The no arbitrage relation between futures and spot prices implies an analogous relation between futures and spot volatilities as measured by daily range. Long memory features of the range-based volatility estimators of the two series are analyzed, and their joint dynamics are modeled via a fractional vector error correction model (FVECM), in order to explicitly consider the no arbitrage constraints. We introduce a two-step estimation procedure for the FVECM parameters and we show the properties by a Monte Carlo simulation. The out-of-sample forecasting superiority of FVECM, with respect to competing models, is documented. The results highlight the importance of giving fully account of long-run equilibria in volatilities in order to obtain better forecasts.
{"title":"A No Arbitrage Fractional Cointegration Analysis of the Range Based Volatility","authors":"E. Rossi, Paolo Santucci de Magistris","doi":"10.2139/ssrn.1434792","DOIUrl":"https://doi.org/10.2139/ssrn.1434792","url":null,"abstract":"The no arbitrage relation between futures and spot prices implies an analogous relation between futures and spot volatilities as measured by daily range. Long memory features of the range-based volatility estimators of the two series are analyzed, and their joint dynamics are modeled via a fractional vector error correction model (FVECM), in order to explicitly consider the no arbitrage constraints. We introduce a two-step estimation procedure for the FVECM parameters and we show the properties by a Monte Carlo simulation. The out-of-sample forecasting superiority of FVECM, with respect to competing models, is documented. The results highlight the importance of giving fully account of long-run equilibria in volatilities in order to obtain better forecasts.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"33 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89107581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many theoretical papers suggest that large informed traders should make misleading or random trades to disguise their trading. Alternatively, informed traders may trade purely on their estimate of stock value. This paper examines the trading behavior of a large institutional insider that periodically trades in the wrong direction, i.e., makes occasional sell (buy) trades within packages of buy (sell) trades. Using a hand-collected data set, we find that three quarters of the trade packages include wrong-direction trades. Wrong trades appear to be used mostly to disguise right-direction trades. We find that the wrong-trade stocks are larger and have less noisy returns, hence, they lack natural disguise. Wrong trades are relatively small, used to accentuate return volatility, distributed evenly during a package of trades, and are not consistently profitable.
{"title":"Strategic Trading in the Wrong Direction By a Large Institutional Insider","authors":"J. Golec, Erasmo Giambona","doi":"10.2139/ssrn.908708","DOIUrl":"https://doi.org/10.2139/ssrn.908708","url":null,"abstract":"Many theoretical papers suggest that large informed traders should make misleading or random trades to disguise their trading. Alternatively, informed traders may trade purely on their estimate of stock value. This paper examines the trading behavior of a large institutional insider that periodically trades in the wrong direction, i.e., makes occasional sell (buy) trades within packages of buy (sell) trades. Using a hand-collected data set, we find that three quarters of the trade packages include wrong-direction trades. Wrong trades appear to be used mostly to disguise right-direction trades. We find that the wrong-trade stocks are larger and have less noisy returns, hence, they lack natural disguise. Wrong trades are relatively small, used to accentuate return volatility, distributed evenly during a package of trades, and are not consistently profitable.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"30 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81305495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I propose a simple generalization of put-call parity that holds for a large class of exotic European options. The result rests on a reasonable generalization of the concepts of put and call. The proof is based on the fundamental theorem of arbitrage pricing and elementary properties of real numbers. I also propose a generalization of the notion of intrinsic value and volatility smile. Here I leverage on the relationship between put-call parity and the smile/smirk in the vanilla case.
{"title":"Put-Call Parity for European Exotic Options","authors":"G. Castellacci","doi":"10.2139/ssrn.1426986","DOIUrl":"https://doi.org/10.2139/ssrn.1426986","url":null,"abstract":"I propose a simple generalization of put-call parity that holds for a large class of exotic European options. The result rests on a reasonable generalization of the concepts of put and call. The proof is based on the fundamental theorem of arbitrage pricing and elementary properties of real numbers. I also propose a generalization of the notion of intrinsic value and volatility smile. Here I leverage on the relationship between put-call parity and the smile/smirk in the vanilla case.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"35 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86273876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a method for volatility computation from listed prices of American options on an underlying close to log-normal. From prices of American calls and puts, traded at an exchange at multiple strikes we compute the underlying volatility and implied volatility of an untraded European contract at each strike.
{"title":"Decoupled American Option Pricing Method: Computation of Implied Volatilities and Further Applications","authors":"Yuriy Shkolnikov","doi":"10.2139/ssrn.1371930","DOIUrl":"https://doi.org/10.2139/ssrn.1371930","url":null,"abstract":"We introduce a method for volatility computation from listed prices of American options on an underlying close to log-normal. From prices of American calls and puts, traded at an exchange at multiple strikes we compute the underlying volatility and implied volatility of an untraded European contract at each strike.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":" 47","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72384331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a general treatment of the Vanna-Volga mark-to-market volatility smile correction in application to pricing of contracts with European exercise on a single underlying. The method remains applicable in cases of delayed or misaligned expiries and absolute dividends. It is also applied to cases of time-dependent instantaneous volatility, multiple underlying assets and random interest rates. We also offer computation of the underlying volatility from market data and most valuable correction using more than three traded options.
{"title":"Generalized Vanna-Volga Method and its Applications","authors":"Yuriy Shkolnikov","doi":"10.2139/ssrn.1186383","DOIUrl":"https://doi.org/10.2139/ssrn.1186383","url":null,"abstract":"We give a general treatment of the Vanna-Volga mark-to-market volatility smile correction in application to pricing of contracts with European exercise on a single underlying. The method remains applicable in cases of delayed or misaligned expiries and absolute dividends. It is also applied to cases of time-dependent instantaneous volatility, multiple underlying assets and random interest rates. We also offer computation of the underlying volatility from market data and most valuable correction using more than three traded options.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"87 1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78038421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geometric Brownian motion framework, we propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. We solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. We also obtain closed form approximations for the option Greeks. We test the model on American crack spread options traded on NYMEX.
{"title":"Meshfree Approximation for Multi-Asset Options","authors":"E. Hanert, Aanand Venkatramanan","doi":"10.2139/ssrn.1424987","DOIUrl":"https://doi.org/10.2139/ssrn.1424987","url":null,"abstract":"We price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geometric Brownian motion framework, we propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. We solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. We also obtain closed form approximations for the option Greeks. We test the model on American crack spread options traded on NYMEX.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"44 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86638536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This review article summarizes the applications of the forward shooting grid method to pricing of various types of strongly path dependent options. The forward shooting grid approach is characterized by augmenting an auxiliary state vector at each node in the usual lattice tree, which serves to capture the path dependent feature of the option. Examples of path dependent derivatives considered include the lookback options, Asian options, callable convertible bonds, and call options with strike reset feature.
{"title":"Lattice Tree Methods for Strongly Path Dependent Options","authors":"Y. Kwok","doi":"10.2139/ssrn.1421736","DOIUrl":"https://doi.org/10.2139/ssrn.1421736","url":null,"abstract":"This review article summarizes the applications of the forward shooting grid method to pricing of various types of strongly path dependent options. The forward shooting grid approach is characterized by augmenting an auxiliary state vector at each node in the usual lattice tree, which serves to capture the path dependent feature of the option. Examples of path dependent derivatives considered include the lookback options, Asian options, callable convertible bonds, and call options with strike reset feature.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73102177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Option pricing models based on an underlying lognormal distribution typically exhibit volatility smiles or smirks where the implied volatility varies by strike price. To adequately model the underlying distribution, a less restrictive model is needed. A relaxed binomial model is developed here that can account for the skewness of the underlying distribution and a relaxed trinomial model is developed that can account for the skewness and kurtosis of the underlying distribution. The new model incorporates the usual binomial and trinomial tree models as restricted special cases. Unlike previous flexible tree models, the size and probability of jumps are held constant at each node so only minor modifications in existing code for lattice models are needed to implement the new approach. Also, the new approach allows calculating implied skewness and implied kurtosis. Numerical results show that the relaxed binomial and trinomial tree models developed in this study are at least as accurate as tree models based on lognormality when the true underlying distribution is lognormal and substantially more accurate when the underlying distribution is not lognormal.
{"title":"Valuing Options Under Nonlognormality Using Relaxed Lattices","authors":"Dasheng Ji, B. Brorsen","doi":"10.2139/ssrn.1418611","DOIUrl":"https://doi.org/10.2139/ssrn.1418611","url":null,"abstract":"Option pricing models based on an underlying lognormal distribution typically exhibit volatility smiles or smirks where the implied volatility varies by strike price. To adequately model the underlying distribution, a less restrictive model is needed. A relaxed binomial model is developed here that can account for the skewness of the underlying distribution and a relaxed trinomial model is developed that can account for the skewness and kurtosis of the underlying distribution. The new model incorporates the usual binomial and trinomial tree models as restricted special cases. Unlike previous flexible tree models, the size and probability of jumps are held constant at each node so only minor modifications in existing code for lattice models are needed to implement the new approach. Also, the new approach allows calculating implied skewness and implied kurtosis. Numerical results show that the relaxed binomial and trinomial tree models developed in this study are at least as accurate as tree models based on lognormality when the true underlying distribution is lognormal and substantially more accurate when the underlying distribution is not lognormal.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"12 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83725786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a new importance sampling method for pricing basket default swaps employing exchangeable Archimedean copulas and nested Gumbel copulas. We establish more realistic dependence structures than existing copula models for credit risks in the underlying portfolio, and propose an appropriate density for importance sampling by analyzing multivariate Archimedean copulas. To justify efficiency and accuracy of the proposed algorithms, we present numerical examples and compare them with the crude Monte Carlo simulation, and finally show that our proposed estimators produce considerably smaller variances.
{"title":"Efficient Algorithms for Basket Default Swap Pricing with Multivariate Archimedean Copulas","authors":"G. Choe, Hyun Jin Jang","doi":"10.2139/ssrn.1414111","DOIUrl":"https://doi.org/10.2139/ssrn.1414111","url":null,"abstract":"We introduce a new importance sampling method for pricing basket default swaps employing exchangeable Archimedean copulas and nested Gumbel copulas. We establish more realistic dependence structures than existing copula models for credit risks in the underlying portfolio, and propose an appropriate density for importance sampling by analyzing multivariate Archimedean copulas. To justify efficiency and accuracy of the proposed algorithms, we present numerical examples and compare them with the crude Monte Carlo simulation, and finally show that our proposed estimators produce considerably smaller variances.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"2010 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73590703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.
{"title":"Asymptotic Implied Volatility at the Second Order with Application to the SABR Model","authors":"L. Paulot","doi":"10.2139/ssrn.1413649","DOIUrl":"https://doi.org/10.2139/ssrn.1413649","url":null,"abstract":"We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90484645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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