《期权基础知识》

1、.期权和波动率交易期权和波动率交易（一）期权简介（一）期权简介-谨献给大商所期货学院 .20042010年 汇福粮油集团 国际贸易公司 期货部20102011年 路易达夫北京 油籽部 2011至今 RJO北京代表处.3美国罗杰欧期货公司（R. J. OBrien & Associates, LLC.，简称RJO）创建于1914年，为O”Brien 家族所有，是目前美国最大、历史最悠久的独立期货经纪机构；公司资本雄厚且稳定，客户管理资产过36亿美元，在非金融机构中名列前茅，与各大跨国金融机构或商业公司没有任何从属关系；RJO是CME的创始成员之一，拥有近百年的从业经验，是CME集团、IC

2、E、NYSE LIFFE和芝加哥气候交易所的全面清算会员；提供最新的下单系统和24小时交易，为八万多客户（其中不乏世界最大金融、工业和农业机构）进行全球任何期货产品的执行和/或清算；严格且富有经验的风控管理使公司历经各大金融危机后仍保持增长势头。公司资产严格用于保护客户利益，不进行任何形式的杠杆交易。利用任何客户资产进行自营业务的做法是被严格禁止的；受NFA 和 CFTC 监管，并且是期货行业协会和资金管理协会的成员；曼氏破产之后，RJO被指定为过渡账户的主要接收方，再度证实了公司强大的管理能力及在业内的良好声望。美国罗杰欧期货公司简介美国罗杰欧期货公司简介.Options Classific

3、ation 期权种类 American Options (American calls & puts) 美式期权 (美式看涨、看跌期权) can be exercised Before options expiration date可在期权到期前执行 European Options (European calls & puts) 欧式期权 (欧式看涨、看跌期权) can only be exercised On options expiration date只在期权到期时执行.Types of Options 期权种类 Call 看涨期权 Buy 买入 Right to bu

4、y futures 购买期货的权利 Sell 卖出 Obligation to sell futures 出售期货的义务 Put 看跌期权 Buy买入 Right to sell futures 出售期货的权利 Sell卖出 Obligation to buy futures购买期货的义务.Options Specification期权规定 Expiration Dates 到期日 Strike Prices 执行价格 Specified by Commodity Exchange由商品交易所规定 Terminology术语 in-the-money (ITM) 实值 at-the-money

5、 (ATM) 平值 out-of-the-money (OTM) 虚值.Options Premium期权贴水 Two parts 两部分 Intrinsic Value/Exercise Value 内在价值/执行价值 Time Value 时间价值Options Premium (Total Value) = Intrinsic Value + Time Value 期权贴水 (总价值) =内在价值 +时间价值.Intrinsic Value内在价值 The positive difference between the strike price and the underlying fu

6、tures prices.期货与期权执行价之间的价差Equations 公式: for puts: Intrinsic Value = Put strike Futures对看跌期权：内在价值 =看跌执行价 期货价 for calls: Intrinsic Value = Futures Call strike对看涨期权：内在价值 =期货价看涨执行价.Call 看涨期权 in-the-money (ITM) 实值 Strike Price Futures Price 执行价格 Futures Price 执行价格 期货价格 .Put 看跌期权 in-the-money (ITM) 实值 Str

7、ike Price Futures Price 执行价格 期货价格 at-the-money (ATM) 平值 Strike Price = Futures Price 执行价格 = 期货价格 out-of-the-money (OTM)虚值 Strike Price Futures Price 执行价格 期货价格.Time Value 时间价值 Four factors affect Time Value 四因素影响时间价值 Volatility 波动率 Supply & Demand 供应及需求 Time 时间 Interest rates 利率.Options Liquidati

8、on期权清算 Offset Expire Expire Exercise 利用场地实值期权对冲期货头寸.Time Decay时间衰退$1$290 days to expire0 days to expireTime Value in an option.Factors affected Option prices影响期权价格的因素Variable 变量Call看涨期权Put看跌期权Current futures price increase现行期货价格增加+-Strike price increase执行价格增加-+Time to expiration increase距离到期时间增加+Vol

9、atility increase波动率增加+Risk-free rate 增加无风险利率增加+-.Options profit期权的利润 Calls 看涨期权 ProfitTerminal Future price0Buy a Call Sell a callXX+Premium.Options profit期权的利润 Puts 看跌期权 ProfitTerminal Future price0Buy a putSell a PutXX - Premium.Synthetics using Put-Call Parity利用看跌-看涨期权等式合成期货或期权捡钱 Long Future = Lo

10、ng Call + Short Put Short Future = Short Call + Long Put Long Call = Long Future + Long Put Long Put = Short Future + Long Call Short Call = Short Future + Short Put Short Put = Long Future + Short Call.Strategies involving a single option and a future用单个期权或期货的交易策略 Long Future, short call (payoff li

11、kes Short Put) ProfitFutures PriceX.Strategies involving a single option and a future用单个期权或期货的交易策略 Short Future, Long Call (Payoff likes Long Put) ProfitFuturesX.Strategies involving a single option and a future用单个期权或期货的交易策略 Long Future, Long Put (Payoff likes Long Call)ProfitFuturesX.Strategies inv

12、olving a single option and a future用单个期权或期货的交易策略 Short Future, Short Put (Payoff likes Long Call)XProfitFutures.Spreads 套利 Bull spreads 看涨套利 Buy a call with x1, sell a call with same expiration day with x2, while x1 = x2FT - x1x2 - FTx2 - x1x1 FT x2FT - x10FT - x1FT = x1000.Spreads 套利 Call spreads 看

13、涨套利 Buy a call with x1, sell a call with same expiration day with x2, while x1 = x2FT - x1x2 - FTx2 - x1x1 FT x2FT - x10FT - x1FT = x1000.Spreads 套利Butterfly spreads 蝶式套利 buy a call with x1, sell 2 calls with the same expiration day with x2, and buy a call with same expiration day with x3, while x1

14、x3 = x20000 x1 FT x2FT - x100FT - x1x2 FT x3FT - x10-2(FT - X2)x3 - FTFT X1 The goal being to reduce the total cost of the spread while maintaining a reasonable risk/reward profile Take advantage of high implied volatility .Combinations Straddle Buy a call and a put with the same expiration day and

15、strike price, used when the market will be very volatile in the short-term. xProfitFuturesPayoff from a straddleFutures pricerangePayoff fromcallPayoff from putoptionsTotal payoffFT xFT - x0FT - x.Combinations Strangles Buy a call and a put with the same expiration day and strike price, used when th

16、e market will not be volatile within a broadish band. x1x2ProfitFuturesPayoff from a strangleFutures pricerangePayoff fromcallPayoff from putoptionsTotal payoffFT = x10 x1 - FTx1 - FTx1 FT = x1FT - x20FT - x2.小测验 1，long call, short put, which is more bullish? 2, long put, short call, which is more b

17、earish?.Options Series TwoOptions valuation and the Greeks系列二:期权定价及期权中希腊字母简介.Options Valuation 期权价格分析The Black-Scholes Model: c = SN(d1) Xe-rTN(d2) p = Xe-rTN(-d2) SN(-d1) Where d1 = ln(S0/X) + (r + 2/2)T *sqrt(T) d2 = d1 *sqrt(T)c: call premium 看涨期权贴水 p: put premium 看跌期权贴水S: current futures price 现

18、行期权价格 e: exponential function (2.7163) 自然指数 T: time to expiration 距离到期日时间 r: continuously compounded risk free interest rate: volatility 波动率 无风险连续复利N: normal distribution 正态分布 ln: natural logarithm 自然对数.Implied Volatilities 隐含波动率 Implied Volatilities: volatility implied by an option price observed i

19、n the marketCURRENT IMPLIED VOLATILITY_ Daily published by RJO.Seasonality and Screw in Implied Volatility Grains and oilseeds exhibit a high degree of seasonality in implied volatility. This typically goes hand-in-hand with the key production periods for each crop. .Make profit by utilizing Implied

20、 Volatility, Seasonality and Screw Treat skew the same as implied volatility itself when constructing trading strategies, in that we always prefer to sell options at higher implied volatility levels and buy options at lower implied volatility levels. Example:1，资金流入做多波动率；资金流出做空波动率，资金流入做多波动率；资金流出做空波动率

21、2，天气市之前做多波动率；天气市之后做空波动率，天气市之前做多波动率；天气市之后做空波动率.The Greek letters Delta希腊字母 DeltaThe measurement of movement in an options premium relative to a move in the price of the underlying futures. A calls delta is quoted as positive and a puts as negativeAs the underlying futures price moves, so will the del

22、ta. An “at-the-money” option will move approximately one half the value of a futures move An “deep-in-the-money” will have a delta near or equal to 1.00 (-1.00) An “out-of-the-money” will have a delta approaching zero as it continuous to move in that direction.The Greek letters Delta Futures have a

23、delta of 1 Long futures = Long Delta Short Futures = Short Delta.The Greek letters Delta Call/Put delta between 0-1 Long Call = Long delta Short Call = Short delta Long Put = Short delta Short Put = Long delta.The Greek letters Delta.The Greek letters Gamma The rate at which an options delta changes

24、 as the price of the underlying futures change Gamma is greatest when at the money and moves toward 0 as it moves further out-of-the-money For underlying assets, gamma is 0.The Greek letters Gamma Gamma is highest on closest to expiration and closest to at the money strikes.The Greek letters Gamma L

25、ong call = Long gamma Short call = Short gamma Long put = Long gamma Short call = Short gamma.The Greek letters Theta The rate at which an option premium loses values as time passes, referred to as the “decay factor” Over time, an option premium loses value at an accelerated rate. The closer the opt

26、ion to at-the-money, the greater the theta nearing expiration .The Greek letters Theta Long call = long theta Short call = short theta Long put = long theta Short put = Short theta.The Greek letters Vega Vega is given in point change in theoritical value for each one percentage point change in volat

27、ility Given same type and same time, an at-the-money option always has great vega than in-the-money or out-of-the-money option. I.e, an at-the-money option is most sensitive to change in volatility.Risk Management using the Greeks Delta neutralDelta hedging 保持风险受益的稳定性 随着期货价格的变动，通过调整投资组合的delta值来控制总体头

28、寸的风险/受益:Example: f0=49,own 100,000 call options Weekfutures PriceDeltano. purchased Cost of futures purchased ($000)Cummulative Cost including interest ($000)Interest cost ($000)049.000.52252,200 2,557.8 2,557.8 2.5 148.120.458(6,400)(308.0)2,252.3 2.2 247.370.400(5,800)(274.7)1,979.8 1.9 350.250.59

29、619,600 984.9 2,996.6 2.9 451.750.6939,700 502.0 3,471.5 3.3 553.120.7748,100 430.3 3,905.1 3.8 653.000.771(300)(15.9)3,893.0 3.7 751.870.706(6,500)(337.2)3,559.5 3.4 .Risk Management using the Greeks Delta neutral应用最广 Delta hedging: NC/NF = -1/deltaThe investor owns a portfolio of futures and 100,0

30、00 call options, at Week 0, futures price at 49, strike price 50, so need 52,200 futures to make the portfolio delta neutral. At week 1, the futures price changes to 48.12, and the delta changes to 0.458 The Strategy The investor now only need 0.458 x 100,000 = 45,800 futures contracts, so he immedi

31、ately sells 52,200 45,800 = 6,400 futures contracts, over the next short period of time, the call price will tend to change by 45.8% of the futures price and the gain (loss) on the call will be offset by the loss (gain) on the futures. As time passes, delta will change and the position in the futures will have to be adjusted. For example, at week 2, the delta decrease further to 0.400, a further 5800 contracts need to be sold. .Risk Management using the Greeks Gamma NeutralMaking a portfolio Gamma neutral Delta 用于平衡期货小幅波动下的风险受益 Gamma 中性用于平衡期货大幅波动下投资组合的风险收益.Risk Management us