The price of a stock... The price of a stock, which pays no dividends, is $30, and the strikeprice of a three-year. The European call option on the stock is $25.The risk-free rate is 4 % (continuously compounded). Which of thefollowing is a lower bound for the option such that there are noarbitrage opportunities if the price is below the lower bound and noarbitrage opportunities if it is above the lower bound?(a) $4.98(b) $6.93(c) $5.98(d) $7.8.

Given formula:-Lower Bound=S0−K×e−rTWhere:S0 is the established current stock priceIt is worth to…

Answered: The price of a stock, which pays no…

FINANCIAL ACCOUNTING

10th Edition

ISBN:9781259964947

Author:Libby

Publisher:Libby

Chapter1: Financial Statements And Business Decisions

Section: Chapter Questions

Problem 1Q

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The current price of a non-dividend-paying stock is $100. The risk free interest rate is 1% per year with continuous compounding. The implied volatility of a one-year at-the-money European vanilla call option is 0.2. (1). What should be the implied volatility of a one-year at-the-money European vanilla put? (2). Compute the price of the put. Express your result in terms of the standard normal cdf (e.g., if you get N(0.01), just keep N(0.01) in your answer.)
(1 point) Suppose that a stock price is currently 57 dollars, and it is known that five months from now, the price will be either 17 percent higher or 17 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 54 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 7 percent. Answer = dollars.
Suppose 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.
Consider an American call and an American put with the same underlying stock share S paying no dividend, the same strike price K = $30 and the same expiration date T = 3 (months). Suppose that the stock price is $31, the risk-free interest rate is 10% per annum compounded continuously, the price of the American call option is $3, and the price of the American put option is $1. Using the no-arbitrage principle, prove that there exists an arbitrage opportunity then.
The price of a stock, which pays no dividends, is $30 and the strike price of a two-year European call option on the stock is $25. The risk-free rate is 8% (continuously compounded). Which of the following is a precise lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? Round your answer to 2 decimal places. a. $8.42 b. $8.76 c. $8.57 d. $8.70
The price of a stock, which pays no dividends, is $30 and the strike price of a three-year European call option on the stock is $27. The risk-free rate is 8% (continuously compounded). Which of the following is a precise lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? Round your answer to 2 decimal places. Question 12Answer a. $8.76 b. $8.42 c. $8.57 d. $8.70
The price of a stock, which pays no dividends, is $30 and the strike price of a three-year European call option on the stock is $27. The risk-free rate is 8% (continuously compounded). Which of the following is a precise lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? Round your answer to 2 decimal places. a. $8.76 b. $8.70 c. $8.42 d. $8.57
Suppose 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.
Without using the Black‐Scholes model, compute the price of a European put option on a non‐dividend‐paying stock with the strike price is $70 when the stock price is $73, the risk‐free interest rate is 10% pa, the volatility is 40% pa, and the time to maturity is 6 months?
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.
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.
The price of a non-dividend-paying stock is $50 and the price of a 4-month European call option on the stock with a strike price of $50 is $3. The risk-free rate is 4% per annum. The price of the corresponding 4-month European put option with same strike price is $2. Establish which of the following options is true. O I. None of the above. O II. There are arbitrage opportunities because the put-call parity relation does not hold. The arbitrage opportunity is given by selling short the put option and the stock and buying the call option. The proceeds of this strategy are invested at the risk-free rate until the expiration date. O II There are no arbitrage opportunities as the put-call parity relation holds. O IV. There are arbitrage opportunities because the put-call parity relation does not hold. The arbitrage opportunity is given by selling short the call option and borrowing money from the bank at the risk-free rate to buy the stock and put option.

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