Describe and explain the use and payoff functions of spread strategies, including bull spread, bear spread, calendar spread, butterfly spread, and diagonal spread

A spread strategy is a position with two or more options of the same type (i.e., two or more calls; or, two or more puts).

… bull spread (type of vertical spread)

buy (long) a call option and sell (short) a call option on the same stock (and same expiration) but with a higher strike price. In this example, long call (strike = $20, premium = $1.99) + short call at higher strike (strike = $23, premium = $0.83)
Features of bull spread:

• Net debit but outlook is bullish

… Bear spread (type of vertical spread)

Buy (long) a call option call option and sell (short) a call option on the same stock (and same expiration) but with a lower stock price. In this example, bear spread: long put (strike = $23, premium = $2.93) + short put at lower strike (strike = $20, premium = $1.20)
Features of bear spread:

• Net debit but outlook is bearish

… Butterfly spread (sideway strategy)

Buy a call option at low strike price K1, buy a call option with high strike price K3, and sell two call options at strike price K2 halfway between K1 and K2. In this example, the butterfly spread: Long call (strike @ $18, premium = $3.21), long call (strike @ $22, premium = $1.13 ), short two calls (strike @ $20, premium = $1.99)

Features of butterfly spread:

• Expects low volatility (range-bound), Capped risk

… Calendar spread

In a calendar spread, the options have the same strike price but different expiration dates. The calendar spread can be created with calls or puts.
Two calls: sell a call option with strike price K1 and buy a call option with same strike price K1 but with a longer maturity term
Two puts: sell a put option with strike price K1 and buy a put option with same strike price K1 but with a longer maturity term

Short call with 1 year maturity (strike = $20, premium = $1.99) +Long call with 1.25 year maturity (strike = $20, premium = $2.27)

… Diagonal spread

In a diagonal spread, both the expiration date and the strike price of the calls are different.

… Box spread

A box spread is a combination of a bull call spread with strike prices K1 and K2 and a bear put spread with the same two strike prices. The payoff from a box spread is always K2 – K1.
The value of the box spread is always the present value of its payoff or (K2-K1)*EXP(-rT).

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