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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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.)
Case:As a speculative investor, you can make profits by combining two option trades. Assume that you expect low volatility for the Delivery Hero share (currently standing at € 104.50). Combine two of the following four possible option trades, all related to Delivery Hero stock:- (1.) Long Call or (2.) Short Call as of 16.12.22, strike price € 105, option price € 5- (3.) Long Put or (4.) Short Put as of 16.12.22, strike price € 104, option price € 4. a) Which two of these four option trades are to be chosen?b) What is the maximum profit of the speculative investor in the example you have chosen?c) At which price or in which price range of the Delivery Hero share is the maximum profit achieved?d) In which price range is the speculative investor at all in the profit zone (i.e. where are the break-even points)?
European plain vanilla call options with strikes 30 and 35 on the same non- dividend paying asset with spot price $ 35 are trading for $ 11.50 and $ 7, respectively. Does arbitrage exist, and if so, how do you take advantage of it?
2. Calculate the put premium according to put-call parity which gives no arbitrage opportunity. Explain what transaction would you do if the put premium is below/above the put premium you calculated. European call option premium: c = $2 Stock price today: So- $30 Life of option: T=0.5 Risk-free rate for maturity T with continous compounding: r= 8% Strike price: K= Decide on the K value yourself (carefully). No dividends paid during life of option.
We have a 2-state, 2-period world (i.e. t = 0, 1, 2). The current stock price is 100 and the risk- free rate each period is 2%. Each period the stock can either go up by 10% or down by 10%. A European call option on this stock with an exercise price of 100 expires at the end of the second period. If the stock moves down in period 1, how would you adjust your t = 0 hedge by trading only stock? (closest answer) buy about 0.39 shares of stock sell about 0.62 shares of stock buy about 0.09 shares of stock sell about 0.39 shares of stock sell about 0.09 shares of stock buy about 0.62 shares of stock
a) Draw the payoff patterns of i) a long call position ii) a long put position. b) A stock is currently trading at $155. The volatility of the stock price is 20% per annum and the risk-free rate is 8% per annum. What is the Black-Sholes price of a one-year call option with a strike price equal to $160? Assume that the stock will pay no dividends.
A) Does this model satisfy the no-arbitrage assumption? B) Calculate the risk-neutral probabilities of up and down movements in the share price. C) Determine the no-arbitrage price of a European call option on the share with strike price K=70 and expiry time T=2.
(a) The table below gives information about European options with a maturity date of 6 months. Type Of option Strike Price Call 65 Call 58 Put 65 Premium 5 8 4 (i) Devise the payoff profile of the hedging strategy from the above for an investor betting on an increase in the stock price and calculate the payoff if the stock price increases to $66 after 6 months. (8 marks) (ii) Suppose that another investor expects a big stock price movement but is not sure of the direction. She however bets that the downward movement is more likely. Devise the corresponding trading strategy and calculate the payoff if the stock price is $55 after 6 months. (8 marks) (b) By analysing the pay off profiles of a protective put strategy and a straddle, discuss in what ways these strategies shield the investor from potential losses.
S2 Q7 Given the following American put option prices and current underlying share price of $304.75, check to see whether the given put options violate the lower bound condition. Where you dettect a violation, devise an arbitrage strategy that will yield a positive cash flow now with zero possible cash flows in the future. Strike Put price 300 7.75 305 8.15 310 8.5 315 9.05
(35) (P-C Parity Arbitrage) A European Call price is C= $ 3.50, on a ZERO dividend. A similar Put price is P= $ 2.50. The stock price S= $ 51 , strike price X= S 50 , T= 1 year, and R = 2%. (a) Determine what the CALL Price SHOULD be. (b) How much should your arbitrage profit be? (c) Focusing on Real vs. Synthetic Call, specify ALL time 0 trade details. (d) At expiration in 1 year at T, show the ending details { both if S is HIGH or LOW }.
5) A certain non-dividend paying stock is trading at $50 and its volatility is o = 25%. The risk-free interest rate is 1.25% per anuum with continuous compounding. a) Use a two-step tree (At = .5) to compute the value of 1-year European put option with strike price of $50? b) What would it be the price if the put were to be American?

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