In this paper, we put forth the notion of “Crisis Utility” as a way of estimating the tail risk of an asset or investment strategy. We believe that Crisis Utility is more functional than traditional, narrowly defined definitions of tail risk since it incorporates the concept of “resiliency,” or recovery rate, as well as the traditional concept of maximum loss potential. Our argument for the inclusion of resiliency comes from our observations of the recent credit crisis. During the depths of the crisis we observed (1) that allocations, particularly institutional allocations, were “sticky,” which is to say that investors either had trouble adjusting asset allocations or were not inclined to do so, and (2) high water marks, or the arrangement that allows investors to recoup losses before a manager can charge additional performance fees, proved to be a significant benefit for resilient strategies. In an environment of sticky allocations and high water marks, we feel that the resiliency of a strategy becomes an important allocation point, particularly for institutions seeking to make long-term, strategic allocations as opposed to short-term, tactical allocations. Our study shows that lower volatility, low correlation strategies have a demonstrably higher Crisis Utility Rating than higher volatility, high correlation strategies. Specifically, using the HFR dataset, we found the strategies with the highest Crisis Utility Ranking were Short Bias, Equity Market Neutral, our bond proxy, Relative Value (Total), Systematic Diversified, Merger Arbitrage, Convertible Arbitrage and Fund of Funds: Defensive. We anticipate that these strategies will receive a relative increase in allocations as investors adjust their allocation models to account for tail risk, all else being equal and free of constraint. We also analyze the VIX Index within our Crisis Utility framework and find that it handily outscores all other strategies in our study. Although it is currently difficult to find active long volatility managers, we conclude that this is an important area for growth.
{"title":"Analyzing Tail Risk Using Crisis Utility Rankings","authors":"K. Wakeman","doi":"10.2139/ssrn.1710705","DOIUrl":"https://doi.org/10.2139/ssrn.1710705","url":null,"abstract":"In this paper, we put forth the notion of “Crisis Utility” as a way of estimating the tail risk of an asset or investment strategy. We believe that Crisis Utility is more functional than traditional, narrowly defined definitions of tail risk since it incorporates the concept of “resiliency,” or recovery rate, as well as the traditional concept of maximum loss potential. Our argument for the inclusion of resiliency comes from our observations of the recent credit crisis. During the depths of the crisis we observed (1) that allocations, particularly institutional allocations, were “sticky,” which is to say that investors either had trouble adjusting asset allocations or were not inclined to do so, and (2) high water marks, or the arrangement that allows investors to recoup losses before a manager can charge additional performance fees, proved to be a significant benefit for resilient strategies. In an environment of sticky allocations and high water marks, we feel that the resiliency of a strategy becomes an important allocation point, particularly for institutions seeking to make long-term, strategic allocations as opposed to short-term, tactical allocations. Our study shows that lower volatility, low correlation strategies have a demonstrably higher Crisis Utility Rating than higher volatility, high correlation strategies. Specifically, using the HFR dataset, we found the strategies with the highest Crisis Utility Ranking were Short Bias, Equity Market Neutral, our bond proxy, Relative Value (Total), Systematic Diversified, Merger Arbitrage, Convertible Arbitrage and Fund of Funds: Defensive. We anticipate that these strategies will receive a relative increase in allocations as investors adjust their allocation models to account for tail risk, all else being equal and free of constraint. We also analyze the VIX Index within our Crisis Utility framework and find that it handily outscores all other strategies in our study. Although it is currently difficult to find active long volatility managers, we conclude that this is an important area for growth.","PeriodicalId":103169,"journal":{"name":"CGDET: Risk Management","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130478691","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}
We introduce a new criterion to perform hedging of contingent claims in incomplete markets. Our approach is close to the one proposed by Schweizer [Stochastic Process. Appl., 37 (1991), pp. 339-363] in that it uses the concept of locally risk-minimizing strategies. But we aim at being more general by defining the local risk as a general, nonnecessarily quadratic, convex function of the local cost process. We derive the corresponding optimal strategies and value function in both discrete and continuous time settings. Finally we give an application of our hedging method in the stochastic volatility case as well as in the jump diffusion case. We work with a single traded asset, but our approach may be generalized to deal with claims depending on multiple assets.
本文引入了不完全市场中或有债权套期保值的新准则。我们的方法接近于Schweizer[随机过程]提出的方法。达成。， 37 (1991)， pp. 339-363]，因为它使用了局部风险最小化策略的概念。但我们的目标是通过将局部风险定义为局部成本过程的一般的、不一定是二次的凸函数来实现更一般的目的。在离散和连续两种情况下，分别推导出相应的最优策略和值函数。最后给出了套期保值方法在随机波动情况和跳跃扩散情况下的应用。我们处理单个交易资产，但我们的方法可以推广到处理依赖于多个资产的索赔。
{"title":"Non Quadratic Local Risk-Minimization for Hedging Contingent Claims in Incomplete Markets","authors":"F. Abergel, Nicolas Millot","doi":"10.2139/ssrn.1647626","DOIUrl":"https://doi.org/10.2139/ssrn.1647626","url":null,"abstract":"We introduce a new criterion to perform hedging of contingent claims in incomplete markets. Our approach is close to the one proposed by Schweizer [Stochastic Process. Appl., 37 (1991), pp. 339-363] in that it uses the concept of locally risk-minimizing strategies. But we aim at being more general by defining the local risk as a general, nonnecessarily quadratic, convex function of the local cost process. We derive the corresponding optimal strategies and value function in both discrete and continuous time settings. Finally we give an application of our hedging method in the stochastic volatility case as well as in the jump diffusion case. We work with a single traded asset, but our approach may be generalized to deal with claims depending on multiple assets.","PeriodicalId":103169,"journal":{"name":"CGDET: Risk Management","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122721387","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 this paper, we develop asymptotic formulas for long-dated Foreign Exchange (FX) and swaptions implied volatilities. We extend the method exposed in Decamps and De Schepper (2009b) to a generic model with time-dependent parameters. Imposing a condition on the skew, we derive averaging formulas for the parameters. The method is applied to the pricing of FX options when the domestic and foreign interest rate curves are driven by Gaussian short-term rate models and to the pricing of swaptions in the Libor market model.
{"title":"Duru-Kleinert Asymptotic Expansions for Long-Term Foreign Exchange and Swaptions Implied Volatility Smile","authors":"M. Decamps, A. De Schepper","doi":"10.2139/ssrn.1514294","DOIUrl":"https://doi.org/10.2139/ssrn.1514294","url":null,"abstract":"In this paper, we develop asymptotic formulas for long-dated Foreign Exchange (FX) and swaptions implied volatilities. We extend the method exposed in Decamps and De Schepper (2009b) to a generic model with time-dependent parameters. Imposing a condition on the skew, we derive averaging formulas for the parameters. The method is applied to the pricing of FX options when the domestic and foreign interest rate curves are driven by Gaussian short-term rate models and to the pricing of swaptions in the Libor market model.","PeriodicalId":103169,"journal":{"name":"CGDET: Risk Management","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121373895","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}
We live in a world that is increasingly uncertain. For the first time in history humans dominate the planet and yet, paradoxically, the success of globalization hasincreased the risks we face.
{"title":"Catastrophic Risks: The Need for New Tools, Financial Instruments and Institutions","authors":"G. Chichilnisky","doi":"10.2139/ssrn.1377903","DOIUrl":"https://doi.org/10.2139/ssrn.1377903","url":null,"abstract":"We live in a world that is increasingly uncertain. For the first time in history humans dominate the planet and yet, paradoxically, the success of globalization hasincreased the risks we face.","PeriodicalId":103169,"journal":{"name":"CGDET: Risk Management","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133017280","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}
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