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1、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 Com
2、modity 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,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E
3、0。 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 great
4、er 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
5、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
6、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 inter
7、national 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 Posit
8、ions,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
9、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
10、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
11、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 $135m
12、illion in the market for one month and, to minimize trading costs, chooses to buy the S 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 follo
13、ws 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 an
14、d 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
15、 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 con
16、tracts. 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 = .8S 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
