International Financial Management
14th Edition
ISBN: 9780357130698
Author: Madura
Publisher: Cengage
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An investor buys a European call option at a price of 7.6 yuan. The stock price is 52 yuan and the strike price is 55 yuan. Under what circumstances will the investor make a profit ? Under what circumstances will the option be executed ? Draw a diagram of the relationship between investor profitability and stock price at maturity.
Suppose 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?
Suppose 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?
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- Write and describe the Black-Scholes formulas for pricing European call and put options. The stock price three months from the expiration of an option is R1040, the exercise price of the option is R1000, the risk-free interest rate is 11% per annum, and the volatility is 22% per annum. Calculate the prices of European call and put options.arrow_forwardSuppose that a stock price is currently 35 dollars, and it is known that four months from now, the price will be either 51 dollars or 29 dollars. Find the value of a European call option on the stock that expires four months from now, and has a strike price of 39 dollars. Assume that no arbitrage opportunities exist and a risk-free interest rate of 10 percent.Answer =dollars.arrow_forwardA put option and a call option written on the same stock will expire in three months. They both have an exercise price of $45. And they sell for $2.65 and $5.23, respectively. If the underlying stock is currently selling at $47.30, what is the effective annual interest rate? Assume that both options are European options, and that compounding is not continuous.arrow_forward
- 1. Consider an option on a non-dividend paying stock when the stock price is $30, the exercise price is $28, the annual interest rate is 5%, the annual volatility is 25%, and the time to maturity is 6 months. Show the details of your calculations. a) What is the price of the option if it is a European call?arrow_forwardConsider a European call option on DELL that has an exercise price of $100 and four months (14%) until expiration. The annual risk-free rate of interest is 0.07%, compounded continuously. DELL call option and stock are priced at $5.79 and $97.80 per share, respectively, today. (a) Compute today’s value of a European put option on DELL that has the same exercise price and expiration date as the above call option on DELL. Show numerically which option has a higher time value of option. (b) Compute the profit to the writer of the in/at/out of (circle one) money put option if DELL stock is priced at $95.0 when the option expires. (c) Suppose that DELL has 10 million shares of common stock outstanding, and issues one million warrants that each can be exchanged for 2 shares of common stock. The warrant has the same exercise price and expiration date as the above call option on DELL. (i) Compute the value of each warrant that is in/at/out of (circle one) money. (ii) If you currently own 1,000…arrow_forwardStock options, gold options and index options are examples of options where the underlying assets are stocks, gold and stock market index, respectively. What is the difference between European and American option? Are European options available exclusively in Europe and American options available exclusively in the United States? You own a call option on Intuit stock with a strike price of RM36. The option will expire in exactly three months’ time. If the stock is trading at RM46 in three months, what will be the payoff of the call? If the stock is trading at RM32 in three months, what will be the payoff of the call? Draw a payoff diagram showing the value of the call at expiration as a function of the stock price at expiration. Suppose that a June put option to sell a share for RM10 costs RM2 and is held until June. Under what circumstances will the seller of the option make a profit? Under what circumstances will the option exercised?arrow_forward
- 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. a) What is the price of the option if it is a European put?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
- You are considering a European put option and a European call option on ABC Ltd and have available the following information. The put option with an exercise price of $15 and time to maturity of 60 days is priced at $2.00. The call option with the same exercise price and time to maturity is priced at $3.00. The underlying asset price is $15. The risk-free rate is 2% per 60 days. Could an arbitrage profit be earned? If so, how much the arbitrage profit is? Show your works (Hint: use discrete put-call parity equation and consider two scenarios for stock price at maturity of the options: $10 or $20).arrow_forward. A European put option written on a non-dividend paying stock that is currently worth ₺100 in the stockmarket has a strike price of ₺100 and exactly five months left until its expiration date. If the continuouslycompounded annual risk-free rate is observed as 20% per year across all maturities and the put option iscurrently priced at ₺3.20 in the option market, what should be the theoretical price of a European call optionwritten on the same stock that has the same strike price and expiration date as the put option described?arrow_forwardSuppose that a stock price is currently 56 dollars, and it is known that five months from now, the price will be either 22 percent higher or 22 percent lower. Find the value of a European put option on the stock that expires five months from now, and has a strike price of 55 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 6 percent.arrow_forward
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