第一小问：volatility arbitrage策略

NO.PZ2019092801000006问题如下Sushil Wallais the chief investment officer of a large pension fun Wallawants to increase the pension funs allocation to hee fun anrecently met with three hee funmanagers. These hee fun focus on the following strategies:Hee FunSpecialist—Follows relative value volatility arbitrageHee FunMulti-Manager—Multi-strategy funee FunMulti-Manager—Funof-fun1. scrithree paths for implementing the strategy of Hee FunA.After a significant amount of internscussion, Wallaconclus ththe pension funshoulinvest in either Hee FunB or C for the versification benefits from the fferent strategies employe However, after fine ligenis complete Wallarecommen investing only in Hee Funnoting its many aantages over Hee FunC.2. scuss two aantages of Hee FunB relative to Hee FunC with respeto investment characteristics. 1. Hee FunA’s volatility trang strategy cimplementefollowing multiple paths. One path is through simple exchange-traoptions. The maturity of suoptions typically exten to no more thtwo years. In terms of expiry, the longer-teoptions will have more absolute exposure to volatility levels thshorter-teoptions, but the shorter-teoptions will exhibit more lta sensitivity to prichanges.A secon similpath is to implement the volatility trang strategy using OTC options. In this case, the tenor anstrike prices of the options ccustomize The tenor of expiry tes cthen extenbeyonwhis available with exchange-traoptions.A thirpath is to use VIX futures or options on VIX futures a wto more explicitly express a pure volatility view without the neefor constant lta heing of equity put or call for isolating the volatility exposure.A fourth path for implementing a volatility trang strategy woulto purchase OTC volatility swor a varianswfrom a cretworthy counterparty. A volatility swis a forwarcontraon future realizeprivolatility. Similarly, a varianswis a forwarcontraon future realizeprivariance, where varianis the square of volatility. Both volatility anvarianswaps provi “pure” exposure to volatility alone, unlike stanrzeoptions in whithe volatility exposure pen on the priof the unrlying asset anmust isolateanextractevia lta heing. 首先只要 relative value volatility arbitrage，都是short波动率低，long波动率高的，进行套利。这四种都是，只是这四种都有各自的特点，首先就是策略一和策略二都受到lta和gamma的影响（所以要想办法对冲掉），策略三和四不受影响。策略一是通过简单的交易所交易期权。这类期权的到期时间一般不超过两年。从到期日来看，期限较长的期权比期限较短的期权对波动率水平的绝对风险敞口更大，所以是long长期short短期，但期限较短的期权对价格变化表现出更多的lta敏感性，所以对冲掉lta。策略二类似的路径是利用场外期权实施波动率交易策略。在这种情况下，期权的期限和行权价格可以自定义。然后，到期日的期限可以扩展到交易所交易的期权之外。但是会有counterpart risk的风险。对冲掉lta和gamma方法，lta对冲很简答，lta是一阶导，说白了就是同涨同跌，如果lta是,1，那就是stock涨了10，option涨了10，有十张call就做空10股stock，如果是-1，比如put，有十张put，那就做多10股stock。至于gamma，假设100股C股票涨了1%，然后*100股，就涨了100对吧，而买的这个C股票的call因为gamma的原因没有百分百的对冲，涨了1.2%，对应就是涨了120对吧。那现在多了120-100=20，就卖空20股C股票，这样就100%的对冲了。 relative value volatility arbitrage实际就是套利，赚取sprea做空高估volatility的，做多类似的低估volatility。但是有的（比如策略一和策略二，的期权）实施这个策略会有lta和gamma的影响（大概说下就是期权会有方向性的lta和二阶导的gamma等因素影响），但是我不想受除了volatility以外的因素影响，就需要借助工具对冲掉，对吧，但是一般都不能完全对冲干净其它影响因素，这样套利就很受影响。这里策略三 实际VIX Inx futures (or options on VIX futures)，本质就是一个专门交易volatility的inx的future或者volatility的inx的future的期权（有点绕口，可以理解就是前面的future为底层资产的option）。因为只交易volatility，所以影响因素只有volatility，这时候，就只考虑做多低估的volatility的future做空类似的高估的volatility的future。而不用担心受到lta和gamma的影响了。策略四实际就是互换，用现在的波动换将来的波动率，这个好理解。 2. Multi-strategy managers like Hee FunB creallocate capitinto fferent strategy aremore quickly anefficiently thwoulpossible a funof-fun (FoF) manager like Hee FunThe multi-strategy manager hfull transparenana better picture of the interactions of the fferent teams’ portfolio risks thwoulever possible for FoF managers to achieve. Consequently, the multi-strategy manager creafaster to fferent real-time market impacts—for example, rapiy increasing or creasing leverage within fferent strategies penng upon the perceiveriskiness of available opportunities.The fees paiinvestors in a multi-strategy funcstructurein a number of ways, some of whicvery attractive when compareto the FoFs’ aefee layering annetting risk attributes. Conceptually, FoF investors always fanetting risk, wherethey are responsible for paying performanfees e to winning unrlying fun while suffering return from the performanof losing unrlying fun. Even if the FoF’s overall performanis flor wn, FoF investors must still pincentive fees e to the managers of winning fun.这块考点是教材的内容，例题也有，需要背诵。 请问一下策略一里，短期的期权比长期的表现出更多的lta敏感性怎么呢？能举个例子吗？

NO.PZ2019092801000006 问题如下 Sushil Wallais the chief investment officer of a large pension fun Wallawants to increase the pension funs allocation to hee fun anrecently met with three hee funmanagers. These hee fun focus on the following strategies:Hee FunSpecialist—Follows relative value volatility arbitrageHee FunMulti-Manager—Multi-strategy funee FunMulti-Manager—Funof-fun1. scrithree paths for implementing the strategy of Hee FunA.After a significant amount of internscussion, Wallaconclus ththe pension funshoulinvest in either Hee FunB or C for the versification benefits from the fferent strategies employe However, after fine ligenis complete Wallarecommen investing only in Hee Funnoting its many aantages over Hee FunC.2. scuss two aantages of Hee FunB relative to Hee FunC with respeto investment characteristics. 1. Hee FunA’s volatility trang strategy cimplementefollowing multiple paths. One path is through simple exchange-traoptions. The maturity of suoptions typically exten to no more thtwo years. In terms of expiry, the longer-teoptions will have more absolute exposure to volatility levels thshorter-teoptions, but the shorter-teoptions will exhibit more lta sensitivity to prichanges.A secon similpath is to implement the volatility trang strategy using OTC options. In this case, the tenor anstrike prices of the options ccustomize The tenor of expiry tes cthen extenbeyonwhis available with exchange-traoptions.A thirpath is to use VIX futures or options on VIX futures a wto more explicitly express a pure volatility view without the neefor constant lta heing of equity put or call for isolating the volatility exposure.A fourth path for implementing a volatility trang strategy woulto purchase OTC volatility swor a varianswfrom a cretworthy counterparty. A volatility swis a forwarcontraon future realizeprivolatility. Similarly, a varianswis a forwarcontraon future realizeprivariance, where varianis the square of volatility. Both volatility anvarianswaps provi “pure” exposure to volatility alone, unlike stanrzeoptions in whithe volatility exposure pen on the priof the unrlying asset anmust isolateanextractevia lta heing. 首先只要 relative value volatility arbitrage，都是short波动率低，long波动率高的，进行套利。这四种都是，只是这四种都有各自的特点，首先就是策略一和策略二都受到lta和gamma的影响（所以要想办法对冲掉），策略三和四不受影响。策略一是通过简单的交易所交易期权。这类期权的到期时间一般不超过两年。从到期日来看，期限较长的期权比期限较短的期权对波动率水平的绝对风险敞口更大，所以是long长期short短期，但期限较短的期权对价格变化表现出更多的lta敏感性，所以对冲掉lta。策略二类似的路径是利用场外期权实施波动率交易策略。在这种情况下，期权的期限和行权价格可以自定义。然后，到期日的期限可以扩展到交易所交易的期权之外。但是会有counterpart risk的风险。对冲掉lta和gamma方法，lta对冲很简答，lta是一阶导，说白了就是同涨同跌，如果lta是,1，那就是stock涨了10，option涨了10，有十张call就做空10股stock，如果是-1，比如put，有十张put，那就做多10股stock。至于gamma，假设100股C股票涨了1%，然后*100股，就涨了100对吧，而买的这个C股票的call因为gamma的原因没有百分百的对冲，涨了1.2%，对应就是涨了120对吧。那现在多了120-100=20，就卖空20股C股票，这样就100%的对冲了。 relative value volatility arbitrage实际就是套利，赚取sprea做空高估volatility的，做多类似的低估volatility。但是有的（比如策略一和策略二，的期权）实施这个策略会有lta和gamma的影响（大概说下就是期权会有方向性的lta和二阶导的gamma等因素影响），但是我不想受除了volatility以外的因素影响，就需要借助工具对冲掉，对吧，但是一般都不能完全对冲干净其它影响因素，这样套利就很受影响。这里策略三 实际VIX Inx futures (or options on VIX futures)，本质就是一个专门交易volatility的inx的future或者volatility的inx的future的期权（有点绕口，可以理解就是前面的future为底层资产的option）。因为只交易volatility，所以影响因素只有volatility，这时候，就只考虑做多低估的volatility的future做空类似的高估的volatility的future。而不用担心受到lta和gamma的影响了。策略四实际就是互换，用现在的波动换将来的波动率，这个好理解。 2. Multi-strategy managers like Hee FunB creallocate capitinto fferent strategy aremore quickly anefficiently thwoulpossible a funof-fun (FoF) manager like Hee FunThe multi-strategy manager hfull transparenana better picture of the interactions of the fferent teams’ portfolio risks thwoulever possible for FoF managers to achieve. Consequently, the multi-strategy manager creafaster to fferent real-time market impacts—for example, rapiy increasing or creasing leverage within fferent strategies penng upon the perceiveriskiness of available opportunities.The fees paiinvestors in a multi-strategy funcstructurein a number of ways, some of whicvery attractive when compareto the FoFs’ aefee layering annetting risk attributes. Conceptually, FoF investors always fanetting risk, wherethey are responsible for paying performanfees e to winning unrlying fun while suffering return from the performanof losing unrlying fun. Even if the FoF’s overall performanis flor wn, FoF investors must still pincentive fees e to the managers of winning fun.这块考点是教材的内容，例题也有，需要背诵。 请问直接写exchange-traoptions, OTC options, VIX inx futures, OTC volatility swap/varianswap可以么

NO.PZ2019092801000006 问题如下 Sushil Wallais the chief investment officer of a large pension fun Wallawants to increase the pension funs allocation to hee fun anrecently met with three hee funmanagers. These hee fun focus on the following strategies:Hee FunSpecialist—Follows relative value volatility arbitrageHee FunMulti-Manager—Multi-strategy funee FunMulti-Manager—Funof-fun1. scrithree paths for implementing the strategy of Hee FunA.After a significant amount of internscussion, Wallaconclus ththe pension funshoulinvest in either Hee FunB or C for the versification benefits from the fferent strategies employe However, after fine ligenis complete Wallarecommen investing only in Hee Funnoting its many aantages over Hee FunC.2. scuss two aantages of Hee FunB relative to Hee FunC with respeto investment characteristics. 1. Hee FunA’s volatility trang strategy cimplementefollowing multiple paths. One path is through simple exchange-traoptions. The maturity of suoptions typically exten to no more thtwo years. In terms of expiry, the longer-teoptions will have more absolute exposure to volatility levels thshorter-teoptions, but the shorter-teoptions will exhibit more lta sensitivity to prichanges.A secon similpath is to implement the volatility trang strategy using OTC options. In this case, the tenor anstrike prices of the options ccustomize The tenor of expiry tes cthen extenbeyonwhis available with exchange-traoptions.A thirpath is to use VIX futures or options on VIX futures a wto more explicitly express a pure volatility view without the neefor constant lta heing of equity put or call for isolating the volatility exposure.A fourth path for implementing a volatility trang strategy woulto purchase OTC volatility swor a varianswfrom a cretworthy counterparty. A volatility swis a forwarcontraon future realizeprivolatility. Similarly, a varianswis a forwarcontraon future realizeprivariance, where varianis the square of volatility. Both volatility anvarianswaps provi “pure” exposure to volatility alone, unlike stanrzeoptions in whithe volatility exposure pen on the priof the unrlying asset anmust isolateanextractevia lta heing. 首先只要 relative value volatility arbitrage，都是short波动率低，long波动率高的，进行套利。这四种都是，只是这四种都有各自的特点，首先就是策略一和策略二都受到lta和gamma的影响（所以要想办法对冲掉），策略三和四不受影响。策略一是通过简单的交易所交易期权。这类期权的到期时间一般不超过两年。从到期日来看，期限较长的期权比期限较短的期权对波动率水平的绝对风险敞口更大，所以是long长期short短期，但期限较短的期权对价格变化表现出更多的lta敏感性，所以对冲掉lta。策略二类似的路径是利用场外期权实施波动率交易策略。在这种情况下，期权的期限和行权价格可以自定义。然后，到期日的期限可以扩展到交易所交易的期权之外。但是会有counterpart risk的风险。对冲掉lta和gamma方法，lta对冲很简答，lta是一阶导，说白了就是同涨同跌，如果lta是,1，那就是stock涨了10，option涨了10，有十张call就做空10股stock，如果是-1，比如put，有十张put，那就做多10股stock。至于gamma，假设100股C股票涨了1%，然后*100股，就涨了100对吧，而买的这个C股票的call因为gamma的原因没有百分百的对冲，涨了1.2%，对应就是涨了120对吧。那现在多了120-100=20，就卖空20股C股票，这样就100%的对冲了。 relative value volatility arbitrage实际就是套利，赚取sprea做空高估volatility的，做多类似的低估volatility。但是有的（比如策略一和策略二，的期权）实施这个策略会有lta和gamma的影响（大概说下就是期权会有方向性的lta和二阶导的gamma等因素影响），但是我不想受除了volatility以外的因素影响，就需要借助工具对冲掉，对吧，但是一般都不能完全对冲干净其它影响因素，这样套利就很受影响。这里策略三 实际VIX Inx futures (or options on VIX futures)，本质就是一个专门交易volatility的inx的future或者volatility的inx的future的期权（有点绕口，可以理解就是前面的future为底层资产的option）。因为只交易volatility，所以影响因素只有volatility，这时候，就只考虑做多低估的volatility的future做空类似的高估的volatility的future。而不用担心受到lta和gamma的影响了。策略四实际就是互换，用现在的波动换将来的波动率，这个好理解。 2. Multi-strategy managers like Hee FunB creallocate capitinto fferent strategy aremore quickly anefficiently thwoulpossible a funof-fun (FoF) manager like Hee FunThe multi-strategy manager hfull transparenana better picture of the interactions of the fferent teams’ portfolio risks thwoulever possible for FoF managers to achieve. Consequently, the multi-strategy manager creafaster to fferent real-time market impacts—for example, rapiy increasing or creasing leverage within fferent strategies penng upon the perceiveriskiness of available opportunities.The fees paiinvestors in a multi-strategy funcstructurein a number of ways, some of whicvery attractive when compareto the FoFs’ aefee layering annetting risk attributes. Conceptually, FoF investors always fanetting risk, wherethey are responsible for paying performanfees e to winning unrlying fun while suffering return from the performanof losing unrlying fun. Even if the FoF’s overall performanis flor wn, FoF investors must still pincentive fees e to the managers of winning fun.这块考点是教材的内容，例题也有，需要背诵。 你好老师，麻烦给我批改下答案，谢谢！！不知道我能拿到多少分呢？1. scrithree paths for implementing the strategy of Hee FunA:Specialist—Follows relative value volatility arbitrage1. Long VIX futures. 2. Long call option on VIX futures. 3. Long varianswap. 2. scuss two aantages of Hee FunB relative to Hee FunC with respeto investment characteristics.FOFs are more versifiethMulti-strategy funbecause FOFs invest in fferent hee fun anthey are less correlateMulti-strategy funhmore manager-specific risks(left-tail risk) while FOFs hless extreme risk.

NO.PZ2019092801000006问题如下Sushil Wallais the chief investment officer of a large pension fun Wallawants to increase the pension funs allocation to hee fun anrecently met with three hee funmanagers. These hee fun focus on the following strategies:Hee FunSpecialist—Follows relative value volatility arbitrageHee FunMulti-Manager—Multi-strategy funee FunMulti-Manager—Funof-fun1. scrithree paths for implementing the strategy of Hee FunA.After a significant amount of internscussion, Wallaconclus ththe pension funshoulinvest in either Hee FunB or C for the versification benefits from the fferent strategies employe However, after fine ligenis complete Wallarecommen investing only in Hee Funnoting its many aantages over Hee FunC.2. scuss two aantages of Hee FunB relative to Hee FunC with respeto investment characteristics. 1. Hee FunA’s volatility trang strategy cimplementefollowing multiple paths. One path is through simple exchange-traoptions. The maturity of suoptions typically exten to no more thtwo years. In terms of expiry, the longer-teoptions will have more absolute exposure to volatility levels thshorter-teoptions, but the shorter-teoptions will exhibit more lta sensitivity to prichanges.A secon similpath is to implement the volatility trang strategy using OTC options. In this case, the tenor anstrike prices of the options ccustomize The tenor of expiry tes cthen extenbeyonwhis available with exchange-traoptions.A thirpath is to use VIX futures or options on VIX futures a wto more explicitly express a pure volatility view without the neefor constant lta heing of equity put or call for isolating the volatility exposure.A fourth path for implementing a volatility trang strategy woulto purchase OTC volatility swor a varianswfrom a cretworthy counterparty. A volatility swis a forwarcontraon future realizeprivolatility. Similarly, a varianswis a forwarcontraon future realizeprivariance, where varianis the square of volatility. Both volatility anvarianswaps provi “pure” exposure to volatility alone, unlike stanrzeoptions in whithe volatility exposure pen on the priof the unrlying asset anmust isolateanextractevia lta heing. 首先只要 relative value volatility arbitrage，都是short波动率低，long波动率高的，进行套利。这四种都是，只是这四种都有各自的特点，首先就是策略一和策略二都受到lta和gamma的影响（所以要想办法对冲掉），策略三和四不受影响。策略一是通过简单的交易所交易期权。这类期权的到期时间一般不超过两年。从到期日来看，期限较长的期权比期限较短的期权对波动率水平的绝对风险敞口更大，所以是long长期short短期，但期限较短的期权对价格变化表现出更多的lta敏感性，所以对冲掉lta。策略二类似的路径是利用场外期权实施波动率交易策略。在这种情况下，期权的期限和行权价格可以自定义。然后，到期日的期限可以扩展到交易所交易的期权之外。但是会有counterpart risk的风险。对冲掉lta和gamma方法，lta对冲很简答，lta是一阶导，说白了就是同涨同跌，如果lta是,1，那就是stock涨了10，option涨了10，有十张call就做空10股stock，如果是-1，比如put，有十张put，那就做多10股stock。至于gamma，假设100股C股票涨了1%，然后*100股，就涨了100对吧，而买的这个C股票的call因为gamma的原因没有百分百的对冲，涨了1.2%，对应就是涨了120对吧。那现在多了120-100=20，就卖空20股C股票，这样就100%的对冲了。 relative value volatility arbitrage实际就是套利，赚取sprea做空高估volatility的，做多类似的低估volatility。但是有的（比如策略一和策略二，的期权）实施这个策略会有lta和gamma的影响（大概说下就是期权会有方向性的lta和二阶导的gamma等因素影响），但是我不想受除了volatility以外的因素影响，就需要借助工具对冲掉，对吧，但是一般都不能完全对冲干净其它影响因素，这样套利就很受影响。这里策略三 实际VIX Inx futures (or options on VIX futures)，本质就是一个专门交易volatility的inx的future或者volatility的inx的future的期权（有点绕口，可以理解就是前面的future为底层资产的option）。因为只交易volatility，所以影响因素只有volatility，这时候，就只考虑做多低估的volatility的future做空类似的高估的volatility的future。而不用担心受到lta和gamma的影响了。策略四实际就是互换，用现在的波动换将来的波动率，这个好理解。 2. Multi-strategy managers like Hee FunB creallocate capitinto fferent strategy aremore quickly anefficiently thwoulpossible a funof-fun (FoF) manager like Hee FunThe multi-strategy manager hfull transparenana better picture of the interactions of the fferent teams’ portfolio risks thwoulever possible for FoF managers to achieve. Consequently, the multi-strategy manager creafaster to fferent real-time market impacts—for example, rapiy increasing or creasing leverage within fferent strategies penng upon the perceiveriskiness of available opportunities.The fees paiinvestors in a multi-strategy funcstructurein a number of ways, some of whicvery attractive when compareto the FoFs’ aefee layering annetting risk attributes. Conceptually, FoF investors always fanetting risk, wherethey are responsible for paying performanfees e to winning unrlying fun while suffering return from the performanof losing unrlying fun. Even if the FoF’s overall performanis flor wn, FoF investors must still pincentive fees e to the managers of winning fun.这块考点是教材的内容，例题也有，需要背诵。 为啥long high volatility，short low volatility 而不short over valuelong unr value问题如上重点针对第一问题中volatility的trang strategy，请解答，谢谢