A stock is currently selling for $61.5 per share. A Europcan call option with an strike price of $65 sells for $5.62 and expires in 3 months. If the risk-free rate of interest is 2.6% per year, compounded continuously, what is the price of a European put option with the same strike price and same expiry time.

A stock is currently selling for $61.5 per share. A Europcan call option with an strike price of $65 sells for $5.62 and expires in 3 months. If the risk-free rate of interest is 2.6% per year, compounded continuously, what is the price of a European put option with the same strike price and same expiry time.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? What is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put–call parity.
A 4-month European call option on a stock (with dividend) is currently selling for RM5. The price of the stock is RM64 and the strike price is RM60. The risk-free interest rate is 12% p.a. A dividend of RM0.80 is expected one month from now. Is there any arbitrage opportunities? Show your working. How much is the profit/loss if at maturity the price of the stock is higher than the strike price? How much is the profit/loss if at maturity the price of the stock is lower than the strike price?
The stock price is currently $100. Over each of the next two six-month periods, it is expected to go up by 20% or down by 20%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? What is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put-call parity.
A European put option written on a non- dividend paying stock that is currently worth ₺100 in the stock market has a strike price of ₺100 and exactly five months left until its expiration date. If the continuously compounded annual risk-free rate is observed as 20% per year across all maturities and the put option is currently priced at ₺3.20 in the option market, what should be the theoretical price of a European call option written on the same stock that has the same strike price and expiration date as the put option described?
A 6-month European put option on a stock with a strike price $63 is selling for $2, the current stock price is $65, and the stock will pay a dividend of $0.51 in 3 months. The 3-month risk-free rate is 8% per annum with quarterly compounding, and the 6-month risk-free rate is 10% per annum with semiannual compounding. What is the price of a 6-month European call option on the stock with the same strike price?
A stock price is currently $30. It is known that at the end of one year, it will be either $36 and $24. The exercise price of a one-year European call option is $32. The risk-free interest rate is 5% per annum. Construct a binomial tree to show the payoff of the call option at the expiration date.
What is the price of a European put option on a non-dividend paying stock when thestock price is K69, the strike price is K70, the risk-free rate is 5% per annum, thevolatility is 35% per annum, and the time to maturity is 6 months?
Suppose that the price of a stock today is at $25. For a strike price of K = $24 a 3-month European call option on that stock is quoted with a price of $2, and a 3-month European put option on the same stock is quoted at $1.5 Assume that the risk-free rate is 10% 3. per annum. (a) Does the put-call parity hold?
The price of a (non-dividend) stock is $21 and the price of a 3-month European call option on the stock with a strike price of $20 is $2. The risk-free rate is 4% per annum with continuous compounding. What is the price of a 3-month European put option with a strike price of $20?
A stock price is currently $30. It is known that at the end of one year, it will be either $36 and $24. The exercise price of a one-year European call option is $32. The risk-free interest rate is 5% per annum. a. Construct a binomial tree to show the payoff of the call option at the expiration date. b. Based on the binomial tree model, what is the value of the call option?
The price of a European call option on a stock with a strike price of $49.38 is $6. The stock price is $52.43, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is 1 year. A dividend of $1.32 is expected in 8 months. What is the price of a 1-year European put option on the stock with a strike price of $49.38?
. 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?

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