Butterfly Spread with Put Options

The Butterfly Spread with Put Options involves a combination of four put options with three different strike prices (K1, K2, K3). The trader buys put options with strike prices K1 and K3 and writes twice the number of put options with strike price K2.

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

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Butterfly Spread with Put Options

The Butterfly Spread with Put Options is used when the option trader believe 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 Put Options with Underlying Asset Price in the middle

Butterfly Spread with Put Options 

 Profit from Butterfly Spread with Put Options

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

Let us assume P1 be buy-in price of put option with underlying strike price K1, P2 be writing price of put option with underlying strike price K2 and P3 be buy-in price of put option with underlying strike price K3.  The assumed price of underlying is at K2.

 Butterfly Spread with Put Options

Profit Table

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

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

In the model of Butterfly Spread using 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 Put Options with Lower Underlying Asset Price

Butterfly Spread with Put Options

 Profit from Butterfly Spread with Put Options

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

Butterfly Spread with Put Options with Higher Underlying Asset Price

Butterfly Spread with Put Options

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 Profit from Butterfly Spread with Put Options

(compute based on: call option volatility 54%, risk free rate on options 10%, K $60, K1 $45, K2 $50, K3 $55, period 6 months, present value of initial cashflow neglected, equity)

 

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