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ARM: The Analytic Recovery Method ARM:分析回收法
Jurnal Derivat Pub Date : 2023-02-28 DOI: 10.3905/jod.2023.1.178
E. Linden
{"title":"ARM: The Analytic Recovery Method","authors":"E. Linden","doi":"10.3905/jod.2023.1.178","DOIUrl":"https://doi.org/10.3905/jod.2023.1.178","url":null,"abstract":"The analytic recovery method (ARM) recovers arbitrage-free density functions from a given set of option prices with maximum accuracy and speed. For arbitrage-free option prices, ARM provides extremely fast convergence and arbitrary accuracy. In the presence of noise, the closest arbitrage-free approximation is identified. Option prices and densities, as well as their moments and other parameters, are easy-to-handle analytic functions defined for arbitrary strike prices. ARM reveals inconsistencies between quoted option prices, particularly for longer durations. ARM is essentially based on the no-arbitrage assumptions; it is not related to a specific model. It has been tested for a selection of S&P 500, EuroStoxx 50, and DAX data. Excellent no-arbitrage fit to call and put prices is obtained; extrapolations are in line with the market.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"8 - 27"},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44621548","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}
引用次数: 0
The Leland Model as a Consistent Framework for Analytic Valuation of Equity and Options on Equity 利兰模型作为股权与股权期权分析估值的一致性框架
Jurnal Derivat Pub Date : 2023-02-02 DOI: 10.3905/jod.2023.1.176
Oh Kang Kwon, Andrew R. Grant, S. Satchell
{"title":"The Leland Model as a Consistent Framework for Analytic Valuation of Equity and Options on Equity","authors":"Oh Kang Kwon, Andrew R. Grant, S. Satchell","doi":"10.3905/jod.2023.1.176","DOIUrl":"https://doi.org/10.3905/jod.2023.1.176","url":null,"abstract":"Although there are many well-established models for valuing corporate debt and equity, option pricing literature rarely takes these models as their starting point. This happens in part because such models value equity as an option on the firm’s assets, and options on equity then become compound options that cannot generally be priced analytically. In this article, the authors present a consistent and unified framework for valuing equity and options on equity within the 1994 Leland model. The authors show that it is possible to value not only European call and put options but also exotic options such as barriers and lookbacks in closed form. Moreover, the authors show that the model produces an implied volatility skew that is typically observed in the equity options market.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"28 - 45"},"PeriodicalIF":0.0,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42062150","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}
引用次数: 0
Malliavin Derivatives of Derivative Securities Malliavin衍生证券衍生品
Jurnal Derivat Pub Date : 2022-11-30 DOI: 10.3905/jod.2022.30.2.065
Tom P. Davis
{"title":"Malliavin Derivatives of Derivative Securities","authors":"Tom P. Davis","doi":"10.3905/jod.2022.30.2.065","DOIUrl":"https://doi.org/10.3905/jod.2022.30.2.065","url":null,"abstract":"The Malliavin calculus has been used successfully to derive efficient formulas for delta and gamma. This article extends these results to all higher-order spatial derivatives with respect to the underlying asset for arbitrary payoffs in both the Black-Scholes (Black and Scholes 1973) (lognormal) and Bachelier (normal) models. The former reproduces a well-known result from Peter Carr (2000), whereas the latter extends this work to the normal case.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"65 - 73"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41526560","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}
引用次数: 0
Deriving Better Second-Order Derivatives 导出更好的二阶导数
Jurnal Derivat Pub Date : 2022-11-30 DOI: 10.3905/jod.2022.30.2.032
R. Galeeva
{"title":"Deriving Better Second-Order Derivatives","authors":"R. Galeeva","doi":"10.3905/jod.2022.30.2.032","DOIUrl":"https://doi.org/10.3905/jod.2022.30.2.032","url":null,"abstract":"In his pioneer paper traced back to 1993, “Deriving Derivatives of Derivatives Securities,” Peter Carr used the operator calculus to show that that all partial derivatives of path independent claims can be represented in terms of the spatial derivatives. We generalized these results for multiasset situations. Reversing the relationships and expressing the higher-order Greeks (as gamma or cross gamma) in terms of the first-order Greeks leads to better numerical stability and convergence properties. We apply the results to evaluation and risk of an important energy asset as storage. In addition, we consider Greeks for the CEV model and the stochastic volatility case. At the time of our discussions, dating back in 2010–2011, I was mostly interested in applications for commodity derivatives. Peter suggested including the exponential Lévy model, his favorite subject; the CEV models; and the stochastic volatility case. In preparing this article, I kept the original draft, dated December 2011, of the write-up we worked out together. I reworked the write-up, and added storage models, numerical examples, and derivations.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"32 - 48"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44774858","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}
引用次数: 0
Editor’s Letter 编辑的信
Jurnal Derivat Pub Date : 2022-11-30 DOI: 10.3905/jod.2022.30.2.001
Andrey Itkin, Alex Lipton, Fabio Mercurio, David Shimko, Liuren Wu
{"title":"Editor’s Letter","authors":"Andrey Itkin, Alex Lipton, Fabio Mercurio, David Shimko, Liuren Wu","doi":"10.3905/jod.2022.30.2.001","DOIUrl":"https://doi.org/10.3905/jod.2022.30.2.001","url":null,"abstract":"","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"1 - 2"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43769063","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}
引用次数: 0
My Reminiscences of Peter Carr 我对彼得·卡尔的回忆
Jurnal Derivat Pub Date : 2022-11-30 DOI: 10.3905/jod.2022.30.2.008
A. Itkin
{"title":"My Reminiscences of Peter Carr","authors":"A. Itkin","doi":"10.3905/jod.2022.30.2.008","DOIUrl":"https://doi.org/10.3905/jod.2022.30.2.008","url":null,"abstract":"","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"8 - 15"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48104730","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}
引用次数: 0
Carr Memorial: Maximum Drawdown Derivatives to a Hitting Time 卡尔纪念:打击时间的最大递减衍生品
Jurnal Derivat Pub Date : 2022-11-30 DOI: 10.3905/jod.2022.30.2.016
K. Atteson, P. Carr
{"title":"Carr Memorial: Maximum Drawdown Derivatives to a Hitting Time","authors":"K. Atteson, P. Carr","doi":"10.3905/jod.2022.30.2.016","DOIUrl":"https://doi.org/10.3905/jod.2022.30.2.016","url":null,"abstract":"Drawdown is defined as the amount a portfolio has decreased from its running maximum. Drawdown has become ensconced in finance practice with some hedge funds shutting down portfolio managers who reach a certain drawdown limit. In this article, we show that, for every continuous local martingale that hits a given point m with probability 1, the running maximum of drawdown at the time of hitting m has the same inverse exponential distribution. We then derive prices and hedge ratios for binary calls on maximum absolute and relative drawdown maturing at the hitting time for m. We also derive prices for call spreads on maximum drawdown at the hitting time for m. These prices and hedge ratios are model independent across all continuous arbitrage-free stochastic processes that, with probability 1, either hit m or reach a drawdown equal to the strike price. This includes stochastic volatility models whose volatility is bounded away from 0 before hitting m or the strike. These results are both simpler and more general than prior work, which, while allowing for a fixed maturity, require infinite series representations, the use of complex derivatives to hedge and greater restrictions on the stochastic process. The key fact that facilitates our form of model independence is that the values of the derivatives at maturity are invariant to time changes.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"16 - 31"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48611074","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}
引用次数: 1
Financial Interpretation of Feller’s Factorization 费勒分解的金融解释
Jurnal Derivat Pub Date : 2022-11-30 DOI: 10.3905/jod.2022.30.2.049
P. Carr, C. Tebaldi
{"title":"Financial Interpretation of Feller’s Factorization","authors":"P. Carr, C. Tebaldi","doi":"10.3905/jod.2022.30.2.049","DOIUrl":"https://doi.org/10.3905/jod.2022.30.2.049","url":null,"abstract":"The infinitesimal generator of a time-homogeneous univariate diffusion process is a second-order linear ordinary differential operator. Feller (1952) famously factorized this generator into successive differentiations with respect to scale and speed measure. Later, Feller (1957) also factored an extended generator that loads also on the identity operator in a particular way. We provide a novel financial interpretation of these factorization results and show that they produce an operator representation of a conditionally linear risk-return tradeoff when the conditioning variable evolves like a one-dimensional diffusion process.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"49 - 63"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46592268","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}
引用次数: 0
Good Volatility, Bad Volatility, and VIX Futures Pricing: Evidence from the Decomposition of VIX 好波动性、坏波动性与波动率指数期货定价——来自波动率指数分解的证据
Jurnal Derivat Pub Date : 2022-11-25 DOI: 10.3905/jod.2022.1.174
Chen Tong, Zhuo Huang
{"title":"Good Volatility, Bad Volatility, and VIX Futures Pricing: Evidence from the Decomposition of VIX","authors":"Chen Tong, Zhuo Huang","doi":"10.3905/jod.2022.1.174","DOIUrl":"https://doi.org/10.3905/jod.2022.1.174","url":null,"abstract":"Realized semivariance, computed from intraday positive/negative squared returns, provides an accurate measure of the upside/downside variations of stock returns. This article investigates the role of realized semivariance in pricing the CBOE VIX and VIX futures, using a realized semivariance-based model. We obtain the closed-form pricing formula for the VIX index and VIX futures prices, and show that the new model provides superior pricing performance, both in-sample and out-of-sample. We further analytically derive the pricing formulas for the upside/downside components of the VIX (risk-neutral semivariance). Such a decomposition shows that the information gains from the conventional unsigned realized variance are concentrated on pricing the downside part of the VIX; the new realized semivariance-based model provides a larger and more balanced improvement for both the upside and downside components of the VIX. Our results provide strong evidence that the spread between upside/downside variance is the main driver of the asymmetry in return distributions.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"117 - 143"},"PeriodicalIF":0.0,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49157529","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}
引用次数: 0
Compound Option Pricing and the Roll-Geske-Whaley Formula under the Conjugate-Power Dagum Distribution 共轭幂Dagum分布下的复合期权定价与Roll-Geske-Whaley公式
Jurnal Derivat Pub Date : 2022-10-20 DOI: 10.3905/jod.2022.1.172
P. Carr, Federico Maglione
{"title":"Compound Option Pricing and the Roll-Geske-Whaley Formula under the Conjugate-Power Dagum Distribution","authors":"P. Carr, Federico Maglione","doi":"10.3905/jod.2022.1.172","DOIUrl":"https://doi.org/10.3905/jod.2022.1.172","url":null,"abstract":"We explore the pricing of compound derivatives under the newly introduced conjugate-power Dagum distribution. Assuming a discrete-time multiplicative conjugate-power Dagum random walk, we first provide an alternative derivation of the price of a married put based on a change of measure, which is helpful for the pricing of compound options. Then, we apply these results to obtain the equivalent of the Roll-Geske-Whaley formula for the pricing of American options in presence of one known discrete dividend under this alternative distribution.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"94 - 125"},"PeriodicalIF":0.0,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41460382","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}
引用次数: 0
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