Question

5. A put option in finance allows you to sell a share of stock in the future at a given price. There are different types of put options. A European put option allows you to sell a share of stock at a given price (called the exercise price) at a particular point in time after the purchase of the option. For example, suppose you purchase an eight-month European put option for a share of stock with an exercise price of $29. If eight months later, the stock price per share is $29 or more, the option has no value. If in six months time the stock price is lower than $29 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $29. If the price per share in eight months is $26.4, you can purchase a share of the stock for $26.4 and then use the put option to immediately sell the share for $29. Your profit would be the difference, $29-$26.4 = $2.6 per share, less the cost of the option. If you paid $1.5 per put option, then your profit would be $2.6-$1.5=$1.1 per share. a) Build a model to calculate the profit of this European put option. b) Construct a data table that shows the profit per share for a share price in eight months between $15 and $35 per share in increments of $1.

Answer #1

a. Put Option Payoff = Strike price - Cost - share price

b. Data Table

STOCK PRICE | EXERCISE PRICE | COST | PROFIT (EX PRICE - STOCK PRICE-COST) |

15 | 29 | 1.5 | 12.5 |

16 | 29 | 1.5 | 11.5 |

17 | 29 | 1.5 | 10.5 |

18 | 29 | 1.5 | 9.5 |

19 | 29 | 1.5 | 8.5 |

20 | 29 | 1.5 | 7.5 |

21 | 29 | 1.5 | 6.5 |

22 | 29 | 1.5 | 5.5 |

23 | 29 | 1.5 | 4.5 |

24 | 29 | 1.5 | 3.5 |

25 | 29 | 1.5 | 2.5 |

26 | 29 | 1.5 | 1.5 |

27 | 29 | 1.5 | 0.5 |

28 | 29 | 1.5 | -0.5 |

29 | 29 | 1.5 | -1.5 |

30 | 29 | 1.5 | -2.5 |

31 | 29 | 1.5 | -3.5 |

32 | 29 | 1.5 | -4.5 |

33 | 29 | 1.5 | -5.5 |

34 | 29 | 1.5 | -6.5 |

35 | 29 | 1.5 | -7.5 |

Suppose you construct the following European option trades on
Apple stock: purchase a put option with exercise price $83 and
premium $2.79, and purchase a call option with exercise price $95
and premium $4.19. What is your maximum dollar net loss, per
share?

A put option has an exercise price of $50 per share. Suppose you
sell the option for $2. Draw a graph of the payout on the option as
a function of the stock price. Label the graph.

A put option has an exercise price of $50 per share. Suppose you
sell the option for $2. Draw a graph of the payout on the option as
a function of the stock price. Label the graph.

A small finance company buys a European put option on Facebook
stock. The option price is $20 with a strike price of $250. The
option will expire in three months while the current spot price of
Facebook stock is $226.
a. Does the finance company have the financial right or
obligation to sell or buy the underlying share on the maturity day
of the option? Please briefly explain your answer.
b. If the spot price of Facebook share is $230...

Suppose you construct the following European option trades on
Apple stock: write a put option with exercise price $33 and premium
$1.57, and write a call option with exercise price $33 and premium
$4.29. What is your maximum dollar net profit, per share?

Consider an option on a non-dividend-paying stock when the stock
price is $30, the exercise price is $29, the risk-free interest
rate is 5% per annum, the volatility is 25% per annum, and the time
to maturity is four months. Assume that the stock is due to go
ex-dividend in 1.5 months. The expected dividend is 50 cents. Using
the Black-Scholes-Merton model, what is the price of the option if
it is a European put?

2. Suppose you purchase a put option to sell IBM common stock at
$100 per share in September. The current price of IBM is $85 and
the option premium is $10.
a. What is the intrinsic value of this option? As the expiration
date on the option approaches, what will happen to the size of the
option premium?
b. What would be in intrinsic value if this was a call
option?

Consider an option on a non-dividend-paying stock when the
stock is $ 30, the exercise price is $29. The risk â€“free rate is 5%
per annum, the volatility is 25% per annum, and the time to
maturity is four months.
(a) What is the price of the option if it is European
call?
(b) What is the price of option if it is an American
call?
(c) What is the price of the option if it is a European
put?

Suppose that a European put option has a strike price of $150
per share, costs $8 per share, and is held until maturity.
a) Under what circumstances will the seller of the option make a
profit?
b) Under what circumstances will the buyer exercise the
option?
c) Draw a diagram (or a table) illustrating how the profit from
a short position in the option depends on the stock price at the
maturity of the option.

Suppose you construct the following European option trades on
Microsoft stock:
purchase a call option with an exercise price of $28 and a premium
of $12 and
write a call option with an exercise price of $62 and a premium of
$6. What is your maximum dollar net profit, per share?

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