衍生工具-第3章-宋凌峰教学文稿.ppt

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,*,衍生工具 第3章 宋凌峰,支持套期保值的观点,Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates,exchange rates,and other market variables,2,反对套期保值的观点,Shareholders are usually well diversified and can make their own hedging decisions,It may increase risk to hedge when competitors do not,Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult,3,基差风险,Basis is usually defined as the spot price minus the futures price,Basis risk arises because of the uncertainty about the basis when the hedge is closed out,4,Long Hedge for Purchase of an Asset,Define,F,1,:,Futures price at time hedge is set up,F,2,:,Futures price at time asset is purchased,S,2,:,Asset price at time of purchase,b,2,:Basis at time of purchase,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,5,Cost of asset,S,2,Gain on Futures,F,2,F,1,Net amount paid,S,2,(,F,2,F,1,)=,F,1,+,b,2,交叉套期保值的情形,F,1,+,(S,2,*-F,2,)+(S,2,-S,2,*),Short Hedge for Sale of an Asset,Define,F,1,:,Futures price at time hedge is set up,F,2,:,Futures price at time asset is sold,S,2,:,Asset price at time of sale,b,2,:Basis at time of sale,Price of asset,S,2,Gain on Futures,F,1,F,2,Net amount received,S,2,+,(,F,1,F,2,)=,F,1,+,b,2,6,期货合约的选择,Choose a delivery month that is as close as possible to,but later than,the end of the life of the hedge,When there is no futures contract on the asset being hedged,choose the contract whose futures price is most highly correlated with the asset price.This is known as,cross hedging,.,7,Optimal Hedge Ratio,(page 57),Proportion of the exposure that should optimally be hedged is,where,s,S,is the standard deviation of,D,S,the change in the spot price during the hedging period,s,F,is the standard deviation of,D,F,the change in the futures price during the hedging period,r,is the coefficient of correlation between,D,S,and,D,F,.,8,Optimal Number of Contracts,Q,A,Size of position being hedged(units),Q,F,Size of one futures contract (units),V,A,Value of position being hedged(=spot price time,Q,A,),V,F,Value of one futures contract (=futures price times,Q,F,),Optimal number of contracts if no tailing adjustment,Optimal number of contracts after tailing adjustment to allow or daily settlement of futures,9,MVHR,假设决策者要通过调整期初持有的期货头寸来最小化期末的期现组合的价值的方差。假设现货价格变化期初为,S0,，期末为,S1,，期货价格期初为,F0,，期末位,F1,。那么最小化,1,单位的现货和,h,单位的期货构成的资产组合价值的方差的话，即,由于方差总存在最小值，仅考虑一阶条件，令,可得,也可写成,10,最小方差套保比,Example,(Pages 59-60),Airline will purchase 2 million gallons of jet fuel in one month and hedges using heating oil futures,From historical data,s,F,=0.0313,s,S,=0.0263,and,r,=0.928,11,Example,continued,The size of one heating oil contract is 42,000 gallons,The spot price is 1.94 and the futures price is 1.99(both dollars per gallon)so that,Optimal number of contracts assuming no daily settlement,Optimal number of contracts after tailing,12,OLS,简单线性回归方程要求模型的残差项是独立同分布的，若回归方程的残差项存在条件异方差，则估计出的,值不在具有有效性和无偏性，针对这个问题，,Engle(1982),首先提出了,ARCH,模型对方差进行建模，,Bollerslev(1986),将,ARCH,模型发展为广义,ARCH,模型（,GARCH,）。,大量实证研究表明,GARCH,模型能够很好地描述金融变量的波动特征。因此可以采用单变量,GARCH,模型，通过最大似然估计（,MLE,）求算最优套期保值比率。,GARCH(p,q),模型的一般形式如下：,残差项：,条件方差方程：,基于,GARCH,模型求套保比,股指期货合约,美国期货合约,S&P 500,股指期货,合约标的,S&P 500,合约乘数,$250,报价单位,指数点,最小变动,0.1,点,合约月份,3,月，,6,月，,9,月，,12,月,每日价格变化限制,最新,2010,年一季度的,熔断,变化点数为：,110,，,220,，,330,。当下降这些点数是熔断，上升不熔断。每季度重新计算一次。,最后交易日,合约到期月份的第三个星期五前的星期四,交割方式,现金交割,交割日期,最后交易日下一日,交易时间,周一到周五,:8:30 a.m.-3:15 p.m,保证金,Span,系统计算,最终结算价,Special Opening Quotation,（通过最后交易日下一交易日的股票开盘价计算）,头寸限制,20,000,手净多头或净空头,使用股指期货保值,(Page 61),To hedge the risk in a portfolio the number of contracts that should be shorted is,where,V,A,is the value of the portfolio,b,is its beta,and,V,F,is the value of one futures contract,16,Example,S&P 500 futures price is 1,000,Value of Portfolio is$5 million,Beta of portfolio is 1.5,What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?,17,改变,Beta,What position is necessary to reduce the beta of the portfolio to 0.75?,What position is necessary to increase the beta of the portfolio to 2.0?,18,Why Hedge Equity Returns,May want to be out of the market for a while.Hedging avoids the costs of selling and repurchasing the portfolio,Suppose stocks in your portfolio have an average beta of 1.0,but you feel they have been chosen well and will outperform the market in both good and bad times.Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market.(,获取,收益）,19,滚动对冲策略,We can roll futures contracts forward to hedge future exposures,Initially we enter into futures contracts to hedge exposures up to a time horizon,Just before maturity we close them out an replace them with new contract reflect the new exposure,etc,20,Liquidity Issues,(See Business Snapshot 3.2),In any hedging situation there is a danger that losses will be realized on the hedge while the gains on the underlying exposure are unrealized,This can create liquidity problems,One example is Metallgesellschaft which sold long term fixed-price contracts on heating oil and gasoline and hedged using stack and roll,The price of oil fell.,21,购销关系,Castle,公司,(,客户,),包销公司所有石油提炼产品，以最近月份的原油价格加成若干美元作为购买价格。,MGRM,公司,用户,以稍高于当时市价的固定价格定期提供给用户总量约,1.6,亿桶石油商品,十年长期合约,十年远期合同,产生风险管理需要,1/17/2025,22,“德国金属”必须为这个合约制定一套套期保值的策略，以把油品价格变动的风险转移到市场上去。它采用了,在,NYME,买入石油标准期货合约、在店头市场做互换合同,的方式来将它与用户的契约中引起的价格风险转移。这也符合其稳健的风格。,1/17/2025,23,交易结构,1/17/2025,24,油品价格涨跌的影响,价格上涨：,期货盈利，互换盈利，现货亏损。,价格下跌：,期货亏损，互换亏损，现货盈利。,价格上涨会使衍生物头寸有盈利。,1/17/2025,25,市场反向变化,1993,年,6,月,:19,美元,/,桶,1993,年,12,月,:15,美元,/,桶,1/17/2025,26,市场反向变化,OPEC,油价下滑,反向变,正向,保证金,追缴,出现庞大,资金缺口,1/17/2025,27,结局,1,在现货上积累的大量潜在利润无法变现,3,花,10,亿美元解除与,Castle,能源公司的合约,2,在能源期货和互换交易上损失,13,亿美元,Rescue,150,家德国和其它国际银行,对,MG,公司采取了一个数额高达,19,亿美元的拯救行动，才使得,MG,公司避免了破产。,1/17/2025,28,德国金属套保案例,29,为了说明MGRM的对冲方案所面临的基差风险，我们先将其简化。假定现在是1993年1月份，MGRM与顾客签订的远期合约是在1993年5月份交割。采取stack-and-roll策略对这一远期合约的空头进行套期保值：在1月，建立1993年2月到期的期货合约多头。到2月时，平掉2月期货的多头，同时建立3月到期的期货合约多头，以此类推到1993年5月时，平掉在4月份建立的5月期货的多头，同时在现货市场购进现货，兑现远期合约。,德国金属套保案例,假定远期合约中商定的交割价为S1(5)，在5月份，现货价格为S5(5)；Fi(j)表示在第i个月里交割月为j的期货合约的价格。,现货市场盈利=S1(5)S5(5),期货市场盈利=F2(2)F1(2)+F3(3)F2(3)+F4(4)F3(4)+F5(5)F4(5),德国金属套保案例,现货与期货的总盈利=S1(5)S5(5)+F2(2)F1(2)+F3(3)F2(3)+F4(4)F3(4)+F5(5)F4(5),由于临近交割时，期货价格趋近现货价格，所以我们大致可以认为S5(5)=F5(5),利用这一假定，重新排列总盈利公式，可得：,总盈利=S1(5)F1(2)+F2(2)F2(3)+F3(3)F3(4)+F4(4)F4(5),=S1(5)F1(2)+2月基差+3月基差+4月基差,德国金属套保案例,在远期升水的市场上,基差为负，这意味着每向前滚动一次，总盈利就要减少。,在远期贴水的市场上，基差为正，这意味着每向前滚动一次，总盈利就会增加。,德国金属套保案例,一般的，商品期货市场上的远期贴水现象仅在近交割期的期货合约上表现明显。由于持有成本会随着交割日的延长而增加，因此远交割期的期货合约还是会表现出一个更高的溢价。,德国金属套保案例,MGRM公司与顾客签订的合约一般长达10年，可以看到影响其盈利的基差个数较多。而且MGRM每次购买的也不只是单纯的一个合约，而是一组不同产品的合约。可见这一策略将公司置于巨大的基差风险下。,德国金属套保案例,由于石油期货市场历史上表现出的大多数时候都是远期贴水市场。并且MGRM的对冲策略中采用的都是近交割期的期货合约。如前所述，近期的石油期货合约更倾向于远期贴水。所以，当时MGRM认为，他们的这个策略是可以带来额外盈利的，即使有亏损，但总体上对冲方案带来的盈利也会超过亏损。,德国金属套保案例,1993年能源期货价格表现的很不寻常，其表现出的是远期升水而不是大多数年份出现的远期贴水。,下图描绘了1985-1995年三种能源期货合约（原油、燃油、汽油）的滚动成本。这里，滚动成本,=,下一个要到期的期货合约价格,即将到期期货合约价格（到期日前三天的结算价）,从图中可以看出，滚动成本在1993年大多为正（即基差为负）。,德国金属套保案例,正是由于1993年基差行为的突然转向使得MGRM遭受了巨大损失。并且在期货交易中，由于每次一组合约到期时产生的损失,MGRM,都要及时确认，所以造成了公司大量的短期现金流的流出，最终致使公司陷入了财务危机。,德国金属套保案例,思考题,基差风险是什么,基差风险如何进行控制,41,此课件下载可自行编辑修改，仅供参考！感谢您的支持，我们努力做得更好！谢谢,