期货与互换的详细分析.ppt

第23章 期货与互换的详细分析 Futures and Swaps: A Closer Look,期货与互换 Futures and Swaps,23.1 外汇期货 23.2 股票指数期货 23.3 利率期货 23.4 商品期货的定价 23.5 互换,期货市场 Futures markets 芝加哥商品交易所 ( 国际货币市场 ) Chicago Mercantile (International Monetary Market) 伦敦国际金融期货交易所 London International Financial Futures Exchange 中美洲商品交易所 MidAmerica Commodity Exchange 活跃的远期市场 Active forward market 期货市场和远期市场的差异 Differences between futures and forward markets,外汇期货 Foreign Exchange Futures,利率平价理论Interest rate parity theorem 用美元和英镑来举例Developed using the US Dollar and British Pound,where F0 : 是远期价格 is the forward price E0: 为当前两种货币的汇率 is the current exchange rate,外汇期货定价 Pricing on Foreign Exchange Futures,定价举例 Text Pricing Example,rus = 5% ruk = 6% E0 = $1.60 per pound T = 1 yr,当r us小于r uk时，F0肯定小于E0，由F0比E0得到的美元升值程度正好可以与两国利率之间 的差额抵消。当然，如果情况相反结论依然成立：当 r us大于r uk时，F0肯定大于E0。 When rus is less than ruk, F0 must be less than E0. The appreciation of the dollar embodied in the ratio of F0 to E0 exactly compensates for the difference in interest rates available in the two countries. Of course, the argument also works in reverse: If rus is greater than ruk, then F0 is greater than E0.,外汇期货 Foreign Exchange Futures,汇率风险套期保值 Hedging Foreign Exchange Risk,汇率风险套期保值 Hedging Foreign Exchange Risk,汇率风险套期保值 Hedging Foreign Exchange Risk,套利的净所得是无风险的，它等于 E0(1rUS)-F0(1r UK)。如果这个值是正的，就在英国借款，在美国贷款，然后建立期货多头头寸以消除汇率风险。如果这个值是负的，就在美国借款，在英国贷款，然后建立英镑期货的空头头寸。当价格正好相符没有套利机会时，这个表达式一定等于零。如果它为正，投资者会攫取套利收益；如果它为负，投资者反向操作还是能获得套利收益。把这个表达式整理一下得到： The net proceeds to the arbitrage portfolio are risk-free and given by E0(1+rUS)- F0(1+rUK). If this value is positive, borrow in the United Kingdom, lend in the United States, and enter a long futures position to eliminate foreign exchange risk. If the value is negative, borrow in the United States, lend in the United Kingdom, and take a short position in pound futures. When prices preclude arbitrage opportunities, the expression must equal zero. Rearranging this expression gives us the relationship,对本国和国际股票都有效 Available on both domestic and international stocks. 与直接购买股票相比的优点 Advantages over direct stock purchase: 更低的交易成本 lower transaction costs 有利市场时机和重组的选择 better for timing or allocation strategies 减少资产组合的时间 takes less time to acquire the portfolio,股票指数期货 Stock Index Contracts,用股指期货建立综合头寸 Using Stock Index Contracts to Create Synthetic Positions,综合股购买Synthetic stock purchase: 购买股指而不是实际的股票 Purchase of the stock index instead of actual shares of stock. 国库券加股指期货综合头寸的建立可得到比仅投资股指期货的双倍收入 Creation of a synthetic T-bill plus index futures that duplicates the payoff of the stock index contract.,使用股指期货建立综合头寸 Using Stock Index Contracts to Create Synthetic Positions,使用股指期货建立综合头寸 Using Stock Index Contracts to Create Synthetic Positions,使用股指期货建立综合头寸 Using Stock Index Contracts to Create Synthetic Positions,例如，假如一机构投资者想在市场上进行为期一个月的 4500 万美元的投资，为了使交易费用最省，他决定购买标准普尔500指数期货合约而不是真正持有股票。如果现在的标准普尔500股指为900点，1月期的期货价格是909点，国库券的月利率是1%， 则该投资者需要买入200份合约(每份合约相当于价值为250美元 900225 000美元的股票，而45000000 美元/225000美元 200)。这样他就有了50000美元乘以标准普尔500指数的多头头寸 (200份合约乘以合约的指数单价250美元)。为了支付期货价格，该投资者在国库券上的投资额必须等于50000美元乘以期货价格的现值，即50000 美元(909/1.01)45000000美元市值的国库券。注意，在国库券上这4500万美元的支出恰好等于直接购买股票所需的资金数额(国库券的面值是50000美元90945 450 000美元)。,使用股指期货建立综合头寸 Using Stock Index Contracts to Create Synthetic Positions,那么到了到期日，该综合股票头寸的价值是多少呢？与以往一样，我们设ST为到期日股指价值， F0为原期货价格：,合约到期日的总收入的确与股指价值成比例，也就是说，除了期中的红利分配与税务处理这两点外，采取这种证券资产组合策略与持有指数股票资产组合本身没什么区别。,使用股指期货建立综合头寸 Using Stock Index Contracts to Create Synthetic Positions,For example, suppose that an institutional investor wants to invest $135 million in the market for one month and, to minimize trading costs, chooses to buy the S&P 500 futures contracts as a substitute for actual stock holdings. If the index is now at 1,350, the one- month delivery futures price is 1,363.50, and the T-bill rate is 1% per month, it would buy 400 contracts. (Each contract controls $2501,350 $337,500 worth of stock, and $135million/$337,500400.) The institution thus has a long position on 100,000 times the S&P 500 index (400 contracts times the contract multiplier of 250). To cover payment of the futures price, it must invest 100,000 times the present value of the futures price in T- bills. This equals 100,000,363.50/1.01)$135 million market value of bills. Notice that the $135 million outlay in bills is precisely equal to the amount that would have been needed to buy the stock directly. (The face value of the bills will be 100,0001,363.50$136.35 million.),使用股指期货建立综合头寸 Using Stock Index Contracts to Create Synthetic Positions,This is an artificial, or synthetic, stock position. What is the value of this portfolio at the maturity date? Call ST the value of the stock index on the maturity date T, and as usual, let F0 be the original futures price:,The total payoff on the contract maturity date is exactly proportional to the value of the stock index. In other words, adopting this portfolio strategy is equivalent to holding the stock index itself, aside from the issue of interim dividend distributions and tax treatment.,股指期货定价 Pricing on Stock Index Contracts,现货与期货价格之间的平价关系是; The spot-futures price parity that was developed in Chapter 22 is given as; F0S0(1r f d ) T 实证研究已经证实期货价格与现货价格密切相关. Empirical investigations have shown that the actual pricing relationship on index contracts follows the spot-futures relationship. d:为年红利率 dividend rate,寻找股票和股指间的价格差 Exploiting mispricing between underlying stocks and the futures index contract. 期货价太高-卖空股指期货买股指股票 Futures Price too high - short the future and buy the underlying stocks. 期货价太低-买股指期货卖空股指股票 Futures price too low - long the future and short sell the underlying stocks.,指数套利 Index Arbitrage,实际上指数套利很难进行 This is difficult to implement in practice. Transactions costs are often too large. Trades cannot be done simultaneously. 程序交易的发展 Development of Program Trading Used by arbitrageurs to perform index arbitrage. Permits acquisition of securities quickly. 三重魔力日 Triple-witching hour Evidence that index arbitrage impacts volatility.,指数套利和程序交易 Index Arbitrage and Program Trading,对冲系统风险 Hedging Systematic Risk,为保护股票市场价格的下降,买空相应数量的股指期货. To protect against a decline in level stock prices, short the appropriate number of futures index contracts. 用股指期货可低成本和更快速 Less costly and quicker to use the index contracts. 使用资产组合来决定对冲率 Use the beta for the portfolio to determine the hedge ratio.,对冲系统风险:举例 Hedging Systematic Risk: Text Example,Portfolio Beta = .8 S&P 500 = 1,000 Decrease = 2.5% S&P falls to 975 投资组合价值Portfolio Value = $30 million Project loss if market declines by 2.5% = (.8) (2.5) = 2% 2% of $30 million = $600,000 Each S&P500 index contract will change $6,250 for a 2.5% change in the index,对冲率:举例 Hedge Ratio: Text Example,H = =,投资组合的变化Change in the portfolio value 一个期货合约的利润Profit on one futures contract $600,000 $6,250,= 96 合约(空头) contracts short,利率期货 Interest Rate Futures,本国利率合约 Domestic interest rate contracts 国库券,票据和债券T-bills, notes and bonds 市政债券municipal bonds 国际合约International contracts 欧洲美元Eurodollar 对冲Hedging 承销商Underwriters 公司发行债务Firms issuing debt,利率套期保值的运用 Uses of Interest Rate Hedges,拥有固定收益资产组合的投资者保护利率的上升Owners of fixed-income portfolios protecting against a rise in rates. 计划发行债券的公司保护利率上升Corporations planning to issue debt securities protecting against a rise in rates. 投资者锁定计划未来投资的收益率（对冲利率的下降） Investor hedging against a decline in rates for a planned future investment.,对冲利率风险 Hedging Interest Rate Risk: Text Example,组合价值Portfolio value = $10 million 定义的久期Modified duration = 9 years 如果利率上升10个基点If rates rise by 10 basis points (.1%) 价值变化Change in value = ( 9 ) ( .1%) = .9% or $90,000 基点现值Present value of a basis point (PVBP) = $90,000 / 10 = $9,000,对冲率:举例 Hedge Ratio: Text Example,H = =,投资组合的PVBP for the portfolio 对冲工具的PVBP for the hedge vehicle $9,000 $90,= 100 contracts,商品期货定价 Commodity Futures Pricing,股票定价原理也可运用到商品期货定价 General principles that apply to stock apply to commodities. 商品有持有成本 Carrying costs are more for commodities.,Where; F0 = futures price P0 = cash price of the asset C = Carrying cost c = C/P0,商品期货定价 Commodity Futures Pricing,因为市场价格不允许存在套利机会，所以这种净投资为零的无风险策略的最终现金流应该为零。如果现金流为正，按照这种方法不需任何投资就可获得可靠的收益。如果现金流为负，采取相反的步骤仍可获利。实际上，反向操作需要卖空商品，这是不常见的， 不过只要卖空合理地考虑了存储成本就仍是可行的 。,商品期货定价 Commodity Futures Pricing,Because market prices should not allow for arbitrage opportunities, the terminal cash flow of this zero net investment, risk-free strategy should be zero. If the cash flow were positive, this strategy would yield guaranteed profits for no in- vestment. If the cash flow were negative, the reverse of this strategy also would yield prof- its. In practice, the reverse strategy would involve a short sale of the commodity. This is unusual but may be done as long as the short sale contract appropriately accounts for storage costs,利率互换Interest rate swap 汇率互换Foreign exchange swap 信用风险互换Credit risk on swaps 互换的其它类型Swap Variations 利率上限合约Interest rate cap 利率下限合约Interest rate floor 利率双限合约Collars 互换期权Swaptions,互换 Swaps,互换是一系列的期货合约 Swaps are essentially a series of forward contracts. 互换和期货合约的不同是：互换在每个周期内有相同的收支而与此同时期货合约在不同的周期有不同的收支 One difference is that the swap is usually structured with the same payment each period while the forward rate would be different each period.,互换定价 Pricing on Swap Contracts,用汇率互换作为例子,互换定价将被由下式定义 Using a foreign exchange swap as an example, the swap pricing would be described by the following formula. 其中 y1与y2分别是用来对一年期与二年期美元现金流进行贴现的收益率，该收益 率可以从收益曲线上得到。 where y1 and y2 are the appropriate yields from the yield curve for discounting dollar cash flows of one- and two-year maturities, respectively.,互换定价 Pricing on Swap Contracts,各种股票市场指数的期货合约都采用现金结算。把这些合约与国库券结合可以构造综合股票头寸，对市场时机决定者来说，这是一种非常有价值的工具。同样，股票指数期货合约也可以被套利者用来从市场的非平价关系中套利。 Futures contracts calling for cash settlement are traded on various stock market indexes. The contracts may be mixed with Treasury bills to construct artificial equity positions, which makes them potentially valuable tools for market timers. Market index contracts are used also by arbitrageurs who attempt to profit from violations of the parity relationship.,Summary,外汇期货合约有好多品种，其中还包括欧洲货币指数。外汇期货的利率平价关系为： Foreign exchange futures trade on several foreign currencies, as well as on a European currency index. The interest rate parity relationship for foreign exchange futures is,Summary,其中汇率是用每单位外币的美元数标价的。如果期货价格偏离了这个价值就意味 着存在套利机会。不过，实证研究表明，通常平价关系都是满足的。 with exchange rates quoted as dollars per foreign currency. Deviations of the futures price from this value imply arbitrage opportunity. Empirical evidence, however, suggests that generally the parity relationship is satisfied.,对冲要求投资者购买那种能抵消其投资组合特殊来源风险的敏感性资产一个对冲头寸要求对冲工具能带来与要保护的头寸相反方向的收入。 Hedging requires investors to purchase assets that will offset the sensitivity of their portfolios to particular sources of risk. A hedged position requires that the hedging vehicle provide profits that vary inversely with the value of the position to be protected.,Summary,由于存在着标的商品的储存成本，所以商品期货的定价比较复杂。当投资者愿意储存商品时，用储存成本扣除便利收益，可以得到如下期货定价方程： F0P0(1rfc) 非利息的净储存成本 c，就相当于一种“负红利”。 Commodity futures pricing is complicated by costs for stor