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

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

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

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

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In this problem we assume the stock price S(t) follows Geometric Brownian Motion described by the following stochastic differential equation: dS = µSdt + o Sdw, where dw is the standard Wiener process and u = 0.13 and o = current stock price is $100 and the stock pays no dividends. 0.20 are constants. The Consider an at-the-money European call option on this stock with 1 year to expiration. What is the most likely value of the option at expiration? Please round your numerical answer to 2 decimal places.
Consider a 3-month European call option on a non-dividend-paying stock. The current stock price is $20, the risk-free rate is 6% per annum, and the strike price is $20. Assume a risk-neutral world. You calculate the following values using the Black-Scholes-Merton model: d1 = 0.2000 N(d1) = 0.5793 d2 = 0.1000 N(d2) = 0.5398 a) What is the probability that the call option will be exercised? b) What is the expected stock price at the option’s expiration in 3 months? Assume that all values of the stock price less than $20 are counted as zero. c) What is the expected payoff on the option at expiration (in 3 months)? d) Calculate the PV of the expected payoff from part c).
Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset … what is the value of the call option?
Consider a European call option struck "at-the-money", meaning the strike price equals current stock price. There is one year until expiration and the risk-free annual interest rate is r = 0.06. We define the call option's "delta" as aCE(S,t) A as Is it possible to determine whether or not the call option's delta is greater than or less than 0.5?
Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset ... what is the value of the call option? Call Option Price = $4.84 Call Option Price = $2.95 Call Option Price = $7.93 Call Option Price = $12.04
Consider a European call on Procter and Gamble stock (PG) that expires in one period. The current stock price is $120, the strike price is $130, and the risk-free rate is 5%. Assume that PG stock will either go up to $150 (probability = .4), or go down to $90 (probability = .6). Construct a replicating portfolio based on shares of PG stock and a position in a risk-free asset, and compute the price of the call option.
please answer as soon as possible?
Suppose that the price of a stock today is at $25. For a strike price of K = $24 a 3-month European call option on that stock is quoted with a price of $2, and a 3-month European put option on the same stock is quoted at $1.5 Assume that the risk-free rate is 10% 3. per annum. (a) Does the put-call parity hold?
please give me answer in relatable
A. Consider a stock worth K12.50 that can go up or down by 15% per period. Assume aperiod process of one. The risk-free rate is 10%. Find the value of the call optiontoday, with the strike price of K11.50. B. What is the price of a European put option on a non-dividend paying stock when thestock price is K69, the strike price is K70, the risk-free rate is 5% per annum, thevolatility is 35% per annum, and the time to maturity is 6 months?
3. A stock has a 15 percent change of moving either up or down per period and is currently priced at $25. Using a one period binomial model, and assuming that the risk-free rate is 10 percent, complete the following. a. Determine the possible stock prices at the end of the first period. b. Calculate the intrinsic values at expiration of an at-the-money European call option. c. Find the value of the option today. d. Construct a hedge by combining a position in stock with a position in the call. Show that the return on the hedge is the risk-free rate regardless of the outcome, assuming that the call sells for the value you obtained in c. e. Determine the rate of return from a riskless hedge if the call is selling for $3.50 when the hedge is initiated.
Consider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.

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