Pub Date : 2019-02-28DOI: 10.3905/jod.2019.26.3.087
László Nagy, M. Ormos
This article shows the fragility of the widely-used Stochastic Volatility Inspired (SVI) methodology in option pricing. The results highlight the sensitivity of SVI to the fitting penalty function. The authors compare different weight functions and propose to use the implied vega weights. They then unveil the relationship between vega weights and the minimization task of observed and fitted price differences, and show that implied vega weights can stabilize the SVI fit to illiquid options.
{"title":"Volatility Surface Calibration to Illiquid Options","authors":"László Nagy, M. Ormos","doi":"10.3905/jod.2019.26.3.087","DOIUrl":"https://doi.org/10.3905/jod.2019.26.3.087","url":null,"abstract":"This article shows the fragility of the widely-used Stochastic Volatility Inspired (SVI) methodology in option pricing. The results highlight the sensitivity of SVI to the fitting penalty function. The authors compare different weight functions and propose to use the implied vega weights. They then unveil the relationship between vega weights and the minimization task of observed and fitted price differences, and show that implied vega weights can stabilize the SVI fit to illiquid options.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"87 - 96"},"PeriodicalIF":0.0,"publicationDate":"2019-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2019.26.3.087","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44666009","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 provides a new methodology for pricing and hedging basket options. The authors approximate the basket by using the shifted log-normal distribution with the polynomial expansion, which can match exactly any required m moments of the basket, to give quasi-analytical formulas for the prices and hedging parameters of basket options. Numerical simulations show that the methodology provides superior results for basket option prices and hedging parameters. This methodology works well not only for regular baskets but also for negative-weight baskets and negative-value baskets. Compared with the best available methods, the authors’ methodology appears to perform better.
{"title":"A General Accurate Approximation for Pricing and Hedging Basket Options with Exact Moment Matching","authors":"Feifan Wu, Xundi Diao, Chongfeng Wu","doi":"10.3905/jod.2019.1.072","DOIUrl":"https://doi.org/10.3905/jod.2019.1.072","url":null,"abstract":"This article provides a new methodology for pricing and hedging basket options. The authors approximate the basket by using the shifted log-normal distribution with the polynomial expansion, which can match exactly any required m moments of the basket, to give quasi-analytical formulas for the prices and hedging parameters of basket options. Numerical simulations show that the methodology provides superior results for basket option prices and hedging parameters. This methodology works well not only for regular baskets but also for negative-weight baskets and negative-value baskets. Compared with the best available methods, the authors’ methodology appears to perform better.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"68 - 86"},"PeriodicalIF":0.0,"publicationDate":"2019-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2019.1.072","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49109718","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 : 2018-11-30DOI: 10.3905/jod.2018.26.2.038
B. Malkiel, Alex Rinaudo, Atanu Saha
Buy-write and put-write strategies have been shown to match market returns with lower volatility, resulting in higher risk-adjusted performance. The strategies benefit from the fact that the implied volatility of options is generally higher than actual realized volatility. In this article, we show that this premium is higher at elevated levels of implied volatility (as represented by the VIX index level). Based on this finding, we propose a simple conditional strategy in which one sells options at elevated levels of the VIX. Using data from 1990 through 2018, we find that this conditional strategy outperforms both the market and continuous option-selling strategies on an absolute and risk-adjusted basis.
{"title":"Option Writing: Using VIX to Improve Returns","authors":"B. Malkiel, Alex Rinaudo, Atanu Saha","doi":"10.3905/jod.2018.26.2.038","DOIUrl":"https://doi.org/10.3905/jod.2018.26.2.038","url":null,"abstract":"Buy-write and put-write strategies have been shown to match market returns with lower volatility, resulting in higher risk-adjusted performance. The strategies benefit from the fact that the implied volatility of options is generally higher than actual realized volatility. In this article, we show that this premium is higher at elevated levels of implied volatility (as represented by the VIX index level). Based on this finding, we propose a simple conditional strategy in which one sells options at elevated levels of the VIX. Using data from 1990 through 2018, we find that this conditional strategy outperforms both the market and continuous option-selling strategies on an absolute and risk-adjusted basis.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"38 - 49"},"PeriodicalIF":0.0,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2018.26.2.038","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46366624","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 : 2018-11-30DOI: 10.3905/jod.2018.26.2.086
M. Costabile
The problem of computing risk measures of life insurance policies is complicated by the fact that two different probability measures, the real-world probability measure along the risk horizon and the risk-neutral one along the remaining time interval, have to be used. This implies that a straightforward application of the Monte Carlo method is not available and the need arises to resort to time consuming nested simulations or to the least squares Monte Carlo approach. We propose to compute common risk measures by using the celebrated binomial model of Cox, Ross, and Rubinstein (1979) (CRR). The main advantage of this approach is that the usual construction of the CRR model is not influenced by the change of measure and a unique lattice can be used along the whole policy duration. Numerical results highlight that the proposed algorithm computes highly accurate values.
寿险保单风险度量的计算问题由于必须使用两种不同的概率度量，即沿风险范围的真实概率度量和沿剩余时间区间的风险中性概率度量而变得复杂。这意味着蒙特卡罗方法的直接应用是不可用的，需要求助于耗时的嵌套模拟或最小二乘蒙特卡罗方法。我们建议使用Cox, Ross, and Rubinstein (1979) (CRR)的著名二项式模型来计算常见的风险度量。该方法的主要优点是CRR模型的通常构造不受度量变化的影响，并且可以在整个策略持续时间内使用唯一的格。数值结果表明，该算法计算精度高。
{"title":"Computing Risk Measures of Life Insurance Policies through the Cox–Ross–Rubinstein Model","authors":"M. Costabile","doi":"10.3905/jod.2018.26.2.086","DOIUrl":"https://doi.org/10.3905/jod.2018.26.2.086","url":null,"abstract":"The problem of computing risk measures of life insurance policies is complicated by the fact that two different probability measures, the real-world probability measure along the risk horizon and the risk-neutral one along the remaining time interval, have to be used. This implies that a straightforward application of the Monte Carlo method is not available and the need arises to resort to time consuming nested simulations or to the least squares Monte Carlo approach. We propose to compute common risk measures by using the celebrated binomial model of Cox, Ross, and Rubinstein (1979) (CRR). The main advantage of this approach is that the usual construction of the CRR model is not influenced by the change of measure and a unique lattice can be used along the whole policy duration. Numerical results highlight that the proposed algorithm computes highly accurate values.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"86 - 94"},"PeriodicalIF":0.0,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2018.26.2.086","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43298500","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 : 2018-11-30DOI: 10.3905/jod.2018.26.2.019
D. Wu, Tianxiang Liu
Curve-fitting methods are widely used in derivatives markets for construction of the implied volatility surface (IVS). Here we discuss the goodness of fit, smoothness, and economic implications of 12 distinctive curve-fitting methods. The choice of method relies on specific requirements. When fitting the Chicago Board Options Exchange data, three interpolation methods were found to provide the best goodness, whereas quadratic regression, the Nadaraya–Watson kernel regression, and the theoretical Carr–Wu model generate the smoothest surfaces. Because of the irregular nature of the emerging options market data, we propose a transformation method to improve three statistical methods to satisfy the Lee’s condition. Empirically, quadratic regression provides the best goodness when fitting the China 50ETF options data. In addition, the Carr–Wu model is a very good alternative because it natively satisfies the Lee’s condition and has economic implications.
{"title":"Curve-Fitting Method for Implied Volatility","authors":"D. Wu, Tianxiang Liu","doi":"10.3905/jod.2018.26.2.019","DOIUrl":"https://doi.org/10.3905/jod.2018.26.2.019","url":null,"abstract":"Curve-fitting methods are widely used in derivatives markets for construction of the implied volatility surface (IVS). Here we discuss the goodness of fit, smoothness, and economic implications of 12 distinctive curve-fitting methods. The choice of method relies on specific requirements. When fitting the Chicago Board Options Exchange data, three interpolation methods were found to provide the best goodness, whereas quadratic regression, the Nadaraya–Watson kernel regression, and the theoretical Carr–Wu model generate the smoothest surfaces. Because of the irregular nature of the emerging options market data, we propose a transformation method to improve three statistical methods to satisfy the Lee’s condition. Empirically, quadratic regression provides the best goodness when fitting the China 50ETF options data. In addition, the Carr–Wu model is a very good alternative because it natively satisfies the Lee’s condition and has economic implications.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"19 - 37"},"PeriodicalIF":0.0,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2018.26.2.019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41633308","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 : 2018-11-30DOI: 10.3905/jod.2018.26.2.007
Amelie Hüttner, Jan-Frederik Mai
Analytical approximations for the price of a convertible bond within defaultable Markov diffusion models are derived in this article. Because convertible bond pricing requires time-consuming finite difference or tree pricing methods in general, such proxy formulas can help to calibrate model parameters more efficiently. The derivation is based on the idea of “Europeanizing” the American conversion option of the holder. Hence, the quality of the approximations stands and falls with the value of the early conversion premium. In practice, the latter is typically close to zero, which implies that the analytical lower bounds are incredibly sharp.
{"title":"Sharp Analytical Lower Bounds for the Price of a Convertible Bond","authors":"Amelie Hüttner, Jan-Frederik Mai","doi":"10.3905/jod.2018.26.2.007","DOIUrl":"https://doi.org/10.3905/jod.2018.26.2.007","url":null,"abstract":"Analytical approximations for the price of a convertible bond within defaultable Markov diffusion models are derived in this article. Because convertible bond pricing requires time-consuming finite difference or tree pricing methods in general, such proxy formulas can help to calibrate model parameters more efficiently. The derivation is based on the idea of “Europeanizing” the American conversion option of the holder. Hence, the quality of the approximations stands and falls with the value of the early conversion premium. In practice, the latter is typically close to zero, which implies that the analytical lower bounds are incredibly sharp.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"18 - 7"},"PeriodicalIF":0.0,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2018.26.2.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48642092","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 : 2018-11-30DOI: 10.3905/jod.2018.26.2.001
Joseph M. Pimbley
It is my honor to write to you now as the Editor of The Journal of Derivatives (see the September 10 press release at http://www. maxwell-consulting.com/jod_editor_announcement.pdf). I inherit this role for a journal that I consider a leading research source for practitioners and academics in the derivatives field. I am grateful for this opportunity. I succeeded the founder, Professor Stephen Figlewski, in this position. The excellence of JOD content is truly the excellence of Professor Stephen Figlewski. His wide-ranging expertise and in-depth reviews created a continuum of excellent issues over a span exceeding 25 years. The press release I link above and my website (maxwell-consulting. com) show my background. In brief, I have mixed heritage. My education is theoretical physics. My first career encompassed applied physics, mathematics, and electrical engineering with industrial research and academic employers. Lured to Citibank in the early 1990s to create derivative risk and pricing models, I learned and practiced quantitative finance, risk and portfolio management, derivative trading, executive roles, and financial investigations over the course of the subsequent quarter-century. My financial employers have been banks, a rating agency, bond insurers, an asset manager, and consulting firms. The “world of derivatives” is both huge and hugely impactful to the global economy. The content and concepts “we”—meaning “readers, authors, reviewers, production editors, Board members, and the publisher”—create have the potential to improve our world. This thought is a great entrée to state our published mission at http://jod .iijournals.com/journal-information:
{"title":"Editor’s Letter","authors":"Joseph M. Pimbley","doi":"10.3905/jod.2018.26.2.001","DOIUrl":"https://doi.org/10.3905/jod.2018.26.2.001","url":null,"abstract":"It is my honor to write to you now as the Editor of The Journal of Derivatives (see the September 10 press release at http://www. maxwell-consulting.com/jod_editor_announcement.pdf). I inherit this role for a journal that I consider a leading research source for practitioners and academics in the derivatives field. I am grateful for this opportunity. I succeeded the founder, Professor Stephen Figlewski, in this position. The excellence of JOD content is truly the excellence of Professor Stephen Figlewski. His wide-ranging expertise and in-depth reviews created a continuum of excellent issues over a span exceeding 25 years. The press release I link above and my website (maxwell-consulting. com) show my background. In brief, I have mixed heritage. My education is theoretical physics. My first career encompassed applied physics, mathematics, and electrical engineering with industrial research and academic employers. Lured to Citibank in the early 1990s to create derivative risk and pricing models, I learned and practiced quantitative finance, risk and portfolio management, derivative trading, executive roles, and financial investigations over the course of the subsequent quarter-century. My financial employers have been banks, a rating agency, bond insurers, an asset manager, and consulting firms. The “world of derivatives” is both huge and hugely impactful to the global economy. The content and concepts “we”—meaning “readers, authors, reviewers, production editors, Board members, and the publisher”—create have the potential to improve our world. This thought is a great entrée to state our published mission at http://jod .iijournals.com/journal-information:","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":" ","pages":"1 - 2"},"PeriodicalIF":0.0,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45637103","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}
Much known about Treasury inflation-protected securities (TIPS) is related to the hedge they offer against inflation, but little is known about their protection against deflation—in the form of a deflation protection option (DPO). In this article, a pricing framework that builds on a Heath–Jarrow–Morton forward-rate economy with codependent inflation- and interest-rate jumps is derived to value this embedded DPO. The model prices for TIPS resulting from this pricing framework are found to most closely fit the 10-year notes issued following the 2008 crisis. Considering these notes accounted for over 70% of the total TIPS-market trading activity, this result underscores the importance of properly assessing DPO value in times of deflationary fears compounded by rising real yields, negligence of which may well be liable for the post-crisis mispricing in TIPS.
{"title":"Pricing the Deflation Protection Option in TIPS Using an HJM Model with Inflation- and Interest-Rate Jumps","authors":"Ming-Che Chuang, Shih-Kuei Lin, Mi-Hsiu Chiang","doi":"10.3905/jod.2018.1.069","DOIUrl":"https://doi.org/10.3905/jod.2018.1.069","url":null,"abstract":"Much known about Treasury inflation-protected securities (TIPS) is related to the hedge they offer against inflation, but little is known about their protection against deflation—in the form of a deflation protection option (DPO). In this article, a pricing framework that builds on a Heath–Jarrow–Morton forward-rate economy with codependent inflation- and interest-rate jumps is derived to value this embedded DPO. The model prices for TIPS resulting from this pricing framework are found to most closely fit the 10-year notes issued following the 2008 crisis. Considering these notes accounted for over 70% of the total TIPS-market trading activity, this result underscores the importance of properly assessing DPO value in times of deflationary fears compounded by rising real yields, negligence of which may well be liable for the post-crisis mispricing in TIPS.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"50 - 69"},"PeriodicalIF":0.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2018.1.069","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47823072","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 investigates the relationship between informed trading activity and CDS spreads; contrary to prior research, the results show that level of information-based trading of stocks should be a key determinant of CDS spreads. Using the panel quantile regression model, this article finds that the effects of informed trading activity on CDS spreads are asymmetrical across firms with different levels of credit conditions. Further, these asymmetric dynamics behave in opposite directions across different economic conditions. In particular, when economic conditions are good, a negative (positive) relation between informed trading activity and CDS spreads is documented for firms with bad (good) credit conditions. When economic conditions are unfavorable, catastrophic news dominates investment decisions, and a reverse asymmetrical dynamic between the two variables is then observed.
{"title":"Asymmetric Dynamics between Informed Trading Activity and Credit Default Swaps","authors":"Wen-Cheng Hu, A. Huang","doi":"10.3905/jod.2018.1.070","DOIUrl":"https://doi.org/10.3905/jod.2018.1.070","url":null,"abstract":"This article investigates the relationship between informed trading activity and CDS spreads; contrary to prior research, the results show that level of information-based trading of stocks should be a key determinant of CDS spreads. Using the panel quantile regression model, this article finds that the effects of informed trading activity on CDS spreads are asymmetrical across firms with different levels of credit conditions. Further, these asymmetric dynamics behave in opposite directions across different economic conditions. In particular, when economic conditions are good, a negative (positive) relation between informed trading activity and CDS spreads is documented for firms with bad (good) credit conditions. When economic conditions are unfavorable, catastrophic news dominates investment decisions, and a reverse asymmetrical dynamic between the two variables is then observed.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"70 - 85"},"PeriodicalIF":0.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2018.1.070","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42380442","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 : 2018-10-04DOI: 10.3905/jod.2019.26.4.035
Alex Garivaltis
This article prices and replicates the financial derivative whose payoff at T is the wealth that would have accrued to a $1 deposit into the best continuously-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. For the single-stock Black–Scholes market, Ordentlich and Cover (1998) only priced this derivative at time-0, giving . Of course, the general time-t price is not equal to . The author completes the Ordentlich–Cover (1998) analysis by deriving the price at any time t. By contrast, the author also studies the more natural case of the best-levered rebalancing rule in hindsight. This yields , where b(S, t) is the best rebalancing rule in hindsight over the observed history [0, t]. The author shows that the replicating strategy amounts to betting the fraction b(S, t) of wealth on the stock over the interval [t, t + dt]. This fact holds for the general market with n correlated stocks in geometric Brownian motion: C(S, t) = (T/t)n/2 exp(rt + b′Σb·t/2), where Σ is the covariance of instantaneous returns per unit time. This result matches the O(Tn/2) “cost of universality” derived by Cover in his “universal portfolio theory” (1986, 1991, 1996, 1998), which super-replicates the same derivative in discrete-time. The replicating strategy compounds its money at the same asymptotic rate as the best-levered rebalancing rule in hindsight, thereby beating the market asymptotically. Naturally enough, the American-style version of Cover’s Derivative is never exercised early in equilibrium. TOPICS: Derivatives, portfolio construction, performance measurement, statistical methods
{"title":"Exact Replication of the Best Rebalancing Rule in Hindsight","authors":"Alex Garivaltis","doi":"10.3905/jod.2019.26.4.035","DOIUrl":"https://doi.org/10.3905/jod.2019.26.4.035","url":null,"abstract":"This article prices and replicates the financial derivative whose payoff at T is the wealth that would have accrued to a $1 deposit into the best continuously-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. For the single-stock Black–Scholes market, Ordentlich and Cover (1998) only priced this derivative at time-0, giving . Of course, the general time-t price is not equal to . The author completes the Ordentlich–Cover (1998) analysis by deriving the price at any time t. By contrast, the author also studies the more natural case of the best-levered rebalancing rule in hindsight. This yields , where b(S, t) is the best rebalancing rule in hindsight over the observed history [0, t]. The author shows that the replicating strategy amounts to betting the fraction b(S, t) of wealth on the stock over the interval [t, t + dt]. This fact holds for the general market with n correlated stocks in geometric Brownian motion: C(S, t) = (T/t)n/2 exp(rt + b′Σb·t/2), where Σ is the covariance of instantaneous returns per unit time. This result matches the O(Tn/2) “cost of universality” derived by Cover in his “universal portfolio theory” (1986, 1991, 1996, 1998), which super-replicates the same derivative in discrete-time. The replicating strategy compounds its money at the same asymptotic rate as the best-levered rebalancing rule in hindsight, thereby beating the market asymptotically. Naturally enough, the American-style version of Cover’s Derivative is never exercised early in equilibrium. TOPICS: Derivatives, portfolio construction, performance measurement, statistical methods","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"26 1","pages":"35 - 53"},"PeriodicalIF":0.0,"publicationDate":"2018-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3905/jod.2019.26.4.035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42053713","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：