The spot price of a non-dividend paying stock is recorded as t70 at the close of the day. You estimate that this price is equally likely to go up or down by 30% over the next nine months and observe that the continuously compounded annual risk-free rate is 20% per year across all maturities. Use a single-step binomial tree together with the mimicking portfolio approach to compute the theoretical price of a European call option written on this stock with a strike price of t55 and exactly nine months until expiration.

The spot price of a non-dividend paying stock is recorded as t70 at the close of the day. You estimate that this price is equally likely to go up or down by 30% over the next nine months and observe that the continuously compounded annual risk-free rate is 20% per year across all maturities. Use a single-step binomial tree together with the mimicking portfolio approach to compute the theoretical price of a European call option written on this stock with a strike price of t55 and exactly nine months until expiration.

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter20: Financing With Derivatives

Section20.A: The Black-scholes Option Pricing Model

Problem 1P

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Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. (a) What is the evolution of the prices of the underlying asset in time? Show it on a binomial tree.
Use the following data for a fictitiously named company OPPS to answer the questions that follow: — The current stock price S is $23. — The time to maturity T is six months. — The continuously compounded, risk-free interest rate r is 5 percent per year. — European option prices are given in the following table: Strike Price Call Price Put Price K1 = $17.5 6.00 0.10 K2 = 20 4.00 0.50 K3 = 22.5 2.00 1.00 K4 = 25 1.00 2.50 You buy a call option with strike price K2 = 20 and sell a call option with strike price of K3 = 22.5. Then which of the following statements is INCORRECT? The derivative has zero-profit when the stock price at expiration is $21.5. You have set up a call spread. You have set up a bullish spread. The maximum loss is –$2 for a stock price at expiration less than or equal to $20. The maximum profit is $0.5 for a stock price at expiration greater than or equal to $22.5.
User A European call option with a strike price of 105 will expire in two years. The current stock price is $ 100. The value of u = 1.3 and the value of d = 0.8. The annual interest rate (based on continuous compounding)is 10%. Using a three-period binomial model （a）Determine the risk-neutral probability values at each end node (Hint: draw a tree) Please draw a binomial tree！！！ Can you give me the steps （b）Find the expected value of the call in two years. （c）Find the current price of the call option.
A stock price is currently $30. It is known that at the end of one year, it will be either $36 and $24. The exercise price of a one-year European call option is $32. The risk-free interest rate is 5% per annum. a. Construct a binomial tree to show the payoff of the call option at the expiration date. b. Based on the binomial tree model, what is the value of the call option?
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.
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).
Give typing answer with explanation and conclusion Stock A is currently traded at $55. Each year, the stock price can either go up by 20% or drop by 20%. Your manager asks you to price a European call option with a strike price of $51 and a maturity of two years from now. The YTM of a one-year zero Treasury bond is 2% and the forward rate from year one to year two is 3%. What is the call option premium as of now if you use the discount rates as given in the question?
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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
Assume only two states will exist one year from today when a call on Delta Transportation, Inc. stock expires. The price of Delta stock will be either $60 or $40 on that date. Today, Delta stock trades for $55. The strike price of the call is $50. The continuously compounded risk - free rate is 9%. a. What is the tracking portfolio (\Delta and b)? b. How much are you willing to pay for the call option?
Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. What is the value of the option. Provide all necessary calculations.
We are using a two-step binomial tree to price a 6-month European put option with a strike price of $60. The current stock price is $50, the risk-free rate is 3% for all maturities. At each step, the price can increase or decrease by 20%. The continuously compounded dividend yield is 3%. What is the option price today? Group of answer choices $13.9 $9.7 $10.1 $12.8