The **Butterfly Spread with Put Options** involves a combination of four put options with three different strike prices (K_{1}, K_{2}, K_{3}). The trader buys put options with strike prices K_{1} and K_{3} and writes twice the number of put options with strike price K_{2}.

The strike price difference amongst these options is K_{2} – K_{1} = K_{3} – K_{2}

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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 K_{2} 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

Profit from Butterfly Spread with Put Options

(compute based on: call option volatility 54%, risk free rate on options 10%, K $50, K_{1} $45, K_{2} $50, K_{3} $55, period 6 months, present value of initial cashflow neglected, equity)

Let us assume P_{1} be buy-in price of put option with underlying strike price K_{1}, P_{2} be writing price of put option with underlying strike price K_{2} and P_{3} be buy-in price of put option with underlying strike price K_{3}. The assumed price of underlying is at K_{2}.

### Butterfly Spread with Put Options

Profit Table

Initial Cash Outlay = – P_{1} +2P_{2} – P_{3} (P_{1} >> P_{2} >> P_{3}); (2P_{2} >> P_{1}+ P_{3})

Underlying Price Range | Payoff from Long Put Options at K_{1} strike |
Payoff from Short Put Option at K_{2} strike |
Payoff from Long Put Options at K_{3} strike |
Total Payoffs |

S_{T} ≤ K_{1} |
0 | 0 | 0 | – P_{1} +2P_{2} – P_{3} |

K_{1} < S_{T} < k_{2} |
K_{1} – S_{T} |
0 | 0 | K_{1} – S_{T} _{ }– P_{1} +2P_{2} – P_{3} |

K_{2} < S_{T} < k_{3} |
K_{1} – S_{T} |
-2(K_{2} – S_{T }) |
0 | S_{T} – K_{3} – P_{1} +2P_{2} – P_{3} |

S_{T} ≥ K_{3} |
K_{1} – S_{T} |
-2(K_{2} – S_{T }) |
K_{3} – S_{T } |
– P_{1} +2P_{2} – P_{3} |

The price difference amongst these the options is K_{2} – K_{1} = K_{3} – K_{2}, giving K_{2} = 0.5 ( K_{1} + K_{3} )

**Three types of Butterfly Spread with Put Options can be distinguished**

- All are initially out of the money
- Some are initially out of the money and others in the money
- 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 K_{1} or above K_{3} on expiry of options. There will be profit if price of underlying is close to K_{2}.

Butterfly Spread with Put Options with Lower Underlying Asset Price

Profit from Butterfly Spread with Put Options

(compute based on: call option volatility 54%, risk free rate on options 10%, K $45, K_{1} $45, K_{2} $50, K_{3} $55, period 6 months, present value of initial cashflow neglected, equity)

Butterfly Spread with Put Options with Higher Underlying Asset Price

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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, K_{1} $45, K_{2} $50, K_{3} $55, period 6 months, present value of initial cashflow neglected, equity)

Best Options Trading for Dummies profits on Butterfly Spread with Put Options using Options Trading 101.