股票交易策略--潘登同学的期权、期货及其他衍生品学习笔记
- 可能的策略
Potential Strategies
- 债券 + 期权 Bond + Options
- 股票 + 期权 Stock + Options
- 两个或多个相同类型的期权 Two or more options of the same type
- 两个或多个不同类型的期权 Two or more options of different types
保本债券 Principal-Protected Notes
用零息债券加一份看涨期权，看涨期权的行权价等于零息债券面值，到期时，可以获得下列两部分收益
- 零息债券面值(保本)
- 股票标的增长超过行权价的部分
A Bond
- 𝑟 = 6% 𝐶𝑜𝑛𝑡. 𝐶𝑜𝑚𝑝.
- 𝐵𝑇 = \$1000
- 𝑇 = 3
- $𝐵_0 = \$1000 ∗ 𝑒^{−6\%∗3} = \$835.27$
- $𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑆_𝑇 − 𝑆_0 = \$164.73$
An European Call Option
- 𝑐 = \$16.473
- $S_0=\$80$
- K=\$100
- T=3
$$ \text{购买1份债券, 购买10份看涨期权}\ 期初： 835.27+10*16.473 = 1000 \ 期末：\begin{cases} 1000,\text{if } S_T < 100\ 10S_T,\text{if } S_T > 100\ \end{cases} $$
- 投资者可以在不承担任何本金风险的情况下建立风险头寸 Investors can build risky positions without taking any principal risk
产品生存能力取决于 Product viability depends on
- 股息水平 Dividend level
- 利率水平 Interest rate level
- 投资组合的波动性 Portfolio Volatility
标准产品的变化 Standard Product Variations
- 价外行使价 Out-of-the-money strike price
- 投资者回报上限 Investor Return Cap
- 退出机制，平均特征等 Exit mechanism, average characteristics, etc.
期权与股票策略
根据Put-Call Parity
$$ c+D+Ke^{-rT}=p+S_0 $$
- 备保看涨期权承约(做多股票，做空看涨期权。 股票多头保护看涨期权的损失)
Writing Covered Call
- 组合A: Long Stock + Short Call Option $\Rightarrow$ Short Put Option $$ S_0 - c = -p +D+Ke^{-rT} $$
- 组合B: Short Stock + Long Call Option $\Rightarrow$ Long Put Option $$ -S_0 + c = p -D-Ke^{-rT} $$
- 保护看跌期权(做多股票，做多看跌期权)
Protective Put
- 组合C: Long Stock + Long Short Option $\Rightarrow$ Long Call Option $$ S_0 + p = c +D+Ke^{-rT} $$
- 组合D: Short Stock + Short Short Option $\Rightarrow$ Short Call Option $$ -S_0 - p = -c -D-Ke^{-rT} $$
差价
差价交易策略是指将相同类型的两份或多份期权(即两份或多份看涨期权，或者两份或多份看跌期权)组合在一起的交易策略。
牛市差价 - 看涨期权 Bull Spread - Call Options
口诀： 买贵卖便宜 (所以看涨期权构建的牛市差价需要启动资金) 核心思路： 买一份低行权价的看涨期权，卖一份高行权价的看涨期权，两份期权的期限相同。
其payoff如下
| Stock price range | Payoff from long call option | Payoff from short call option | Total Payoff |
|---|---|---|---|
| $S_T\leq K_1$ | 0 | 0 | 0 |
| $K_1 < S_T < K_2$ | $S_T-K_1$ | 0 | $S_T-K_1$ |
| $S_T\geq K_2$ | $S_T-K_1$ | $-(S_T-K_2)$ | $K_2-K_1$ |
- 𝑡 = 0
- Long: $c_1 = 3$; $T_1 = 3$ 𝑚𝑜𝑛𝑡ℎ𝑠;$K_1 = 30$
- Short: $c_2 = 1$; $T_2 = 3$ 𝑚𝑜𝑛𝑡ℎ𝑠;$K_2 = 35$
- What are the potential profits?
| Stock price range | Profit |
|---|---|
| $S_T\leq 30$ | -2 |
$30| $S_T-32$ |
|
| $S_T\geq 35$ | 3 |
在市场上有三种不同类型的牛市差价:
- 两份看涨期权最初均为虚值期权。
- 一份看涨期权最初为实值期权，另一份看涨期权为虚值期权。
- 两份看涨期权最初均为实值期权。 第一种牛市差价最为激进，这一策略的成本很低，收到高收益($=K_2-K_1$)的概率也很小。当我们从类型(1) 换到类型(2)，从类型(2) 换到类型(3)时，牛市差价逐渐趋于保守。
牛市差价 - 看跌期权 Bull Spread - Put Options
口诀： 买便宜卖贵 (所以看跌期权构建的牛市差价期初现金流为正，但需要保证金，期间收入为0或负) 核心思路： 买一份低行权价的看跌期权，卖一份高行权价的看跌期权，两份期权的期限相同。
熊市差价 - 看跌期权 Bear Spread - Put Options
口诀： 买贵卖便宜 (所以看跌期权构建的熊市差价需要启动资金) 核心思路： 买一份高行权价的看跌期权，卖一份低行权价的看跌期权，两份期权的期限相同。
其payoff如下
| Stock price range | Payoff from long put option | Payoff from put call option | Total Payoff |
|---|---|---|---|
| $S_T\leq K_1$ | $K_2-S_T$ | $-(K_1-S_T)$ | $K_2-K_1$ |
| $K_1 < S_T < K_2$ | $K_2-S_T$ | 0 | $K_2-S_T$ |
| $S_T\geq K_2$ | 0 | 0 | 0 |
- 𝑡 = 0
- 𝐿𝑜𝑛𝑔: $p_1 = 3$; $T_1 = 3$ 𝑚𝑜𝑛𝑡ℎ𝑠;$K_1 = 35$
- 𝑆ℎ𝑜𝑟𝑡: $p_2 = 1$; $T_2 = 3$ 𝑚𝑜𝑛𝑡ℎ𝑠;$K_2 = 30$
- What are the potential profits?
| Stock price range | Profit |
|---|---|
| $S_T\leq 30$ | 3 |
$30| $33-S_T$ |
|
| $S_T\geq 35$ | -2 |
熊市差价 - 看涨期权 Bear Spread - Call Options
口诀： 买便宜卖贵 (所以看涨期权构建的熊市差价期初现金流为正，但需要保证金，期间收入为0或负) 核心思路： 买一份高行权价的看跌期权，卖一份低行权价的看跌期权，两份期权的期限相同。
牛市差价与熊市差价总结
- 一般普通的牛市差价都是用看涨期权构建，普通的熊市差价都是用看跌期权构建。 都可以记为买贵卖便宜。
- 如果用看跌期权构建牛市差价，则与用看跌期权构造熊市差价相反；记为买便宜卖贵。
- 如果用看涨期权构建熊市差价，则与用看涨期权构造牛市差价相反；记为买便宜卖贵。
盒式差价 Box Spread
- 牛市差价 (看涨期权) + 熊市差价 (看跌期权) Bull Spread (Call Option) + Bear Spread (Put Option)
- 如果所有的期权都是欧式的，那么一个盒式差价的价值就是两个执行价格差值的现值 If all options are European, then the value of a box spread is the present value of the difference between the two strike prices
其payoff如下 (profit应该为0)
| Stock price range | Payoff from bull call spread | Payoff from bear put spread | Total Payoff |
|---|---|---|---|
| $S_T\leq K_1$ | 0 | $K_2-K_1$ | $K_2-K_1$ |
| $K_1 < S_T < K_2$ | $S_T-K_1$ | $K_2-S_T$ | $K_2-K_1$ |
| $S_T\geq K_2$ | $K_2-K_1$ | 0 | $K_2-K_1$ |
蝶式差价 - 看涨期权 Butterfly Spread - Call Option
- 买入一份执行价格为$K_1$的看涨期权 Buy 1 call option with strike price $K_1$
- 卖出两份执行价格为$K_2$的看涨期权 Sell 2 call options with a strike price of $K_2$
- 买入一份执行价格为$K_3$的看涨期权 Buy 1 call option with strike price $K_3$
$K_1,K_2,K_3$的关系为 $$ K_2 = 0.5(K_1+K_2) $$
其payoff如下
| Stock price range | Payoff from first long call | Payoff from second long call | Payoff from short calls | Total Payoff |
|---|---|---|---|---|
| $S_T\leq K_1$ | 0 | 0 | 0 | 0 |
| $K_1 < S_T \leq K_2$ | $S_T-K_1$ | 0 | 0 | $S_T-K_1$ |
| $K_2 < S_T \leq K_3$ | $S_T-K_1$ | 0 | $-2(S_T-K_2)$ | $K_3-S_T$ |
| $S_T \geq K_3$ | $S_T-K_1$ | $S_T-K_3$ | $-2(S_T-K_2)$ | 0 |
蝶式差价 - 看跌期权 Butterfly Spread – Put Option
- 买入一份执行价格为$K_1$的看跌期权 Buy 1 put option with strike price $K_1$
- 卖出两份执行价格为$K_2$的看跌期权 Sell 2 put options with a strike price of K_2$
- 买入一份执行价格为$K_3$的看跌期权 Buy 1 put option with strike price $K_3$
日历差价 - 看涨期权 Calendar Spreads - Call Options
- 两份看涨期权 2 call options
- 买入 (长期)+卖出 (短期) Buy (long term) + Sell (short term)
- 执行价格相同 Same execution price
- 到期日不同 Different due dates
在日历差价的盈利图形中通常假设日历差价的盈利实现是在短期限期权的到期日，而且同时对长期限期权清仓。
为了理解日历差价的盈利形式，
- 我们首先考虑在短期限期权到期时，股票价格很低的情形。这时短期限期权的价值为0，长期限期权的价格也接近于0。因此，此时投资者的损失等于建立日历差价的最初费用。
- 接下来我们考虑当短期限期权到期时，股票价格 $S_T$很高的情形。短期限期权给投资者带来的支付为 $S_T-K$，长期限期权的价值接近 $S_T-K$，这里K为期权的执行价格。这时投资者的净损失量也与建立日历差价时的初始费用很接近。
- 如果 $S_T$接近于K，短期限期权给投资者带来的费用或者为0或者很小，但是长期限期权仍很有价值，这时投资者会得到可观的利润。
日历差价 - 看跌期权 Calendar Spreads - Put Options
- 两份看跌期权 2 put options
- 买入 (长期)+卖出 (短期) Buy (long term) + Sell (short term)
- 执行价格相同 Same execution price
- 到期日不同 Different due dates
跨式组合 Straddle
- 同时买入看涨期权与看跌期权
Simultaneously purchase call and put options
- 执行价格相同 Same execution price
- 到期日相同 Same due date
其payoff如下
| Stock price range | Payoff from call | Payoff from put | Total Payoff |
|---|---|---|---|
| $S_T\leq K$ | 0 | $K-S_T$ | $K-S_T$ |
| $S_T > K$ | $S_T-K$ | $0$ | $S_T-K$ |
序列组合与带式组合 Strips & Straps
- 序列组合 Strips
买入1份看涨期权与2份看跌期权 Buy 1 call and 2 puts
- 执行价格相同 Same execution price
- 到期日相同 Same due date
带式组合 Straps
- 买入2份看涨期权与1份看跌期权
Buy 2 calls and 1 put
- 执行价格相同 Same execution price
- 到期日相同 Same due date
异价跨式组合 Strangle
- 买入一份执行价格为$K_1$的看跌期权 Buy a put option with strike price $K_1$
- 买入一份执行价格为$K_2$的看涨期权 Buy a call option with strike price $K_2$
其payoff如下
| Stock price range | Payoff from call | Payoff from put | Total Payoff |
|---|---|---|---|
| $S_T\leq K_1$ | 0 | $K_1-S_T$ | $K-S_T$ |
$K_1| 0 |
$0$ |
$0$ |
|
| $S_T\geq K_2$ | $S_T-K$ | $0$ | $S_T-K$ |
其他收益形式 Other Payoffs
当执行价格接近时 when the strike price approaches
- 蝶式差价可以提供由小“尖峰”组成的回报 Butterfly spreads can provide returns made up of small "spikes"
- 如果具有所有执行价格的期权都可用
If options with all strike prices are available
- 则可以（至少近似地）通过组合从不同蝶形价差获得的峰值来创建任何收益形式 then it is possible (at least approximately) to create any form of return by combining peaks obtained from different butterfly spreads
- 即蝶式期权可以构造Arrow Debreu市场
returns made up of small "spikes"
- 如果具有所有执行价格的期权都可用
If options with all strike prices are available
- 则可以（至少近似地）通过组合从不同蝶形价差获得的峰值来创建任何收益形式 then it is possible (at least approximately) to create any form of return by combining peaks obtained from different butterfly spreads
- 即蝶式期权可以构造Arrow Debreu市场