期权期货复习题.doc

复习题一、单项选择题(在每题给出的4个选项中，只有1项最符合题目要求，请将正确选项的代码填入括号内)1.金融期权合约是一种权利交易的合约，其价格(C)。A.是期权合约规定的买进或卖出标的资产的价格B.是期权合约标的资产的理论价格C.是期权的买方为获得期权合约所赋予的权利而需支付的费用D.被称为协定价格【解析】金融期权是一种权利的交易。在期权交易中，期权的买方为获得期权合约所赋予的权利而向期权的卖方支付的费用就是期权的价格。2.标的物现价为179.50，权利金为3.75、执行价格为177.50的看涨期叔的时间价值为(B)。A.2B.1.75C.3.75D.5.75【解析】期权的价格即权利金是由两部分构成，一部分是内在价值（立即执行所带来的价值和0取最大），一部分是时间价值，本题内在价值为2，时间价值为3.75-2=1.753.买进执行价格为1200元/吨的小麦期货买权时，期货价格为1190元/吨，若权利金为2元/吨，则这2元/吨为(B)。A.内涵价值B.时间价值C.内在价值+时间价值D.有效价值【解析】虚值期权无内涵价值，只有时间价值。4.下列说法错误的是(B)。A.对于看涨期权来说，现行市价高于执行价格时称期权处于实值状态B.对于看跌期权来说，执行价格低于现行市价时称期权处于实值状态C.期权处于实值状态才可能被执行D.期权的内在价值状态是变化的【解析】 对于看跌期权资产现行市价低于执行价格时称为期权处于“实 值状态”。由于标的资产的价格是随时间变化的，所以内在价值也是变化的。5.期权价值是指期权的现值，不同于期权的到期日价值，下列影响期权价值的因素表述正确的是( A)。A.股价波动率越高，期权价值越大B.股票价格越高，期权价值越大C.执行价格越高，期权价值越大D.无风险利率越高，期权价值越大【解析】 B、C、D三项都要分是看涨期权还是看跌期权，不能笼统而论。6.有一项欧式看涨期权，标的股票的当前市价为20元，执行价格为20元，到期日为1年后的同一天，期权价格为2元，若到期日股票市价为23元，则下列计算错误的是(D)。A.期权空头价值为-3B.期权多头价值3C.买方期权净损益为1元D.卖方净损失为-2【解析】买方(多头)期权价值=市价-执行价格=3，买方净损益=期权价值-期权价格=3-2=1，卖方(空头)期权价值=-3，卖方净损失=-1。7.某投资者买进一份看涨期权同时卖出一份相同标的资产、相同期限相同协议价格的看跌期权，这实际上相当于该投资者在期货市场上( A)。A.做多头B.做空头C.对冲D.套利【解析】当标的资产上涨时，对该投资者有利，当标的资产下跌对该投资者不利。8.以下因素中，对股票期权价格影响最小的是(D)。A.无风险利率B.股票的风险C.到期日D.股票的预期收益率【解析】 影响期权价值的六因素：股票的当前价格，敲定价格，有效期，波动率，无风险利率，有效期内发放的红利，而股票的预期收益率不影响期权的价值9.假定IBM公司的股票价格是每股100美元，一张IBM公司四月份看涨期权的执行价格为100美元，期权价格为5元。如果股价()，忽略委托佣金，看涨期权的持有者将获得一笔利润。A.涨到104美元B.跌到90美元C.涨到107美元D.跌到96美元【答案】C【解析】股价必须涨到105美元以上才有利润,105是看涨期权的损益平衡点。10.某投资者购买了执行价格为25元、期权价格为4元的看涨期权合约，并卖出执行价格为40元、期权价格为2.5元的看涨期权合约。如果该期权的标的资产的价格在到期时上升到50元，并且在到期日期权被执行，那么该投资者在到期时的净利润为()。(忽略交易成本)。A.8.5元B.13.5元C.16.5元D.23.5元【答案】B【解析】MAX（ST-25,0)-MAX(ST-40，0)-4+2.5=(50-25-4)+2.5-(50-40)=13.5(元)。11.如果期货看涨期权的delta为0.4，意味着()。A.期货价格每变动1元，期权的价格则变动0.4元B.期权价格每变动1元，期货的价格则变动0.4元C.期货价格每变动0.4元，期权的价格则变动0.4元D.期权价格每变动0.4元，期货的价格则变动0.4元【答案】A【解析】掌握几个希腊字母的定义：delta期权价值对标的资产的变化率，Gamma是期权的delta对标的资产价格的变化率，Vega是合约价值对标的资产价格波动率的变化率，theta是价值对时间的变化率，12.Gamma指标是反映()的指标。A.与期货头寸有关的风险指标B.与期权头寸有关的风险指标C.因时间经过的风险度量指标D.利率变动的风险【答案】B13.6月1日，武钢CWB1的Gamma值为0.056，也就是说理论上()。A.当武钢股份变化1元时，武钢CWB1的Delta值变化0.056。B.当武钢股份变化1元时，武钢CWB1的Theta值变化0.056。C.当武钢股份变化1元时，武钢CWB1的Vega值变化0.056。D.当武钢股份变化1元时，武钢CWB1的Rh0值变化0.056。【答案】 A14.设S表示标的物价格，X表示期权的执行价格，则看跌期权在到期日的价值可以表示为()。A.Max0，(S-X)B.Max0，(X-S)C.X=SD.XS【答案】B15.下列不是单向二叉树定价模型的假设的是()。A.未来股票价格将是两种可能值中的一个B.允许卖空C.允许以无风险利率借人或贷出款项D.看涨期权只能在到期日执行【答案】D【解析】D项为布莱克-斯科尔斯模型的假设前提，二叉树可以给美式期权定价16.某公司的股票现在的市价是60元，有1股以该股票为标的资产的看涨期权，执行价格为63元，到期时间为6个月。6个月以后股价有两种可能：上升25%或者降低20%，则delta套期保值比率为()。A.0.5B.0.44C.0.4D.1【答案】B17.假设一种不支付红利股票目前的市价为10元，我们知道在3个月后，该股票价格要么是11元，要么是9元。如果无风险年利率为10%，那么一份3个月期协议价格为10.5元的该股票欧式看涨期权的价值为()元。A.0.30B.0.31C.0.45D.0.46【答案】A，18.某股票当前价格50元，以股票为标的物的看涨期权执行价格50元，期权到期日前的时间0.25年，同期无风险利率12%，股票收益率的方差为0.16，假设不发股利，利用布莱克一斯科尔斯模型所确定的股票看涨期权价格为()。N(0.25)=0.5987，N(0.05)=0.5199A.5.23B.3.64C.4.71D.2.71【答案】C19期货交易中套期保值的作用是()。A:消除风险B:转移风险C:发现价格D:交割实物答案B20.下面关于交易量和持仓量一般关系描述正确的是( )。A: 只有当新的买入者和卖出者同时入市时，持仓量才会增加，同时交易量下降B: 当买卖双方有一方作平仓交易时，持仓量和交易量均增加C: 当买卖双方均为原交易者，双方均为平仓时，持仓量下降，交易量增加D: 当双方合约成交后，以交割形式完成交易时，一旦交割发生，持仓量不变答案C 如果交易双方签订一个新合约，那么未平仓合约数增加1个。如果交易双方就同一个合约进行平仓，那么未平仓合约数减少一个。如果一方订立一个新合约，而另一方同时将已有合约平仓，那么未平仓合约数不变。 二 Explanation 名词解释speculators wish to take a position in the market.Either they are betting that a price will go up or they are betting that it will go down. They use derivatives to get extra leverageHedgers are interested in reducing a risk that they already face. Arbitrage involves locking in a risk-less profit by entering simultaneously into transactions in two or more markets. A call option gives the holder the right to buy an asset by a certain date for a certain price. Put option: A put option gives the holder the right to sell an asset by a certain date for a certain price. Futures （forward）contract: It is an agreement to buy or sell an asset for a certain price at a certain time in the future.short selling: The investors broker borrows the shares from another clients account and sells them in the usual way. To close out the position the investor must purchase the shares. The broker then replaces them in the account of the client from whom they were borrowed.In-the-money option：it would lead to a positive cash flow to the holder if it were exercised immediately.risk-neutral valuation: Firstly, assume that the expected return from the stock price is the risk-free rate r, then calculate the expected payoff from the option, at last, discounting the expected payoff at the risk-free rate Factors affecting stock option pricing: stock price, strike price, risk-free interest rate, volatility, time to maturity, and dividends. bottom vertical strangle: a bottom vertical strangle can be created by buy a put with lower strike prices and buy a call with higher strike prices. Bull spreads: A bull spread can be created using two call options with the same maturity and different strike prices. The investor buys the call option with the lower strike price and shorts the call option with the higher strike price. Bull spreads can also be created by buying a put with a low strike price and selling a put with a high strike price.Bear spreads: A bear spread can be created by selling a call with one lower strike price and buying a call with another higher strike price Butterfly spreads: A butterfly spread involves positions in options with three different strike prices: buying two call options with strike prices X1 and X3, and selling two call options with a strike price X2, X1 X2 X3三 .Explain the differences between forward contract and futures contract?Private contract between 2 partiesExchange tradedNon-standard contractStandard contractUsually 1 specified delivery dateRange of delivery datesSettled at maturitySettled dailyDelivery or final cashsettlement usually occursContract usually closed outprior to maturityFORWARDSFUTURES四 .Explain the differences between exchanged traded and Over-the- counter ? Exchange Traded standard products trading floor or computer trading virtually no credit risk Over-the-Counter non-standard products telephone market some credit risk五答：公司X的比较优势在浮动利率投资，而需要的是固定利率投资；公司Y的比较优势在固定利率投资，而需要的是浮动利率投资，因此存在互换的基础。固定利率差为0.8，浮动利率差为0，因此互换总的获利为0.8。已知银行获利0.2，则两公司各获利0.3。即公司X实际上以8.3的固定利率投资，Y实际上以LIBOR+0.3的浮动利率投资。互换安排如下图：8.38.8LIBORLIBOR8.5LIBOR公司X银 行公司Y六 解：公司A的比较优势在英镑而需要美元借款，公司B相反，因此存在互换的基础。英镑上的利差为0.4，美元上的利差为0.8，因此互换的总获利为0.4。已知银行获利0.1，则两个公司各获利0.15。因此A实际上以6.85的利率借美元，而B实际上以10.45的利率借英镑。在银行承担所有市场风险的情况下，互换安排如下图：美元6.85美元6.2英镑11英镑11美元6.2英镑10.45公司A银 行公司B1）互换收益的分配在公司A、公司B和银行间的比例分别为 35%、35%、30%。如何设计 ？2）若分配比例为50%、25%、25%，如何设计 ？美元6.86美元6.2英镑11英镑11美元6.2英镑10.46公司A银 行公司B美元6.8美元6.2英镑11英镑11美元6.2英镑10.5公司A银 行公司B七 基于同一股票的看跌期权有相同的到期日.执行价格为$70、$65和$60，市场价格分为$5、$3和$2. 如何构造蝶式差价期权.请用一个表格说明这种策略带来的盈利性.股票价格在什么范围时，蝶式差价期权将导致损失？ 八 基于同一股票的有相同的到期日敲定价为 $70的期权市场价格为 $4. 敲定价$65 的看跌期权的市场价格为 $6。解释如何构造底部宽跨式期权.请用一个表格说明这种策略带来的盈利性.股票价格在什么范围时，宽跨式期权将导致损失？ 答案： buy a put with the strike prices $65 and buy a call with the strike prices $70, this portfolio would need initial cost $10. The pattern of profits from the strangle is the following:Stock Price RangePayoff from Long PutPayoff from Long CallTotal PayoffTotal ProfitsST 6565- ST065- ST55 - ST65 ST 70000-10ST 700ST-70ST-70ST-80当50ST w1 = 400, w2 = 6,000, w3 =-3240. =The portfolio can be made gamma,vega and delta neutral by including long: (1) 400 of the first traded option (2) 6,000 of the second traded option. And short 3240 underlying asset. 11 1）证明在风险中性环境下，到期的欧式看涨期权被执行的概率为 ,2） 使用风险中性定价原理，假设股票1的价格和股票2的价格分别服从几何布朗运动，且独立，给到期损益为如下形式的欧式衍生品定价： Solution: Since Since Where , 12、Use two-step tree to value an American 2-year put option on a non-dividend-paying stock, current stock price is 50, the strike price is $52, and the volatility of stock price is 30% per annum, the risk-free interest rate is 5% per annum. （保留2位小数）In this case, S=50, X = 52, = 0.3, t =1, r=0.05 , the parameters necessary to construct the tree are , 91.11067.40.93502507.4337.0414.96 27.4424.56 14 If a stock price, S, follows geometric Brownian motion1) What is the process followed by the variable ? Show that also follows geometric Brownian motion.2)The expected value of ST is . What is the expected value of ?3) The varaince of ST is .What is the variance of ?4) Using risk-neutral valuation to value the derivative, whose payoff at maturity is1)We now use Itos lemma to derive the process followed by ,Define , So that also follows geometric Brownian motion. 2) . , 3) Since and varaince of ST is .Similarly, by We get the varaince of is 14、 In a risk-neutral world, suppose stock prices follow geometric Brownian motion1) What is the process followed by the variable by Itos lemma? Show that also follows geometric Brownian motion.2) The expected value of is . What is the expected value of ?4) Using risk-neutral valuation to value the derivative, whose payoff at maturity is 15. Show that the probability that a European call option will be exercised in a risk-neutral world is, . Using risk-neutral valuation to value the complicated digtial option whose payoff at maturity is