Suppose that Stock XYZ is currently trading at $50 and does not pay any dividends. Using abinomial tree with two periods, we would like to price a European down-and-in call optionwritten on this stock with a strike price of $40, barrier level of $48 and expiration date inthree months. Assume that annual continuously compounded interest rate is 5% and thevolatility of the stock is 20% per year. What is the price of the barrier option?0.7.280.9.45O101O 322

Interest Rate - The percentage of the principal that the lender charges for the usage of its funds…

Answered: Suppose that Stock XYZ is currently…

FINANCIAL ACCOUNTING

10th Edition

ISBN:9781259964947

Author:Libby

Publisher:Libby

Chapter1: Financial Statements And Business Decisions

Section: Chapter Questions

Problem 1Q

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Suppose that Stock XYZ is currently trading at $50 and does not pay any dividends. Using a binomial tree with two periods, we would like to price a European call option with a strike of $50 and a maturity of six months. Assume that annual continuously compounded interest rate is 1% and the volatility of the stock is 30% per year. What is the value of q? 0.5565 0.4709 0.5000 0.3401 0.5000. You selected this answer.
Suppose that Stock XYZ is currently trading at $50 and does not pay any dividends. Using a binomial tree with two periods, we would like to'price a European down-and-in call option written on this stock with a strike price of $40, barrier level of $48 and expiration date in three months. Assume that annual continuously compounded interest rate is 5% and the volatility of the stock is 20% per year. What is the price of the barrier option? 1.01 9.45 3.22 7.28
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.
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?
Suppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1-year eective annual interest rate is 10%. (a) Graph the payo and prot diagrams for a forward contract on XYZ stock with a forward price of $55. (b) Is there any advantage to investing in the stock or the forward contract? Why? (c) Suppose XYZ paid a dividend of $2 per year and everything else stayed the same. Now is there any advantage to investing in the stock or the forward contract? Why?
The current price of a non-dividend paying stock is $30. Use a two -step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when the volatility is 20%? (Hint: Calculate u and d using the CRR approach.) A. $1.48 B. $1.08 C. $1.68 D. $1.28
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.
Assume the price of an non-dividend stock is $40, the annual volatility of the stock is 20%, and the continuous compound risk-free interest rate is 5%. What's the price of a European put option on this stock with delivery price of $40 with 1-year expiration? (The standard normal distribution table is in the attachment or you can use excel function NORMSDIST, and please keep the results with 3 decimal places.) (BS Model-Option Pricing)
3. Consider a non-dividend paying stock whose initial stock price is 62 and has a log- volatility of σ = 0.20. The interest rate r = 10%, compounded monthly. Consider a 5-month option with a strike price of 60 in which after exactly 3 months the purchaser may declare this option a (European) call or put option. Assume u = 1.05943 and d = = 0.94390 (a) Compute the values of the binomial lattice for 5 1 month period. 0 1 2 3 4 5 62 (b) Compute the appropriate risk-free rate. (c) Find the risk-neutral probability p of going up? (d) Find the values of call option and put option along this lattice: 0 5.85 1 2 3 4 5 call option 0 1 2 3 4 5 1.40 put 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).
A European put option on a non-dividend paying stock has strike price of $40 and time to maturity 9 months. Assume the risk-free interest rate is 5% per annum, the volatility is 20% per annum and the current stock price is $38. Using the Black-Scholes model, calculate the price of the European put option.
Consider an American call and an American put with the same underlying stock share S paying no dividend, the same strike price K = $30 and the same expiration date T = 3 (months). Suppose that the stock price is $31, the risk-free interest rate is 10% per annum compounded continuously, the price of the American call option is $3, and the price of the American put option is $1. Using the no-arbitrage principle, prove that there exists an arbitrage opportunity then.

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