Butterfly Spread with Call Options

The Butterfly Spread with Call Options involves a combination of four call options with three different strike prices (K1, K2, K3). The trader buys a call option with strike price at K1 and at strike price K3 and writes two call options with strike price K2.

The strike price difference amongst these options is such that K2 – K1 = K3 – K2.

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Butterfly Spread with Call Options

The Butterfly Spread with Call Options is used when the trader believes that the price of underlying asset will stay close to the strike price of K2 on expiry of the Butterfly Spread. The presumption is all options should expire on the same time.

 Butterfly Spread with Call Options with Underlying Asset Price in the middle

 Butterfly Spread with Call Options

 Profit from Butterfly Spread with Call Options

(compute based on: call option volatility 54%, risk free rate on options 10%, K $55, K1 $45, K2 $50, K3 $55, period 6 months, present value of initial cashflow neglected, equity)

In the model of Butterfly Spread with Call Options, there will be a loss resulting from initial cash outlay if underlying asset prices comes in below K1 or above K3 on expiry of options. There will be profit if price of underlying is close to K2.

Butterfly Spread with Call Options 

Profit Table

Initial Cash Outlay = – P1 +2P2 – P3 (P1 >> P2 >> P3); (2P2 >> P1+ P3)

Underlying Price Range Payoff from Long Call Options at K1 strike Payoff from Short Call Option at K2 strike Payoff from Long Call Options at K3 strike Total Payoffs
ST ≤ K1 0 0 0 – P1 +2P2 – P3
K1 < ST < k2 ST – K1 0 0 ST – K1 – P1 +2P2 – P3
K2 < ST < k3 ST – K1 -2(ST – K2) 0 K3– ST – P1 +2P2 – P3
ST ≥ K3 ST – K1 -2(ST – K2) ST – K3 – P1 +2P2 – P3

 

The price difference amongst these the options is K2 – K1 = K3 – K2, giving K2 = 0.5 ( K1 + K3 )

Three types of Butterfly Spread with Call Options can be distinguished

  1. All are initially out of the money
  2. Some are initially out of the money and others in the money
  3. All are initially in the money

 Butterfly Spread with Call Options with Lower Underlying Asset Price

 Butterfly Spread with Call Options

 Profit from Butterfly Spread with Call Options

(compute based on: call option volatility 54%, risk free rate on options 10%, K $40, K1 $45, K2 $50, K3 $55, period 6 months, present value of initial cashflow neglected, equity)

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In the above model of Butterfly Spread with Call Options, there will be a loss resulting from initial cash outlay if underlying asset price swings wider than band given by K1- – K2 =K2  – K3 on expiry of options.

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