3 A European option on two stocks that pays atmaturity, max(0, ST1-ST2-K), is what sort ofoption?a. A call spread optionb. A put spread optionc. Worst-of rainbow calld. An option spread

Answered: A European option on two stocks that…

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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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.
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.
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. b. By observing the prices of call and put options on a stock, one can recover an estimate of the expected stock return. c. An investor would like to purchase a European call option on an underlying stock index with a strike price of 210 and a time to maturity of 3 months, but this option is not actively traded. However, two otherwise identical call options are traded with strike prices of 200 and 220 respectively, hence the investor can replicate a call with a strike price of 210 by holding a static position in the two traded calls. d. In a binomial world,if a stock is more likely to go up in price than to go down, an increase in volatility would increase the price of a call option and reduce…
Consider an european call option on a stock that is not paying dividends with the following characteristics. (i) The stock price at t = 0 is S = $30. (ii) The stricke price is $31. (iii) The volatility of the stock is 20%. (iv) The free risk interest rate is 7%. Construct a 2 period recombining Binomial tree diagram and specty tne varue or the can optron at eacn node of the tree diagram.
Which of the following statements about European option contracts is true? Question 2Answer a. Typically American options are cheaper than otherwise similar European options due to the uncertainty regarding the date of exercise. b. The price of an option can be obtained by computing the true probabilities of each state of nature, working out the expected option payoff across those states and then discounting back to the present. c. A long call position and a short put position both involve buying the underlying and so are equivalent d. One can synthesise a long forward position in the underlying by being long a call and short a put
Which of the following statements is correct? A) The gamma of a long position in a European option takes the highest value for deep in-the-money options. B) The delta of a short position in a European put is between -1 and 0. C) The delta of a long position in a deep in-the-money European put is close to zero. D) The gamma and the vega of a long position in a European put are positive. Please explain and justify your choice.
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?
An up-and-out barrier call option with barrier B, strike price K and exercise time T has payoff H(T) = (S(T) − K) + if max {S(t)| 0 ≤ t ≤ T} < B, 0 otherwise, that is, the payoff is that of a call option if the underlying stock price does not reach or exceed the barrier B at any time up to and including time T, and 0 otherwise. For an up-and-out barrier call option with barrier B = 140, strike price K = 90 and exercise time T = 3 in the binomial model with parameters U = 0.2, D = −0.1, R = 0.1 and S(0) = 100 compute the following. (a) The option price at time 0;
Let C be the price of a call option that enables its holder to buy one share of a stock at an exercise price K at time t; also, let P be the price of a European put option that enables its holder to sale one share or the stock for the amount K at time t. Let S be the price of the stock at time 0. Then, assuming that interest is continuously discounted at a nominal rate r, either S+P-C=Ke-rt or there is an arbitrage opportunity. Question: How do I verify that the strategy of selling one share of stock, selling one put option, and buying one call option always results in a positive win if S+P-C>Ke-rt ?
Use the put-call parity relationship to demonstrate that an at-the-money call option on a nondividend-paying stock must cost more than an at-the-money put option. Show that the prices of the put and call will be equal if S0 = (1 + r)T..
Consider two put options on different stocks. The table below reports the relevant information for both options: Put optionTime to maturityCurrent price of underlying stockStrike priceVolatility ( )X1 year$27$1830%Y1 year$25$2030%All else equal, which put option has a lower premium? A.Put option Y B.Put option X
Consider a portfolio that consists of the following four derivatives: 1) a put option written(sold) with strike price K − 5, 2) a call option purchased with strike price K − 5, 3) a call option written(sold) with strike price K + 5, and 4) a put option purchased at strike price K + 5. All options are European.The risk-free rate is rf , the time to expiration is T, the initial stock price is S0, and the stock price atmaturity is ST . What are the payoffs at expiration of this portfolio? What must the price of this portfoliobe?

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A European option on two stocks that pays at maturity, max(0, ST1-ST2-K), is what sort of option? a. A call spread option b. A put spread option c. Worst-of rainbow call d. An option spread