Suppose that you noticed the following prices: C=$12; S-$60; X-$50, for a one year European call option. The simple risk-free interest rate is 10% per year. Is there an arbitrage profit opportunity here? Yes or no? If yes, how would you exploit it? If no, explain why not. PS: In all questions above X denotes the exercise price of the options, C-call premium, P-put premium, and S-stock price.

Suppose that you noticed the following prices: C=$12; S-$60; X-$50, for a one year European call option. The simple risk-free interest rate is 10% per year. Is there an arbitrage profit opportunity here? Yes or no? If yes, how would you exploit it? If no, explain why not. PS: In all questions above X denotes the exercise price of the options, C-call premium, P-put premium, and S-stock price.

International Financial Management

14th Edition

ISBN:9780357130698

Author:Madura

Publisher:Madura

Chapter11: Managing Transaction Exposure

Section: Chapter Questions

Problem 35QA

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Similar questions

1. Suppose that, in each period, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0. c) Assuming the strike price of a European call option on this security is $90, compute the possible payoffs of the call option given that the option expires in two periods.
Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.
Eagletron’s current stock price is $10. Suppose that over the current year, the stock price will either increase by 100% or decrease by 50%. Also, the risk-free rate is 25% (EAR). a) What is the value today of a one-year at-the-money European put option on Eagletron stock?b) What is the value today of a one-year European put option on Eagletron stock with a strike price of $20?c) Suppose the put options in parts a and b could either be exercised immediately, or in one year. What would their values be in this case?
Consider a 2-year EUROPEAN PUT with a strike price of $65 on a stock whose current stock price is $60. Suppose that there are two time steps, and in each time step the stock price either moves up by 20% or moves down by 20%. Also suppose that risk-free rate is 5% per annum with continuous compounding . What is the value of the European put option?
Consider a 3-month European call option on a non-dividend-paying stock. The current stock price is $20, the risk-free rate is 6% per annum, and the strike price is $20. Assume a risk-neutral world. You calculate the following values using the Black-Scholes-Merton model: d1 = 0.2000 N(d1) = 0.5793 d2 = 0.1000 N(d2) = 0.5398 a) What is the probability that the call option will be exercised? b) What is the expected stock price at the option’s expiration in 3 months? Assume that all values of the stock price less than $20 are counted as zero. c) What is the expected payoff on the option at expiration (in 3 months)? d) Calculate the PV of the expected payoff from part c).
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.)
Suppose you pay 10 to buy a European (K=100, t=2) call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is 110.
The price of a European call option on a stock with a strike price of $50.9 is $5.6. The stock price is $40.1, the continuously compounded risk-free rate (all maturities) is 5.2% and the time to maturity is one year. A dividend of $0.6 is expected in six months. What is the price of a one-year European put option on the stock with a strike price equal to the call's strike price? Please state the formula and steps, thanks
User A European call option with a strike price of 105 will expire in two years. The current stock price is $ 100. The value of u = 1.3 and the value of d = 0.8. The annual interest rate (based on continuous compounding)is 10%. Using a three-period binomial model （a）Determine the risk-neutral probability values at each end node (Hint: draw a tree) Please draw a binomial tree！！！ Can you give me the steps （b）Find the expected value of the call in two years. （c）Find the current price of the call option.
6. Suppose that stock price is $21, the exercise price is $23, the risk-free interest rate is 4% per annum, the price of a three-month European call option is $1.5. What will be the price of three-month European put option on the stock?
Consider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.
Assume the spot Swiss franc is $0.7015 and the six-month forward rate is $0.6980. What is the Value of a six-month call and a put option with a strike price of $0.6815 should sell for in a rational market? Assume the annualized six-month Eurodollar rate is 3.50 percent. Assume the annualized volatility of the Swiss franc is 14.20 percent. Use the European option-pricing models to value the call and put option. This problem can be solved using the FXOPM.xls spreadsheet. (Do not round intermediate calculations. Round your answers to 2 decimal places.)