Problem 1. Assume that the interest rate is 5%, contimuously compounded annually, and considercall and put options of both American and European style expiring in 6 months onnon-dividend paying stock. For each of the following scenarios, check if you can findan arbitrage opportunity and, if you can, describe it:(i) The strike price of a European put option is $3 and the option is traded at $4.(ii) The shares are traded at $3 and the American call option is traded at $3.20.

Arbitrage is a trading strategy capitalizing on price differences between related financial…

Answered: roblem 1. Assume that the interest rate…

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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The current price of a non-dividend-paying stock is $25. Over the next six months it is expected to rise to $30 or fall to $21. An investor buys put options with a strike price of $27. What is the value of each option? The risk-free interest rate is 5% per annum with continuous compounding. Answer to 3dps. Group of answer choices 1.578 2.840 3.018 0.935
Suppose that a stock price is currently 51 dollars, and it is known that one month from now, the price will be either 6 percent higher or 6 percent lower. Find the value of an American call option on the stock that expires one month from now, and has a strike price of 49 dollars. Assume that no arbitrage opportunities exist, and a risk free interest rate of 10 percent
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You are given the following information about the stock of Company ABC: Share price $80 risk free rate of interest is 6%, time to expiration is 6 months, annualised standard deviationis 0.5 and exercise price is $85. Calculate the appropriate call value of the stock according to the Black-Scholes option pricing formula. (Show your workings in full) Calculate an appropriate put premium. (Show your workings in full)
6. A 4-month European call option on a dividend paying stock is selling for C = $4. So = $54, K = $50. A dividend of $0.90 is expected in 2 months. r = .12. Assume continuous discounting. Are there opportunities for arbitrage? Explain and show these opportunities.
3. Consider a European call option on a non-dividend paying stock with exercise price 100 USD and expiration in one month. Interest rate is 1 percent and volatility of the stock is 0.4. Stock price 90 USD. Option price?? Use excel.
You observe the price of a European put option that expires in nine months and has a strike price of$45 is $3. The underlying stock price is $49.50. The term structure is flat, with all risk-free interestrates being 8%.a. What is the price of a European call option that expires in nine months and has a strike priceof $45? b. You observe next that the price of the call option (in part (a)) in the market is $9.59. Statewhy an arbitrage opportunity exists and explain how you would take advantage of thisopportunity. (Hint: answer should include an outline general strategy, net cost ofstrategy at initiation and net profit at expiration using the numbers in the question)
A stock is currently selling for $30. Over the next two periods, the stock will move up by a factor of 1.13 or down by a factor of 0.82 each period. A call option with a strike price of $29 is available. If the risk-free rate of Interest is 3.2 percent per period, what is the value of the call option? Note: Do not round Intermediate calculations. Round your answer to 2 decimal places. Answer is complete but not entirely correct. Value of the call option 1.55 x
You have written (sold) a three-month European call option at a strike price of $500. The current stock price (So) is $492.00, the annual risk-free interest rate is 4%, and the volatility of the underlying is 10%. Construct a delta hedge of this position using the underlying asset. Report your answer in the number of shares of the underlying purchased/sold. (Positive values indicate a purchase, negative a short)
The price of an American call on a non-dividend paying stock is $2. The stock price is $15.50, the strike price is $15, the expiration date is in 6 months, and the risk free interest rate is 4% continuously compounded. Which of the following is correct, regarding the option premium of an American put on the stock with a strike price of $15 and an expiration date in 6 months? a. The upper bound for the price of the American put is $14.70 and the lower bound is $0 b. The lower bound for the price of the American put is 0 and the upper bound is $1.50 c. The lower bound for the price of the American put is $1.20 and the upper bound is $1.50
Suppose that a June call option to buy a share for $65 costs $3.5 and is held until June. Under what circumstances will the holder of the option make profit Under what circumstances will the option be exercised? Draw a diagram showing how the profit on a long position in the option depends on the stock price at the maturity of the option.
A stock is currently priced at $42 and will move up by a factor of 1.23 or down by a factor of .91 each period over each of the next two periods. The risk-free rate of interest is 3 percent. What is the value of a put option with a strike price of $49? (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Value of a put option

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