The volatility/time horizon connection is critical for estimating risk and for constructing downside-risk management and upside capture strategies. Differences in perceived risk depend on the return interval over which volatility is measured and should be aligned with the horizon for monitoring and rebalancing an investment strategy. A comparison of realized S&P 500 volatility measured from daily versus monthly returns over the 2000–2021 period showed that daily returns were about 30% more volatile on average than monthly returns. This time variation in volatility also impacts the selection of strike prices for option strategy design. The distribution of S&P 500 total returns for investment horizons ranging from 1 to 12 months was examined to assess the differences in the frequency of outcomes relative to threshold levels across holding periods. The net delta of an option strategy is the best guide for comparing options of different terms, enabling investors with different horizons to select option strike prices consistent with their targeted return distributions.
{"title":"The Time Dimension of Volatility: Implications for Option Strategy Design","authors":"Joanne M. Hill","doi":"10.3905/jod.2022.1.152","DOIUrl":"https://doi.org/10.3905/jod.2022.1.152","url":null,"abstract":"The volatility/time horizon connection is critical for estimating risk and for constructing downside-risk management and upside capture strategies. Differences in perceived risk depend on the return interval over which volatility is measured and should be aligned with the horizon for monitoring and rebalancing an investment strategy. A comparison of realized S&P 500 volatility measured from daily versus monthly returns over the 2000–2021 period showed that daily returns were about 30% more volatile on average than monthly returns. This time variation in volatility also impacts the selection of strike prices for option strategy design. The distribution of S&P 500 total returns for investment horizons ranging from 1 to 12 months was examined to assess the differences in the frequency of outcomes relative to threshold levels across holding periods. The net delta of an option strategy is the best guide for comparing options of different terms, enabling investors with different horizons to select option strike prices consistent with their targeted return distributions.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"97 - 109"},"PeriodicalIF":0.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45627257","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}
Pub Date : 2022-02-13DOI: 10.3905/jod.2022.30.2.141
P. Carr, A. Itkin, D. Muravey
This article develops the generalized integral transform (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier), whereby the option price is represented in a semi-analytical form as a two-dimensional (2D) integral. This integral depends on the as yet unknown function Φ(t, v), which is the gradient of the solution at the moving boundary S = L(t), and solves a linear mixed Volterra–Fredholm equation of the second kind, also derived in this article. Thus, the authors generalize the one-dimensional (1D) GIT method developed in Itkin, Lipton, and Muravey (2021) and the corresponding articles to the 2D case. In other words, we show that the GIT method can be extended to stochastic volatility models (two drivers with inhomogeneous correlation). As such, this 2D approach naturally inherits all advantages of the corresponding 1D methods—in particular, their speed and accuracy. This result is new and has various applications not only in finance, but also in physics. Numerical examples illustrate the high speed and accuracy of the method compared with the finite-difference approach.
本文发展了基于时间依赖的Heston模型(也具有时间依赖的障碍)中定价障碍期权的广义积分变换(GIT)方法，其中期权价格以半解析形式表示为二维(2D)积分。该积分依赖于目前未知的函数Φ(t, v)，该函数是移动边界S = L(t)处解的梯度，并解出了第二类线性混合Volterra-Fredholm方程，该方程也在本文中导出。因此，作者将Itkin, Lipton, and Muravey(2021)和相应文章中开发的一维(1D) GIT方法推广到二维情况。换句话说，我们表明GIT方法可以扩展到随机波动率模型(两个非齐次相关的驱动因素)。因此，这种二维方法自然继承了相应的一维方法的所有优点，特别是它们的速度和准确性。这个结果是新的，不仅在金融方面，而且在物理学方面都有各种各样的应用。数值算例表明，与有限差分法相比，该方法具有较高的速度和精度。
{"title":"Semi-Analytical Pricing of Barrier Options in the Time-Dependent Heston Model","authors":"P. Carr, A. Itkin, D. Muravey","doi":"10.3905/jod.2022.30.2.141","DOIUrl":"https://doi.org/10.3905/jod.2022.30.2.141","url":null,"abstract":"This article develops the generalized integral transform (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier), whereby the option price is represented in a semi-analytical form as a two-dimensional (2D) integral. This integral depends on the as yet unknown function Φ(t, v), which is the gradient of the solution at the moving boundary S = L(t), and solves a linear mixed Volterra–Fredholm equation of the second kind, also derived in this article. Thus, the authors generalize the one-dimensional (1D) GIT method developed in Itkin, Lipton, and Muravey (2021) and the corresponding articles to the 2D case. In other words, we show that the GIT method can be extended to stochastic volatility models (two drivers with inhomogeneous correlation). As such, this 2D approach naturally inherits all advantages of the corresponding 1D methods—in particular, their speed and accuracy. This result is new and has various applications not only in finance, but also in physics. Numerical examples illustrate the high speed and accuracy of the method compared with the finite-difference approach.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"141 - 171"},"PeriodicalIF":0.0,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42110205","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 a low-rate environment, government bonds may not mitigate equity risk as well as they have in the past. This structural shift has profound implications for asset allocation. Historically, the expected return of government bonds has been positive, and they have mitigated downside risk. In other words, they have offered something even better than free insurance: they have paid investors to buy insurance. In contrast, many option-based protection strategies are costly. Unlike government bonds, options almost always come with a negative expected return. But with real yields on most government bonds in negative territory, the tradeoffs may have changed. To control for downside risk in a low-rate environment, should asset allocators sell stocks to buy more government bonds, or should they keep a high(er) stock allocation and “hedge the tails”? We show that the answer depends on both your view on bonds and how tail risk hedging is implemented. Adding a delta-hedging program can significantly reduce, but not eliminate, the cost of tail risk hedging in addition to reducing path dependent equity exposure. The ultimate benefit of a tail risk hedging program to a multi-asset investor increases the more bearish you are on bonds.
{"title":"Tail Risk Hedging in a Low-Rate Environment","authors":"R. L. Harlow, Stefan Hubrich, Sébastien Page","doi":"10.3905/jod.2022.1.150","DOIUrl":"https://doi.org/10.3905/jod.2022.1.150","url":null,"abstract":"In a low-rate environment, government bonds may not mitigate equity risk as well as they have in the past. This structural shift has profound implications for asset allocation. Historically, the expected return of government bonds has been positive, and they have mitigated downside risk. In other words, they have offered something even better than free insurance: they have paid investors to buy insurance. In contrast, many option-based protection strategies are costly. Unlike government bonds, options almost always come with a negative expected return. But with real yields on most government bonds in negative territory, the tradeoffs may have changed. To control for downside risk in a low-rate environment, should asset allocators sell stocks to buy more government bonds, or should they keep a high(er) stock allocation and “hedge the tails”? We show that the answer depends on both your view on bonds and how tail risk hedging is implemented. Adding a delta-hedging program can significantly reduce, but not eliminate, the cost of tail risk hedging in addition to reducing path dependent equity exposure. The ultimate benefit of a tail risk hedging program to a multi-asset investor increases the more bearish you are on bonds.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"110 - 120"},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46129882","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}
Paul Bouchey, Benjamin Hood, A. Kramer, Clint Talmo
In this article, we cover the basics of how derivatives currently are taxed and the key considerations of which investors and portfolio managers should be aware, such as wash sales, tax straddles, and constructive sales. We also highlight an example of how derivatives can be used to tax-efficiently hedge and monetize a concentrated stock position. Often, articles addressing taxation focus on nuance and the specific cases in which exceptions apply. In this article, we seek clarity over completeness. Our goal is to summarize the tax rules for derivatives in a way that is accessible to investors and investment professionals. We limit our discussion to securities products, not other sorts of investments, and to those taxpayers that are classified as investors, not dealers or business hedgers. The piecemeal nature of the US tax law with respect to derivatives creates complications for portfolio managers. Some trades are taxed more heavily than others, which emphasizes the need for careful tax consideration when using derivatives.
{"title":"Taxes and Derivatives: An Investor’s Perspective","authors":"Paul Bouchey, Benjamin Hood, A. Kramer, Clint Talmo","doi":"10.3905/jod.2022.1.149","DOIUrl":"https://doi.org/10.3905/jod.2022.1.149","url":null,"abstract":"In this article, we cover the basics of how derivatives currently are taxed and the key considerations of which investors and portfolio managers should be aware, such as wash sales, tax straddles, and constructive sales. We also highlight an example of how derivatives can be used to tax-efficiently hedge and monetize a concentrated stock position. Often, articles addressing taxation focus on nuance and the specific cases in which exceptions apply. In this article, we seek clarity over completeness. Our goal is to summarize the tax rules for derivatives in a way that is accessible to investors and investment professionals. We limit our discussion to securities products, not other sorts of investments, and to those taxpayers that are classified as investors, not dealers or business hedgers. The piecemeal nature of the US tax law with respect to derivatives creates complications for portfolio managers. Some trades are taxed more heavily than others, which emphasizes the need for careful tax consideration when using derivatives.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"139 - 151"},"PeriodicalIF":0.0,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47251199","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}
Research suggests that systematic tail risk affects the cross-sectional variation in hedge fund returns. High tail risk hedge funds are known to be exposed to higher-moment risks; they sell market volatility risk and buy market skewness risk. The relationship between a tail risk strategy and a market skewness factor is expected to be positive, but I find it to be negative. Using equity-oriented hedge fund return data, I find that equity market skewness risk explains a major part of variation in hedge funds’ tail risk. My results suggest that the observed negative relationship relates to the problem of price pressure associated with “crowded trades” of mutual funds. In particular, in times when investors shift their funds from bond to equity mutual funds, short selling in the index options market induces a negative relationship between risk-neutral market skewness and returns. Accordingly, the long leg of the tail risk strategy appears to be negatively exposed to market skewness risk, which is in contrast to the usual interpretation of option-implied skewness as an indicator of downside risk.
{"title":"Is Risk-Neutral Skewness an Indicator of Downside Risk? Evidence from Tail Risk Taking of Hedge Funds","authors":"T. Lehnert","doi":"10.3905/jod.2022.1.148","DOIUrl":"https://doi.org/10.3905/jod.2022.1.148","url":null,"abstract":"Research suggests that systematic tail risk affects the cross-sectional variation in hedge fund returns. High tail risk hedge funds are known to be exposed to higher-moment risks; they sell market volatility risk and buy market skewness risk. The relationship between a tail risk strategy and a market skewness factor is expected to be positive, but I find it to be negative. Using equity-oriented hedge fund return data, I find that equity market skewness risk explains a major part of variation in hedge funds’ tail risk. My results suggest that the observed negative relationship relates to the problem of price pressure associated with “crowded trades” of mutual funds. In particular, in times when investors shift their funds from bond to equity mutual funds, short selling in the index options market induces a negative relationship between risk-neutral market skewness and returns. Accordingly, the long leg of the tail risk strategy appears to be negatively exposed to market skewness risk, which is in contrast to the usual interpretation of option-implied skewness as an indicator of downside risk.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"65 - 84"},"PeriodicalIF":0.0,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45941532","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 valuation of an American-style contingent claim is discussed in a hidden Markov regime-switching jump-diffusion market, where the evolution of a hidden economic state process over time is described by a continuous-time, finite-state, hidden Markov chain. Filtering theory is applied to introduce a filtered market where the valuation problem is discussed. A probabilistic approach to American option pricing is considered, where a decomposition formula for the price of an American put option is given as the sum of its European counterpart and an early exercise premium. Then the valuation of a perpetual American put option is considered. A (semi-)analytical approximation to the perpetual American put price is obtained. Numerical results for the perpetual American put prices and critical values are provided to illustrate the approximation and to examine the impacts of probability beliefs on hidden economic regimes and jumps on the put prices and critical values.
{"title":"American Option Pricing and Filtering with a Hidden Regime-Switching Jump Diffusion","authors":"T. Siu, R. Elliott","doi":"10.3905/jod.2022.1.147","DOIUrl":"https://doi.org/10.3905/jod.2022.1.147","url":null,"abstract":"The valuation of an American-style contingent claim is discussed in a hidden Markov regime-switching jump-diffusion market, where the evolution of a hidden economic state process over time is described by a continuous-time, finite-state, hidden Markov chain. Filtering theory is applied to introduce a filtered market where the valuation problem is discussed. A probabilistic approach to American option pricing is considered, where a decomposition formula for the price of an American put option is given as the sum of its European counterpart and an early exercise premium. Then the valuation of a perpetual American put option is considered. A (semi-)analytical approximation to the perpetual American put price is obtained. Numerical results for the perpetual American put prices and critical values are provided to illustrate the approximation and to examine the impacts of probability beliefs on hidden economic regimes and jumps on the put prices and critical values.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"106 - 123"},"PeriodicalIF":0.0,"publicationDate":"2022-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47369022","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 use of credit derivatives has grown considerably over the past decade, with participation from a diverse set of institutional investors. Specifically, investors increasingly are using credit default swaps (CDS), credit default swap indices (CDX), and options on CDX to manage their portfolios. In this article, the authors demonstrate how investors apply credit derivatives in the context of portfolio management. The authors show how CDS can be used to create synthetic corporate bonds and how investors structure basis trading opportunities by taking advantage of mispricing between CDS and corporate bonds. Further, the authors illustrate how investors apply options on CDX for the purpose of hedging the tail risks of a fixed income portfolio, and they include a discussion on various methods to reduce the cost of such tail-risk-hedging strategies.
{"title":"Application of Credit Derivatives in Portfolio Management","authors":"S. Kackar, Kelly Rogal","doi":"10.3905/jod.2022.1.146","DOIUrl":"https://doi.org/10.3905/jod.2022.1.146","url":null,"abstract":"The use of credit derivatives has grown considerably over the past decade, with participation from a diverse set of institutional investors. Specifically, investors increasingly are using credit default swaps (CDS), credit default swap indices (CDX), and options on CDX to manage their portfolios. In this article, the authors demonstrate how investors apply credit derivatives in the context of portfolio management. The authors show how CDS can be used to create synthetic corporate bonds and how investors structure basis trading opportunities by taking advantage of mispricing between CDS and corporate bonds. Further, the authors illustrate how investors apply options on CDX for the purpose of hedging the tail risks of a fixed income portfolio, and they include a discussion on various methods to reduce the cost of such tail-risk-hedging strategies.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"81 - 96"},"PeriodicalIF":0.0,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45457440","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 use of options by individual investors has grown dramatically in recent years. The authors evaluate several popular options strategies, including portfolio insurance, life cycle investing, buy-write, and single-stock call-buying, from the perspective of an individual investor. The authors suggest that Expected Utility is the most appropriate metric for such evaluation, as it accounts for both return and risk, and naturally handles non-linear payoffs. They assess the different options strategies under a range of assumptions of asset price behavior, investor risk appetite, and option market pricing relative to fair value. They find that for a representative investor the benefit of adding options to the portfolio is at best quite small, and most of this improvement also can be achieved through periodic portfolio rebalancing. However, the benefits of options can be greater for several special investor categories and in certain market environments. The authors also identify several popular uses of options that are likely to be quite harmful to investor welfare.
{"title":"Do Options Belong in the Portfolios of Individual Investors?","authors":"Victor Haghani, V. Ragulin, James White","doi":"10.3905/jod.2022.1.145","DOIUrl":"https://doi.org/10.3905/jod.2022.1.145","url":null,"abstract":"The use of options by individual investors has grown dramatically in recent years. The authors evaluate several popular options strategies, including portfolio insurance, life cycle investing, buy-write, and single-stock call-buying, from the perspective of an individual investor. The authors suggest that Expected Utility is the most appropriate metric for such evaluation, as it accounts for both return and risk, and naturally handles non-linear payoffs. They assess the different options strategies under a range of assumptions of asset price behavior, investor risk appetite, and option market pricing relative to fair value. They find that for a representative investor the benefit of adding options to the portfolio is at best quite small, and most of this improvement also can be achieved through periodic portfolio rebalancing. However, the benefits of options can be greater for several special investor categories and in certain market environments. The authors also identify several popular uses of options that are likely to be quite harmful to investor welfare.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"13 - 38"},"PeriodicalIF":0.0,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42854104","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}
After the global financial crisis in 2008–2009, the transition from LIBOR to risk-free rates (RFRs) began. As the transition heads into the end game, term RFRs have become one of the most critical tasks to guarantee the success of the transition. In this review article, we present different methodologies of publishing term RFRs, compare their features, and raise potential concerns. Specifically, we display practical examples that demonstrate challenges brought up by publishing and referencing term RFRs. We conclude that the “engineered” term RFRs do not fully achieve the goals of the LIBOR transition. At the end, we discuss alternatives and the future of term RFRs. We hope this review article can serve as a caveat and cautionary document for regulators and market participants who are interested in interacting with term RFRs.
{"title":"Term Risk-Free Rates: Methodologies, Challenges, and the Future","authors":"Xi (Figo) Liu, Yu Bai","doi":"10.3905/jod.2022.1.144","DOIUrl":"https://doi.org/10.3905/jod.2022.1.144","url":null,"abstract":"After the global financial crisis in 2008–2009, the transition from LIBOR to risk-free rates (RFRs) began. As the transition heads into the end game, term RFRs have become one of the most critical tasks to guarantee the success of the transition. In this review article, we present different methodologies of publishing term RFRs, compare their features, and raise potential concerns. Specifically, we display practical examples that demonstrate challenges brought up by publishing and referencing term RFRs. We conclude that the “engineered” term RFRs do not fully achieve the goals of the LIBOR transition. At the end, we discuss alternatives and the future of term RFRs. We hope this review article can serve as a caveat and cautionary document for regulators and market participants who are interested in interacting with term RFRs.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"30 - 45"},"PeriodicalIF":0.0,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43651542","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}
Investors have always tried to use various trading strategies to juice their returns. Writing options has often been thought of as a low-risk way to get some additional income (premiums) while not disturbing the underlying asset allocation. Sometimes, however, investors are caught off guard when their option strategy does more harm than good. In this educational piece we describe one of the most common option writing strategies–covered call writing–and the practicalities of how to manage these strategies so they hopefully don’t backfire. The key is to recognize that the returns from covered call strategies are related to the volatility risk premium (also known as the variance risk premium) as well as the equity risk premium.
{"title":"Income Enhancement with Options","authors":"Megan Miller, Brian Jacobsen, Martijn de Vree","doi":"10.3905/jod.2021.1.143","DOIUrl":"https://doi.org/10.3905/jod.2021.1.143","url":null,"abstract":"Investors have always tried to use various trading strategies to juice their returns. Writing options has often been thought of as a low-risk way to get some additional income (premiums) while not disturbing the underlying asset allocation. Sometimes, however, investors are caught off guard when their option strategy does more harm than good. In this educational piece we describe one of the most common option writing strategies–covered call writing–and the practicalities of how to manage these strategies so they hopefully don’t backfire. The key is to recognize that the returns from covered call strategies are related to the volatility risk premium (also known as the variance risk premium) as well as the equity risk premium.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"29 1","pages":"153 - 167"},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47028296","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}
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：