jensen’s inequality, their prices increase as a function of maturity in the absence of interest rates. This results in long-dated call option premia being excessively expensive in relation to the fraction of a corresponding insured portfolio. We show that replacing the simple return payoff with the log return call option payoff leads to substantial premium savings while providing the similar insurance protection. Call options on log returns have favorable prices for very long maturities on the scale of decades. This property enables them to be attractive securities for long-term investors, such as pension funds. TOPICS: Options, pension funds Key Findings ▪ This article develops valuation and risk techniques for a log return payoff option under a Geometric Brownian Motion. ▪ A comparison is made between premium advantages of the log return contract to those of traditional European options. ▪ A pricing and optimal excise boundary formula for perpetual and finite maturity American log return options id derived. ▪ This article examines long-term insurance applications of the new contract that are prohibitively expensive for traditional options.
{"title":"The Premium Reduction of European, American, and Perpetual Log Return Options","authors":"Stephen Michael Taylor, J. Vecer","doi":"10.2139/ssrn.3467150","DOIUrl":"https://doi.org/10.2139/ssrn.3467150","url":null,"abstract":"Traditional plain vanilla options may be regarded as contingent claims whose value depends upon the simple returns of an underlying asset. These options have convex payoffs, and as a consequence of Jensen’s inequality, their prices increase as a function of maturity in the absence of interest rates. This results in long-dated call option premia being excessively expensive in relation to the fraction of a corresponding insured portfolio. We show that replacing the simple return payoff with the log return call option payoff leads to substantial premium savings while providing the similar insurance protection. Call options on log returns have favorable prices for very long maturities on the scale of decades. This property enables them to be attractive securities for long-term investors, such as pension funds. TOPICS: Options, pension funds Key Findings ▪ This article develops valuation and risk techniques for a log return payoff option under a Geometric Brownian Motion. ▪ A comparison is made between premium advantages of the log return contract to those of traditional European options. ▪ A pricing and optimal excise boundary formula for perpetual and finite maturity American log return options id derived. ▪ This article examines long-term insurance applications of the new contract that are prohibitively expensive for traditional options.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"28 1","pages":"7 - 23"},"PeriodicalIF":0.0,"publicationDate":"2019-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46196814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article shows that previous findings of the superior performance of covered calls on the S&P 500 are spurious because they ignore or dismiss skewness. While academics have previously identified this problem, the financial industry has largely ignored it. The authors show how the problem manifests in that traditional performance measures used in other studies show superior performance even with correctly priced options. They present two new estimates of covered call alphas—one that embeds a benchmark and the other that subtracts the benchmark—and find little basis for these prior claims. The authors also identify a bias in previous studies in which the chosen holding period disguises the effect of skewness. Their results, which are supported in both monthly and daily data, are consistent with intuition that holding the index and selling these widely traded options cannot generate alpha, as has been highly promoted in several practitioner articles. TOPICS: Options, performance measurement, exchange-traded funds and applications Key Findings • The documented abnormal performance of covered call writing is largely driven by disregard of skewness. • There are simple measures that can adjust the alpha of an option strategy for skewness. • The positioning of the holding period during the expiration month can disguise the problem.
{"title":"The “Superior Performance” of Covered Calls on the S&P 500: Rethinking an Anomaly","authors":"R. Brooks, D. Chance, M. L. Hemler","doi":"10.3905/jod.2019.1.087","DOIUrl":"https://doi.org/10.3905/jod.2019.1.087","url":null,"abstract":"This article shows that previous findings of the superior performance of covered calls on the S&P 500 are spurious because they ignore or dismiss skewness. While academics have previously identified this problem, the financial industry has largely ignored it. The authors show how the problem manifests in that traditional performance measures used in other studies show superior performance even with correctly priced options. They present two new estimates of covered call alphas—one that embeds a benchmark and the other that subtracts the benchmark—and find little basis for these prior claims. The authors also identify a bias in previous studies in which the chosen holding period disguises the effect of skewness. Their results, which are supported in both monthly and daily data, are consistent with intuition that holding the index and selling these widely traded options cannot generate alpha, as has been highly promoted in several practitioner articles. TOPICS: Options, performance measurement, exchange-traded funds and applications Key Findings • The documented abnormal performance of covered call writing is largely driven by disregard of skewness. • There are simple measures that can adjust the alpha of an option strategy for skewness. • The positioning of the holding period during the expiration month can disguise the problem.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"27 1","pages":"50 - 61"},"PeriodicalIF":0.0,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46945724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The objective of this article is to evaluate the performance of the option pricing model at the cross-sectional level. For that purpose, the authors propose a statistical framework, in which they in particular account for the uncertainty associated with the reported pricing performance. Instead of a single figure, the authors determine an entire probability distribution function for the loss function that is used to measure the performance of the option pricing model. This method enables them to visualize the effect of parameter uncertainty on the reported pricing performance. Using a data-driven approach, the authors confirm previous evidence that standard volatility models with clustering and leverage effects are sufficient for the option pricing purpose. In addition, they demonstrate that there is short-term persistence but long-term heterogeneity in cross-sectional option pricing information. This finding has two important implications. First, it justifies the practitioner’s routine to refrain from time series approaches and instead estimate option pricing models on a cross section by cross section basis. Second, the long-term heterogeneity in option prices pinpoints the importance of measuring, comparing, and testing the option pricing model for each cross section separately. To the authors’ knowledge no statistical testing framework has previously been applied to a single cross section of option prices. They propose a method that addresses that need. The proposed framework can be applied to a broad set of models and data. In the empirical part of the article, they show by means of example, an application that uses a discrete time volatility model on S&P 500 index options. TOPICS: Options, volatility measures Key Findings • Absolute pricing performance, measured by a loss-function, is an inappropriate criteria to benchmark competing option pricing models at the cross-sectional level. • The long-term heterogeneity in cross-sectional option pricing information and the uncertainty of reported pricing performance calls for the necessity to rely on an entire probability distribution function of the loss function when comparing models performance. • This article proposes a statistical framework, based on a data-driven approach, to compare model performance accounting for model uncertainty applicable to a single cross-section of option prices.
{"title":"Model Uncertainty and Pricing Performance in Option Valuation","authors":"D. Bams, Gildas Blanchard, T. Lehnert","doi":"10.3905/jod.2019.1.086","DOIUrl":"https://doi.org/10.3905/jod.2019.1.086","url":null,"abstract":"The objective of this article is to evaluate the performance of the option pricing model at the cross-sectional level. For that purpose, the authors propose a statistical framework, in which they in particular account for the uncertainty associated with the reported pricing performance. Instead of a single figure, the authors determine an entire probability distribution function for the loss function that is used to measure the performance of the option pricing model. This method enables them to visualize the effect of parameter uncertainty on the reported pricing performance. Using a data-driven approach, the authors confirm previous evidence that standard volatility models with clustering and leverage effects are sufficient for the option pricing purpose. In addition, they demonstrate that there is short-term persistence but long-term heterogeneity in cross-sectional option pricing information. This finding has two important implications. First, it justifies the practitioner’s routine to refrain from time series approaches and instead estimate option pricing models on a cross section by cross section basis. Second, the long-term heterogeneity in option prices pinpoints the importance of measuring, comparing, and testing the option pricing model for each cross section separately. To the authors’ knowledge no statistical testing framework has previously been applied to a single cross section of option prices. They propose a method that addresses that need. The proposed framework can be applied to a broad set of models and data. In the empirical part of the article, they show by means of example, an application that uses a discrete time volatility model on S&P 500 index options. TOPICS: Options, volatility measures Key Findings • Absolute pricing performance, measured by a loss-function, is an inappropriate criteria to benchmark competing option pricing models at the cross-sectional level. • The long-term heterogeneity in cross-sectional option pricing information and the uncertainty of reported pricing performance calls for the necessity to rely on an entire probability distribution function of the loss function when comparing models performance. • This article proposes a statistical framework, based on a data-driven approach, to compare model performance accounting for model uncertainty applicable to a single cross-section of option prices.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"27 1","pages":"31 - 49"},"PeriodicalIF":0.0,"publicationDate":"2019-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41541145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mainstream option valuation theory relies implicitly on the assumption that latent states (such as stochastic volatility) and parameters are perfectly known, an assumption that is dubious in many ways. Computing the value of options under the assumption of perfect knowledge will typically introduce bias. Correcting for the bias is straightforward but can be computationally expensive. Fourier-based methods for computing option values are nowadays the preferred computational technique in the financial industry as a result of speed and accuracy. The author shows that the bias correction for parameter and state uncertainty for a large class of processes can be incorporated into the Fourier framework, resulting in substantial computational savings compared with Monte Carlo methods or deterministic quadrature rules previously used. In addition, the author proposes extensions, such as time varying parameters and hyperparameters, to the class of uncertainty models. The author finds that the proposed Fourier method is retaining all the good properties that are associated with Fourier methods; it is fast, accurate, and applicable to a wide range of models. Furthermore, the empirical performance of the corrected models is almost uniformly better than that of their noncorrected counterparts when evaluated on S&P 500 option data. TOPICS: Derivatives, options, factor-based models, analysis of individual factors/risk premia Key Findings • Parameter and state uncertainty in option models is often ignored but this leads to bias. • The bias correction introduced in this paper can be computed through the standard Fourier methodology, being fast and accurate. • The methodology results in better model in-sample and out-of-sample for a wide range of models, and the best results are found for parameters where the uncertainty is substantial.
{"title":"Fourier Method for Valuation of Options under Parameter and State Uncertainty","authors":"Erik Lindström","doi":"10.3905/jod.2019.1.085","DOIUrl":"https://doi.org/10.3905/jod.2019.1.085","url":null,"abstract":"Mainstream option valuation theory relies implicitly on the assumption that latent states (such as stochastic volatility) and parameters are perfectly known, an assumption that is dubious in many ways. Computing the value of options under the assumption of perfect knowledge will typically introduce bias. Correcting for the bias is straightforward but can be computationally expensive. Fourier-based methods for computing option values are nowadays the preferred computational technique in the financial industry as a result of speed and accuracy. The author shows that the bias correction for parameter and state uncertainty for a large class of processes can be incorporated into the Fourier framework, resulting in substantial computational savings compared with Monte Carlo methods or deterministic quadrature rules previously used. In addition, the author proposes extensions, such as time varying parameters and hyperparameters, to the class of uncertainty models. The author finds that the proposed Fourier method is retaining all the good properties that are associated with Fourier methods; it is fast, accurate, and applicable to a wide range of models. Furthermore, the empirical performance of the corrected models is almost uniformly better than that of their noncorrected counterparts when evaluated on S&P 500 option data. TOPICS: Derivatives, options, factor-based models, analysis of individual factors/risk premia Key Findings • Parameter and state uncertainty in option models is often ignored but this leads to bias. • The bias correction introduced in this paper can be computed through the standard Fourier methodology, being fast and accurate. • The methodology results in better model in-sample and out-of-sample for a wide range of models, and the best results are found for parameters where the uncertainty is substantial.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"27 1","pages":"62 - 80"},"PeriodicalIF":0.0,"publicationDate":"2019-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43067661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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