Question

A trader creates a long strangle with put options with a strike price of $90 per share, and call options with a strike of $105 per share by trading a total of 40 option contracts (buy 20 put contracts and buy 20 call contracts). Each contract is written on 100 shares of stock. The put option is worth $10.5 per share, and the call option is worth $6.5 per share.

A) What is the value of the strangle at maturity as a function of the then stock price?

B) What is the profit of the strangle at maturity as a function of the then stock price? Make sure to derive the exact range of then stock prices where the trade is profitable.

Answer #1

Payoff from a strangle,

Range of Stock Price | Payoff from Call | Payoff from Put | Total Payoff |

S<=K_{1} |
0 | K_{1}-S |
K_{1}-S |

K_{1}<S<K_{2} |
0 | 0 | 0 |

S=>K_{2} |
S-K_{2} |
0 | S-K_{2} |

Where, K_{2} = call strike price, K_{1}= Put
Strike price, K_{2}> K_{1}, S= Stock price at
maturity

Contracts | Strike Price | Price | Cost |
---|---|---|---|

20 | 105 | 6.5 | -13000 |

20 | 90 | 10.5 | -21000 |

S | 65 | 73 | 85 | 90 | 98 | 105 | 110 | 122 | 140 |

20 (Call) | 0 | 0 | 0 | 0 | 0 | 10000 | 34000 | 70000 | |

20 (Put) | 50000 | 34000 | 10000 | 0 | 0 | 0 | 0 | 0 | 0 |

Value | 50000 | 34000 | 10000 | 0 | 0 | 0 | 10000 | 34000 | 70000 |

Cost | -34000 | -34000 | -34000 | -34000 | -34000 | -34000 | -34000 | -34000 | -34000 |

Profit | 16000 | 0 | -24000 | -34000 | -34000 | -34000 | -24000 | 0 | 36000 |

**When Stock price is S<73 or S>122, this trade is
profitable**

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