We study the estimation, the dynamics, and the predictability of option-implied risk-neutral moments (variance, skewness, and kurtosis) for individual stocks from various perspectives. We first show that it is in the estimation of the higher moments essential to use an interpolation with a narrow grid as well as a wide interval. We show that implied moments are well explained cross-sectionally by a number of firm characteristics. We use the characteristics that have been shown to exhibit correlation with expected returns (like size and the market-to-book ratio of equity). In a next step, we investigate the joint dynamics of the three moments in a vector autoregressive model. We find that the moments are significantly linked to each other over time. Finally, adding exogenous variables to the vector autoregression improves the explanatory power of our model even further. Granger causality tests show significant differences between the three implied moments.
{"title":"The Dynamics of Risk-Neutral Implied Moments: Evidence from Individual Options","authors":"Alexandra Hansis, Christian Schlag, G. Vilkov","doi":"10.2139/ssrn.1470674","DOIUrl":"https://doi.org/10.2139/ssrn.1470674","url":null,"abstract":"We study the estimation, the dynamics, and the predictability of option-implied risk-neutral moments (variance, skewness, and kurtosis) for individual stocks from various perspectives. We first show that it is in the estimation of the higher moments essential to use an interpolation with a narrow grid as well as a wide interval. We show that implied moments are well explained cross-sectionally by a number of firm characteristics. We use the characteristics that have been shown to exhibit correlation with expected returns (like size and the market-to-book ratio of equity). In a next step, we investigate the joint dynamics of the three moments in a vector autoregressive model. We find that the moments are significantly linked to each other over time. Finally, adding exogenous variables to the vector autoregression improves the explanatory power of our model even further. Granger causality tests show significant differences between the three implied moments.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"40 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2010-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86384852","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}
Libor derivative pricing has changed with the crisis; Libor is not anymore one unambiguous curve as a large basis has appeared between different Libor tenors. A previous approach to derivative discounting is reviewed at the light of those changes. The valuation of so called linear derivatives, the yield curve construction and the valuation of vanilla options is analyzed.
{"title":"The Irony in the Derivatives Discounting Part II: The Crisis","authors":"Marc Henrard","doi":"10.2139/ssrn.1433022","DOIUrl":"https://doi.org/10.2139/ssrn.1433022","url":null,"abstract":"Libor derivative pricing has changed with the crisis; Libor is not anymore one unambiguous curve as a large basis has appeared between different Libor tenors. A previous approach to derivative discounting is reviewed at the light of those changes. The valuation of so called linear derivatives, the yield curve construction and the valuation of vanilla options is analyzed.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"258 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77135149","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 paper analyzes the dynamic relationship between CDS spreads and stock market implied credit spreads (ICS) for a large international set of companies during the period 2002-2004. We find the relationship between these credit spread measures to be stronger, and the probability of the stock market leading credit risk discovery to be higher, at the lower credit quality levels. However, consistent with the argument of insider trading in credit derivatives, we document a positive relationship between the frequency of severe credit downturns and the probability of the CDS market leading price discovery. Apart from these findings, our results suggest a slight informational dominance of the stock market that declines over time.
{"title":"Credit Risk Discovery in the Stock and CDS Markets: Who Leads, When, and Why‘","authors":"Santiago Forte, Lidija Lovreta","doi":"10.2139/ssrn.1183202","DOIUrl":"https://doi.org/10.2139/ssrn.1183202","url":null,"abstract":"This paper analyzes the dynamic relationship between CDS spreads and stock market implied credit spreads (ICS) for a large international set of companies during the period 2002-2004. We find the relationship between these credit spread measures to be stronger, and the probability of the stock market leading credit risk discovery to be higher, at the lower credit quality levels. However, consistent with the argument of insider trading in credit derivatives, we document a positive relationship between the frequency of severe credit downturns and the probability of the CDS market leading price discovery. Apart from these findings, our results suggest a slight informational dominance of the stock market that declines over time.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82197188","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}
Alessandro Beber, Francis Breedon, Andrea Buraschi
This paper studies the importance of heterogeneous beliefs for the dynamics of asset prices. We focus on currency markets, where the absence of short-selling constraints allows us to perform sharper tests of theoretical predictions. We examine both option and underlying markets, so that we can study a richer array of empirical implications that include both volatility risk premia and expected returns. Using a unique data set with detailed information on the foreign-exchange forecasts of about 50 market participants over more than ten years, we construct an empirical proxy for differences in beliefs. We show that this proxy has a statistically and economically strong effect on the implied volatility of currency options beyond the volatility of current macroeconomic fundamentals. We document that differences in beliefs impact also on the shape of the implied volatility smile, on the volatility risk-premia, and on future currency returns. Our evidence demonstrates that a process related to the uncertainty about fundamentals has important asset pricing implications.
{"title":"Differences in Beliefs and Currency Risk Premia","authors":"Alessandro Beber, Francis Breedon, Andrea Buraschi","doi":"10.2139/ssrn.965802","DOIUrl":"https://doi.org/10.2139/ssrn.965802","url":null,"abstract":"This paper studies the importance of heterogeneous beliefs for the dynamics of asset prices. We focus on currency markets, where the absence of short-selling constraints allows us to perform sharper tests of theoretical predictions. We examine both option and underlying markets, so that we can study a richer array of empirical implications that include both volatility risk premia and expected returns. Using a unique data set with detailed information on the foreign-exchange forecasts of about 50 market participants over more than ten years, we construct an empirical proxy for differences in beliefs. We show that this proxy has a statistically and economically strong effect on the implied volatility of currency options beyond the volatility of current macroeconomic fundamentals. We document that differences in beliefs impact also on the shape of the implied volatility smile, on the volatility risk-premia, and on future currency returns. Our evidence demonstrates that a process related to the uncertainty about fundamentals has important asset pricing implications.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"28 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72677529","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 paper considers the pricing and hedging of collateralized debt obligations (CDOs). CDOs are complex derivatives on a pool of credits which we choose to analyse in the top down model proposed in Filipovic et al. (2009). We reflect on the implied forward rates and bring them in connection with the top-down framework in Lipton and Shelton (2009) and Schonbucher (2005). Moreover, we derive variance-minimizing hedging strategies for hedgeing single tranches with the full index. The hedging strategies are given for the general case. We compute them also explicitly for a parsimonious one-factor affine model.
{"title":"Pricing and Hedging of CDOs: A Top Down Approach","authors":"D. Filipović, Thorsten Schmidt","doi":"10.2139/ssrn.1472942","DOIUrl":"https://doi.org/10.2139/ssrn.1472942","url":null,"abstract":"This paper considers the pricing and hedging of collateralized debt obligations (CDOs). CDOs are complex derivatives on a pool of credits which we choose to analyse in the top down model proposed in Filipovic et al. (2009). We reflect on the implied forward rates and bring them in connection with the top-down framework in Lipton and Shelton (2009) and Schonbucher (2005). Moreover, we derive variance-minimizing hedging strategies for hedgeing single tranches with the full index. The hedging strategies are given for the general case. We compute them also explicitly for a parsimonious one-factor affine model.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"45 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75700052","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}
The terms of stock option contracts are adjusted in the event of unexpected corporate actions, and the nature of the adjustments may result in windfall gains or losses to open option positions. This paper evaluates the fairness of the two different procedures used for special cash dividends. We show that, while neither procedure is technically correct, the absolute adjustment used in the U.S. and Canada minimizes the windfall change in option value when the dividend is announced. In addition, the proportional adjustment used in Australia and Europe depends on stock price and is therefore vulnerable to temporary aberrations in the stock market.
{"title":"Stock Option Contract Adjustments: The Case of Special Dividends","authors":"K. Barraclough, H. Stoll, R. Whaley","doi":"10.2139/SSRN.1430558","DOIUrl":"https://doi.org/10.2139/SSRN.1430558","url":null,"abstract":"The terms of stock option contracts are adjusted in the event of unexpected corporate actions, and the nature of the adjustments may result in windfall gains or losses to open option positions. This paper evaluates the fairness of the two different procedures used for special cash dividends. We show that, while neither procedure is technically correct, the absolute adjustment used in the U.S. and Canada minimizes the windfall change in option value when the dividend is announced. In addition, the proportional adjustment used in Australia and Europe depends on stock price and is therefore vulnerable to temporary aberrations in the stock market.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81277070","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 new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of 'forward implied variance' in the original derivation of Gatheral, who introduced this representation in his book 'The Volatility Surface'.
{"title":"A Remark on Gatheral's 'Most-Likely Path Approximation' of Implied Volatility","authors":"Martin Keller-Ressel, J. Teichmann","doi":"10.2139/ssrn.1499082","DOIUrl":"https://doi.org/10.2139/ssrn.1499082","url":null,"abstract":"We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of 'forward implied variance' in the original derivation of Gatheral, who introduced this representation in his book 'The Volatility Surface'.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"23 11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82922016","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}
In this paper, we introduce a new technique for calibrating local volatility extensions of arbitrary multi-factor stochastic volatility models to market smiles. Although approximate, this technique is both fast and accurate. The procedure is illustrated with the Bergomi variance curve model and the $2$-factor log-normal model.
{"title":"Calibration of Local Stochastic Volatility Models to Market Smiles: A Monte-Carlo Approach","authors":"P. Henry-Labordère","doi":"10.1201/b16332-16","DOIUrl":"https://doi.org/10.1201/b16332-16","url":null,"abstract":"In this paper, we introduce a new technique for calibrating local volatility extensions of arbitrary multi-factor stochastic volatility models to market smiles. Although approximate, this technique is both fast and accurate. The procedure is illustrated with the Bergomi variance curve model and the $2$-factor log-normal model.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"16 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82564884","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}
SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed this model, derived a closed form approximation for european options and showed that it provides consistent and stable hedges. Here I prove a new exact closed formula for the joint probability density of underlying and volatility processes, when correlation is zero. I argue that this formula remains a very good approximation when correlation is different from zero. I deduce from this expression different formulae for European options. After reviewing the Libor Market Model and its stochastic volatility extensions, I will show how to specify a unified SABR-LMM with a smile, where the term structure of skew is captured, and where closed formulae for caplets and robust approximations for swaptions are available.
{"title":"Solving SABR in Exact Form and Unifying it with LIBOR Market Model","authors":"Othmane Islah","doi":"10.2139/ssrn.1489428","DOIUrl":"https://doi.org/10.2139/ssrn.1489428","url":null,"abstract":"SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed this model, derived a closed form approximation for european options and showed that it provides consistent and stable hedges. Here I prove a new exact closed formula for the joint probability density of underlying and volatility processes, when correlation is zero. I argue that this formula remains a very good approximation when correlation is different from zero. I deduce from this expression different formulae for European options. After reviewing the Libor Market Model and its stochastic volatility extensions, I will show how to specify a unified SABR-LMM with a smile, where the term structure of skew is captured, and where closed formulae for caplets and robust approximations for swaptions are available.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"53 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85439561","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 paper extends the approach of measuring and stress-testing the systemic risk of a banking sector in Huang, Zhou, and Zhu (2009) to identifying various sources of financial instability and to allocating systemic risk to individual financial institutions. The systemic risk measure, defined as the insurance cost to protect against distressed losses in a banking system, is a risk-neutral concept of capital based on publicly available information that can be appropriately aggregated across different subsets. An application of our methodology to a portfolio of twenty-two major banks in Asia and the Pacific illustrates the dynamics of the spillover effects of the global financial crisis to the region. The increase in the perceived systemic risk, particularly after the failure of Lehman Brothers, was mainly driven by the heightened risk aversion and the squeezed liquidity. The analysis on the marginal contribution of individual banks to the systemic risk suggests that ``too-big-to-fail" is a valid concern from a macroprudential perspective of bank regulation.
本文扩展了Huang, Zhou, and Zhu(2009)对银行业系统性风险的测量和压力测试方法，以识别金融不稳定的各种来源，并将系统性风险分配给单个金融机构。系统性风险度量，定义为防止银行系统不良损失的保险成本，是一种风险中性的资本概念，基于可以在不同子集中适当汇总的公开可用信息。将我们的方法应用于亚太地区22家主要银行的投资组合，说明了全球金融危机对该地区溢出效应的动态。感知到的系统性风险的增加，尤其是在雷曼兄弟(Lehman Brothers)破产之后，主要是由风险厌恶情绪加剧和流动性紧缩所驱动的。对单个银行对系统性风险的边际贡献的分析表明，从银行监管的宏观审慎角度来看，“太大而不能倒”是一个合理的担忧。
{"title":"Assessing the Systemic Risk of a Heterogeneous Portfolio of Banks during the Recent Financial Crisis","authors":"Xin Huang, Hao Zhou, Haibin Zhu","doi":"10.2139/ssrn.1459946","DOIUrl":"https://doi.org/10.2139/ssrn.1459946","url":null,"abstract":"This paper extends the approach of measuring and stress-testing the systemic risk of a banking sector in Huang, Zhou, and Zhu (2009) to identifying various sources of financial instability and to allocating systemic risk to individual financial institutions. The systemic risk measure, defined as the insurance cost to protect against distressed losses in a banking system, is a risk-neutral concept of capital based on publicly available information that can be appropriately aggregated across different subsets. An application of our methodology to a portfolio of twenty-two major banks in Asia and the Pacific illustrates the dynamics of the spillover effects of the global financial crisis to the region. The increase in the perceived systemic risk, particularly after the failure of Lehman Brothers, was mainly driven by the heightened risk aversion and the squeezed liquidity. The analysis on the marginal contribution of individual banks to the systemic risk suggests that ``too-big-to-fail\" is a valid concern from a macroprudential perspective of bank regulation.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"67 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2009-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87063206","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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