PRIN.OF CORPORATE FINANCE
13th Edition
ISBN: 9781260013900
Author: BREALEY
Publisher: RENT MCG
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Chapter 20, Problem 27PS
Option values You’ve just completed a month-long study of energy markets and conclude that energy prices will be much more volatile in the next year than historically. Assuming you’re right, what types of option strategies should you undertake? (Note: You can buy or sell options on oil-company stocks or on the price of future deliveries of crude oil, natural gas, fuel oil, etc.)
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Consider the following options portfolio. You write an August expiration call option on IBM with exercise price $150. You write an August IBM put option with exercise price $145.a. Graph the payoff of this portfolio at option expiration as a function of IBM’s stock price at that time.b. What will be the profit/loss on this position if IBM is selling at $153 on the option expiration date? What if IBM is selling at $160? c. At what two stock prices will you just break even on your investment?d. What kind of “bet” is this investor making; that is, what must this investor believe about IBM’s stock price to justify this position?
Consider a European call option struck "at-the-money", meaning the strike price equals
current stock price. There is one year until expiration and the risk-free annual interest
rate is r = 0.06. We define the call option's "delta" as
aCE(S,t)
A
as
Is it possible to determine whether or not the call option's delta is greater than or less
than 0.5?
Consider a put option on a stock that currently sells for £100, but may rise to £120 or
fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90.
(a) Calculate the value of the put option using the risk-neutral valuation relationship
(RNVR). Explain the reasoning behind your calculations.
Chapter 20 Solutions
PRIN.OF CORPORATE FINANCE
Ch. 20 - Vocabulary Complete the following passage: A _____...Ch. 20 - Option payoffs Note Figure 20.12 below. Match each...Ch. 20 - Option payoffs Look again at Figure 20.12. It...Ch. 20 - Option payoffs What is a call option worth at...Ch. 20 - Option payoffs The buyer of the call and the...Ch. 20 - Option combinations Suppose that you hold a share...Ch. 20 - Option combinations Dr. Livingstone 1. Presume...Ch. 20 - Option combinations Suppose you buy a one-year...Ch. 20 - Option combinations Suppose that Mr. Colleoni...Ch. 20 - Option combinations Option traders often refer to...
Ch. 20 - Prob. 11PSCh. 20 - Option combinations Discuss briefly the risks and...Ch. 20 - Put-call parity A European call and put option...Ch. 20 - Putcall parity a. If you cant sell a share short,...Ch. 20 - Putcall parity The common stock of Triangular File...Ch. 20 - Put-call parity What is put-call parity and why...Ch. 20 - Putcall parity There is another strategy involving...Ch. 20 - Putcall parity It is possible to buy three-month...Ch. 20 - Putcall parity In April 2017, Facebooks stock...Ch. 20 - Option bounds Pintails stock price is currently...Ch. 20 - Option values How does the price of a call option...Ch. 20 - Option values Respond to the following statements....Ch. 20 - Option values FX Bank has succeeded in hiring ace...Ch. 20 - Option values Is it more valuable to own an option...Ch. 20 - Option values Youve just completed a month-long...Ch. 20 - Option values Table 20.4 lists some prices of...Ch. 20 - Option bounds Problem 21 considered an arbitrage...Ch. 20 - Prob. 30PSCh. 20 - Prob. 31PSCh. 20 - Prob. 32PS
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- A put option in finance allows you to sell a share of stock at a given price in the future. 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 a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 - $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 - $1.00 =…arrow_forwardA put option in finance allows you to sell a share of stock at a given price in the future. 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 a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 – $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 – $1.00 =…arrow_forwardA put option in finance allows you to sell a share of stock at a given price in the future. 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 a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 − $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 − $1.00 =…arrow_forward
- Consider a European Call Option with a strike of 82. The current price of the underlying asset is 80, and the time to expiry is 5 months. The current market price of the option is 6.22. The risk-free rate is 4.1%. (b) You believe the true volatility is 28.4%. Is the option under-priced or overpriced? Hence what position should you take in option to make money. Explain. (Please provide Screenshots.)arrow_forwardUsing the Black-Scholes-Merton model, calculate the value of an European call option under the following parameters: The underlying stock's current market price is $30; the exercise price is $35; the time to expiry is 4 months; the standard deviation is 0.5; and the risk free rate of return is 5%. Group of answer choices $1.91 Cannot be determined from the given information. $3.91 $2.91arrow_forwardSuppose we have both a European call option and put option with an exercise price of $53 and the underlying stock is currently priced at $50. We are to note also that both options will expiry in six months. Further, market surveys suggest that the price of the stock can either go up by 20% or decrease by 25%. The current risk-free rate of interest is 2% per annum. Required: (a) What is the expected price of the underlying asset at expiry date? (b) What is the value of the call option, using the binomial model? (c) If the put option is selling for $4.80, what should be the price of the call option to avoid arbitrage?arrow_forward
- Real Options & Game Theory Consider a stock that is priced at $200 today and a call option on that stock that gives you the right but not the obligation to buy the stock at $225 in one year’s time. There are only two scenarios: either an upside, on which the price rises to $300 or a downside that leads to a drop of $100. The risk free interest rate (rf) is 8%. What is the value of this option?arrow_forwardSuppose we have both a European call option and put option with an exercise price of $53 and the underlying stock is currently priced at $50. We are to note also that both options will expiry in six months. Further, market surveys suggest that the price of the stock can either go up by 20% or decrease by 25%. The current risk-free rate of interest is 2% per annum. (a) What is the expected price of the underlying asset at expiry date? (b) What is the value of the call option, using the binomial model? (c) If the put option is selling for $4.80, what should be the price of the call option to avoidarbitrage?arrow_forwardIn a financial market a stock is traded with a current price of 50. Next period the price of the stock can either go up with 30 per cent or go down with 25 per cent. Risk-free debt is available with an interest rate of 8 per cent. Also traded are European options on the stock with an exercise price of 45 and a time to maturity of 1, i.e. they mature next period. Calculate the price of a call option by constructing and pricing a replicating portfolio.arrow_forward
- What is the value of the following call option according to the Black Scholes Option Pricing Model? What is the value of the put options? Stock Price = $62.50 Strike Price = $60.00 Time to Expiration = 9 Months = 0.75 years. Risk-Free Rate = 2.0%. Stock Return Standard Deviation = 0.45. Draw the payoff picture at expiration for a long position in a call option that has a premium of $1.75 and a strike price of $40. Draw the payoff picture for a short position in the call option given in Problem 2. Draw the payoff picture at expiration for a long position in a put option that has a premium of $3.50 and a strike price of $35. Draw the payoff picture for a short position in the put option given in Problem 4.arrow_forwardYou are interested to value a put option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it either increases to $120 or decreases to $80. The risk-free rate of interest is 10%. Calculate the put option's value using the binomial pricing model, presenting your calculations and explanations as follows: a. Draw tree-diagrams to show the possible paths of the share price and put payoffs over one year period. (Note: Show the numbers that are known and use letter(s) for what is unknown in your diagrams.) b. Compute the hedge ratio. c. Find the put option price. Explain your calculations clearly. d. Use put-call parity, find the price of a call option with the same exercise price and the same expiration date.arrow_forwardA put option in finance allows you to sell a share of stock at a given price in the future. 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 a she-month European put option for a share of stock with an exercise price of $25. tf six months later, the stock price per share is $26 more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $25-$22.50-$3.50 per share, less the cost of the option. If you paid $1.00 per put ption, then your profit would be $3.30-11.00-$2.50 per…arrow_forward
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