一个关于期权的问题（FLY）

A butterfly spread is one of hedging strategies that is popularly used in the options market. Your task is to construct a butterfly spread with three put options which have the same expiration date and strike prices of $55, $60, and 65. The market prices of these options are $3, $5 and $8 respectively. 1) Explain how the butterfly spread can be created. Draw a profit/loss diagram which is consisted with three put options and a profit line. You must clearly label the location of strike price of each option. 2) For what range of stock prices would the butterfly spread lead to a loss? Explain or illustrate your answer. 3) For what range of stock prices would the butterfly spread lead to a profit? Explain or illustrate your answer. 4) Between these two following economic situations: 1) Normal market situation or 2) Crisis-situation. A butterfly spread could become an appropriate option strategy for which situation, explain your choice.

我特意做了个spreadsheet给你，另外除了答题之外，这里随便说说，butterfly在交易里面简称fly, 当然还有不同的产品，像iron fly。
这是floor里面很常用的一种结构，我作了oil trading一段时间，所以给出几个我的见解:

1.fly比较便宜，比单买一个call要便宜的多。当然更重要是你的策略不同，但是对于价格，fly是很便宜的

2. fly在floor上很常见，最常见的是straddle，但是你不能说是short the fly，straddle有straddle的交易方法，straddle run, 可以很方便的check at the money vol。

3. 最后么，fly用在市场vol不大的时候用的。至少教科书上这么说。

4.还有么，hmmm，同学请你给我金币把，有什么问题直接联系我，谢谢

1) Explain how the butterfly spread can be created. Draw a profit/loss diagram which is consisted with three put options and a profit line. You must clearly label the location of strike price of each option.

Ans: Long 1 put@55, short 2 puts@60, and long 1 put @65. I have created a payoff excel, you can check the diagram in that spread sheet.

2) For what range of stock prices would the butterfly spread lead to a loss? Explain or illustrate your answer.

Ans, when the stock prices is either lower then 56, or higher then 64. It will leads the loss. The reason is that it COST 1 dollar to buy this fly ( premium = 3 - 2*5 + 8). Again, please check the spreadsheet, everything there.

3) For what range of stock prices would the butterfly spread lead to a profit? Explain or illustrate your answer.
Ans: Between 56 and 64. Check spreadsheet and see the payoff column I.

4) Between these two following economic situations:
1) Normal market situation or

In normal market situation, we assume the market is rational and the volatility is small. In this case, this benefits the buyer of the fly.

2) Crisis-situation.

In Crsis situation, the market is volatile, and sometimes one way market, in this case, the buyer will get 0 payoff from the fly, which means the buyer will lose the premium (in this example 1 dollar).

不过，为什么你认为是买入FLY, 而不是卖出呢？是因为这道题可以从两方面来答吗？