Which of the following is true? O An American call on a non-dividend paying stock will be worth more than a Europea that same stock. O A stock is equivalent to a long call, short put and long risk-free bond. The put-call parity rule for American options is stated as equalities. The time value of a call is greatest when the stock price is very high.

Which of the following is true? O An American call on a non-dividend paying stock will be worth more than a Europea that same stock. O A stock is equivalent to a long call, short put and long risk-free bond. The put-call parity rule for American options is stated as equalities. The time value of a call is greatest when the stock price is very high.

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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1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.
Consider two European call options with strike K and the same underlying non- dividend paying stock. The stock price is currently at So. Option 1 has price C₁ maturity T₁ and Option 2 has price C₂ and maturity T2, where T₂ > T₁. The risk-free interest rate is r. Use a no-arbitrage argument to prove that C₂ > C₁-
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). *
D3) Finance a) What does the option delta refer to? For a standard European put option, draw the graph of the delta as a function of the price of the underlying asset. b) You have delta hedged a long call position on a stock. The stock price drops. Explain how you would adjust your hedge
Imagine a situation where European options on some underlying stock have the following relationship. p+S > c+ K*exp(-rT). (a) Describe the arbitrage opportunities that are available with an example. (b) Now change those options to American-style options. Does the arbitrage strategy still work? Explain your answer.
In this problem, we derive the put-call parity relationship for European options on stocks that pay dividends before option expiration. For simplicity, assume that the stock makes one dividend payment of $D per share at the expiration date of the option.a. What is the value of a stock-plus-put position on the expiration date of the option?b. Now consider a portfolio comprising a call option and a zero-coupon bond with the same maturity date as the option and with face value (X + D). What is the value of this portfolio on the option expiration date? You should find that its value equals that of the stock-plus-put portfolio regardless of the stock price.c. What is the cost of establishing the two portfolios in parts (a) and (b)? Equate the costs of these portfolios, and you will derive the put-call parity relationship.
Problem 4a: State whether the following statements are true or false. In each case, provide a brief explanation. a. In a risk averse world, the binomial model states that, other things being equal, the greater the probability of an up movement in the stock price, the lower the value of a European put option.
Question Which of the following statement(s) is/are true regarding a single-period binominal model with a time period h? I) If X is the expected payoff of a European option in the real world, then the price of the option can be obtained by discounting X at the risk-free interest rate II) To calculate the risk-neutral probability of an increase in stock price, the risk premium of the stock is needed II) In the risk-neutral world, the expected stock price at time h is the forward price for the stock delivering at time h Possible Answers A 1) only B III) only C I) and II) only D 1) and III) only E None of the statement is true
3. A Consider two portfolios: Portfolio A consists of one European call option plus an zero which pays K at time T; Portfolio B consists of one European put option plus a share of the underlying stock. The stock pays no dividend. Both options have the same underlying stock, the same expiration date T and the strike price K. Graph the time-T value of both portfolios (in separate pictures) as functions of the stock price S = S(T).
Which of the following describes a situation where an American call option on a stock becomes more likely to be exercised early? Select one alternative: O All of the others. O The stock price volatility increases. O Maturity is longer. O Expected dividends increase.
Consider a European call option for a non-dividend paying stock currently priced at S(0) with strike price K at maturity T. If the price of the call C(0) at time t = 0 is greater than the stock's price S(0), then which of the following trading strategies, if any, produces an arbitrage opportunity? Select one option. Short sell a call option and use the funds to buy the stock. Invest the O remaining cash at the risk-free rate. O Buy a call option by borrowing cash at the risk-free rate. O Short sell a call option. Invest the funds at the risk-free rate. O No arbitrage opportunities exist.
Assume that the current price of a stock is S0 = 100. An investor holds long one European put option with a strike price of K = 100 and short one European call option with strike K = 105. Both options mature at the same time T. Assume that the stock price at maturity is ST = 102. What is the payoff to the investor? Select one: a. 2 b. 1 c. 0 d. -1 e. -2 f. None of the above

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