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. Thne 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. O1. 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.

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. Thne 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. O1. 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.

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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Question 2. What is the price of a European call option on a non-dividend paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is 3 months?
2
At t = 0; the price of a certain stock is S(0) = $50: At t = 1; the price is either S(1) = $80 or S(1) = $30: A certain option contract is worth $10 if the stock price is $80; and is worth $0 if the stock price is $30. Assuming no arbitrage opportunities, and continuously compounded interests of 5%; what is the price of the option at time t = 0? Please solve by hand and show all the steps of answer in order me to understand it at best :)
The price S(t) of a share follows the geometric Brownian motion S(t) = Se µt+σW(t) . The price of the share at t = 0 is S = £25 and µ = 0.1. The continuously compounded interest rate is 8%. However, the volatility σ is not known. (a) Explain the definition of implied volatility. (b) A European call option on the above share with the strike price K = £23 and expiration time of 6 months has the market price £3.1. Does the equation defining the implied volatility have a solution? [6] Hint. You are not supposed to solve the equation defining the volatility to answer this question.
The price of a European call option on a non dividend paying stock with a strike price of $79 is $8. The stock price is $75, the continuously compounded risk-free rate (all maturities) is 4.50% and the time to maturity is one year. a. What is the price of a one year European put option on the stock with a strike price of $79? (Hint: Use the Put-Call Parity Formula).
Using put-call parity formula, derive expressions for the lower bounds for European call and put options. What is a lower bound for the price of (i) a three-month call option on a non-dividend-paying stock when the stock price is R860, the strike price is R760, and the risk-free interest rate is 10% per annum? (ii) a three-month European put option on a non-dividend-paying stock when the stock price is R500, the strike price is R610, and the discrete risk-free interest rate is 9% per annum?
Optival’s stock is currently trading at $60 per share with a historical volatility of 20%. The risk-free rate is 4%. Consider a European call and put option on Optival’s stock with an exercise price of $55 that expires in 2 years. Use excel or a similar program to determine the option price using the Black-Scholes formula. (a): What is the value the European call and put option on Optival’s stock with a strike price of $60? (b): To the nearest cent, how much does the option value change for the following adjustments to the input values: ∆ in Call Value ∆ in Put Value ↑ stock price by $1 to $61 ↑ strike price by $1 to $56 ↑ the rF by 1% to 5% ↑ volatility by 1% to 21% ↑ time to maturity by 1 yr (c): Why does the value of the call increase by less than $1 when the stock price increases by $1? (d): To the nearest percent and holding all else constant, how high would the risk-free rate need to be for a 1 year increase in time to maturity to have a negative impact on the value of…
You think that there is an arbitrage opportunity on the market. The current stock price of Wesley corp. is $20 per share. A one- year put option on Wesley corp. with a strike price of $18 sells for $3.33, while the identical call sells for $7. The one-year risk- free interest rate is 8%. Assuming that the put option is fairly priced, compute the fair price of the call option and explain what you must do to exploit this arbitrage opportunity and what will be your gain.
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
4. Which of the following statements about the current value of a short European call option on Warwick plc stock, a non-dividend-paying stock, is/are true? (a) The current value of a short European call option is less than or equal to zero. (b) The current value of a short European call option decreases as the volatility of returns on Warwick plc stock increases, holding all else constant. (c) The current value of a short European call option decreases as the price of Warwick plc stock increases, holding all else constant. (a) only. (b) only. (c) only. (b) and (c) only. (a), (b) and (c). *
d. Briefly explain why you would pay more for a European call option ona (non-dividend paying) stock which has an annual return volatility of50% than for a European call on a (non-dividend paying) stock thathas annual volatility of 10% (assuming that all other variables thataffect option prices are the same for the two options.)
Suppose there is also a 1-year European put option on the same stock as in Question 3 with exercise price $30. The current stock price is also $25 and the stock price, in 1 year, will be either $35 (up by 40%) or $20 (down by 20%). The interest rate is 8%. This stock does not pay dividend. What is the value of the put option? Please use risk neutral probability method and assume discrete discounting. (2) What is put-call parity in option pricing? What needs to be true in order for put-call parity to hold?

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