A stock that does not pay dividend is trading at $40. A European call option with strike price of $30 and maturing in one year is trading at $6. An American call option with strike price of $30 and maturing in one year is trading at $16. You can borrow or lend money at any time at risk-free rate of 5% per annum with continuous compounding. Devise an arbitrage strategy

A stock that does not pay dividend is trading at $40. A European call option with strike price of $30 and maturing in one year is trading at $6. An American call option with strike price of $30 and maturing in one year is trading at $16. You can borrow or lend money at any time at risk-free rate of 5% per annum with continuous compounding. Devise an arbitrage strategy

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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7) Consider a European call option on a -dividend-paying stock where the stock price is $40, the strıke price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. A dividend of $1 is expected in 3 months' time a. Calculate u, d̟ and p for a two-step tree b. Value the option using a two-step tree. c. Value the option with 5 time steps using DerivaGem software.
Problem 1. Assume that the interest rate is 5%, contimuously compounded annually, and consider call and put options of both American and European style expiring in 6 months on non-dividend paying stock. For each of the following scenarios, check if you can find an arbitrage opportunity and, if you can, describe it: (i) The strike price of a European put option is $3 and the option is traded at $4. (ii) The shares are traded at $3 and the American call option is traded at $3.20.
A stock is selling today for $110. The stock has an annual volatility of 64 percent and theannual risk-free rate is 7 percent.a. Calculate the fair price for a 1-year European call option with an exercise price of $95.b. Calculate how much the current stock price would need to change for the purchaser ofthe call option to break even in one year.c. Calculate the fair price for a 1 year European put option with an exercise price of $95
Without using the Black‐Scholes model, compute the price of a European put option on a non‐dividend‐paying stock with the strike price is $70 when the stock price is $73, the risk‐free interest rate is 10% pa, the volatility is 40% pa, and the time to maturity is 6 months?
A 6-month European call option on a dividend-paying stock is cur- rently selling for $1.75. The stock price is $58.56, the strike price is $55, and a dividend of $1.20 is expected in 2 months and 5 months. The risk-free interest rate is 3% per annum for all maturities. (a) What opportunities are there for an arbitrageur? Detail your answer. (b) In this market a European put option with same strike price and maturity is also available for trading. Derive the no-arbitrage $3. price of the put option if the call option has a price of c = %3D (c) The European put option in the above section is trading at $3. What opportunities are there for an arbitrageur? Detail your answer.
A stock price is currently $52. Its volatility is 35% p.a. . The risk-free interest rate is 8% p.a. with continuous compounding. What is the value of a 2-year European call option with a strike price of $55, using a 2-step binomial tree? Without doing any calculations, explain what would happen to the value of the option if the stock volatility decreases
You observe that a non-dividend paying stock currently trades for ₺150 on Borsa Istanbul. The annual standard deviation of its returns is expected to be 41% per year over the next year and the continuously compounded risk-free rate of interest is flat at 18% per year over all investment horizons. Compute the theoretical price of a European call option with a strike price of ₺200 and five months remaining until expiration written on a single share of this stock using to the Black-Scholes option pricing model
A European call option and put option on a stock both have a strike price of $20 and an expiration date in nine months. Both sell for $3. The risk-free interest rate is 15% per annum, the current stock price is $19.75, and a $1 dividend is expected in one month. Identify the arbitrage opportunity open to a trader.
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?
A European call that will expire in one year is currently trading for $3. Assume the risk-free rate (based on continuous compounding) is 5%, the underlying stock price is $60 and the strike price is $55. a. Is there an arbitrage opportunity? b. Describe exactly what a trader should do to take advantage of the arbitrage opportunity assuming it exists. c. Determine the present value of the profit that the trader can earn assuming you identify an arbitrage opportunity. Use at least four decimal places for those questions that require a numerical answer.
5) A certain non-dividend paying stock is trading at $50 and its volatility is o = 25%. The risk-free interest rate is 1.25% per anuum with continuous compounding. a) Use a two-step tree (At = .5) to compute the value of 1-year European put option with strike price of $50? b) What would it be the price if the put were to be American?
Suppose that an American put option with a strike price of $70.0 and maturity of 4.0 months costs $13.2. The underlying stock price equals 55. The continuously compounded risk-free rate is 8.5 percent per year. What is the potential arbitrage profit from buying a put option on one share of stock? 1.9783 no arbitrage profit available 3.8117 4.2693 1.80

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