# More option spreads

In this article, we cover more complex option strategies that involve options on the same underlying asset at the same expiration, but at different strike prices. In particular, we will discuss call butterfly spreads, straddles, and strangles.

Below we will use the following notation:Â *C(K, T)*Â refers to a call position at strike priceÂ *KÂ *and expiration timeÂ *T*, and similarly,Â *P(K, T)*Â refers to a put position with strike priceÂ *KÂ *and expiration timeÂ *T*.

**Straddle**

The long straddle has theÂ payoff function shown above, and is constructed with the call positionÂ *C(K, T)Â *and put position P*(K, T)*. In this example,Â *K=100*, so this strategy would be constructed by going longÂ *C(100, T)*Â and longÂ *P(100, T).*

This strategy is typically used when investors expect the price of the underlier to experience a large change in either direction in a specific period of time, or that the volatility of the underlier will remain high or increase.

**Strangle**

Closely related to the straddle is the strangle. A long strangle has the payoff function shown above, and is constructed with the call positionÂ *C(K + Î”K, T)Â *and put position*Â P(K -Î”K, T).*Â In this example,Â *K=100Â *andÂ *Î”K=25*, So, this strategy could be constructed by buying bothÂ *C(125,T)*Â andÂ *P(75,T)*. Note that the premium is at leastÂ *Pâ‚€ =Â *50.

This strategy is typically used when investors expect the price of the underlier to experience a large change in either direction in a specific period of time, or that the volatility of the underlier will remain high or increase. Compared to the straddle, the strangle costs less but incurs greater risk as the underlying must move a greater amount for the investor to profit.

**Long call butterfly spread**

The butterfly spread has the payoff function shown above and is constructed with the two long call positionsÂ *C(K -*Î”*K, T)Â *andÂ *C(K +Â *Î”*K, T)*, with Î”*K>0Â *in combination with the short position -2*C(K, T).Â *In the example above,Â *K=100Â *and Î”*K=*50, so this spread would be constructed by going long (buying)Â *C(50 , T)*Â andÂ *C(150, T)*Â and going short (selling)Â *2 * C(100, T).*

This strategy is typically used when investors expect the price of the underlier to remain near its current price within the specified time frame, or that the volatility (the extent to which the price of the underlier is varying with time) will remain low or decrease.

**Further Reading**

The strategies covered in this post cover more complex option strategies and illustrate the varied payoff possibilities that options enable, as well as the particular scenarios in which they profit. In a future post, we will cover more advanced strategies involving options of varying expiration dates. These are often termed calendar spreads or horizontal spreads. Stay tuned!