A two-year at-the-money European put option on a stock is priced using the Black- Scholes formula. The stock pays dividend at the rate of 5% per annum and its expected rate of appreciation is 18% per annum. The volatility of the stock is 25% per annum. Given that the stock's Sharpe ratio is 0.56, calculate: (1) The elasticity of the put option. (ii) The put option's volatility.

A two-year at-the-money European put option on a stock is priced using the Black- Scholes formula. The stock pays dividend at the rate of 5% per annum and its expected rate of appreciation is 18% per annum. The volatility of the stock is 25% per annum. Given that the stock's Sharpe ratio is 0.56, calculate: (1) The elasticity of the put option. (ii) The put option's volatility.

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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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?
The stock price 6 months from the expiration of an option is $42, the exercise price of the option is $40, the risk-free rate is 10% per annum, and the volatility is 20% per annum. a) What is the price on a European call? b) What is the price of a European put? c) Check the put-call parity is satisfied.
Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. a) What is the price of the option if it is a European put?
Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.
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.
The market price of a one-year European call option is $9.243, written on a stock that is currently selling for $70. The stock is expected to go ex‑dividend in 6 months on a declared dividend of $5. The exercise price of the call is $80 and the current riskless rate of return is 3% per annum. What is the volatility (standard deviation) implied by the market price of this call option and an appropriate option pricing model allowing for dividends? Your answer should be within 2% of the correct solution (i.e., the correct σ ± .02).
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 a one-year European put option on a stock has an exercise price of $30 and oneyear European call option on the same stock has the same exercise price of $30. The call is worth 3$ and the put is worth 2$. If the one-year interest rate is 1.5%, what is the price of the underlying stock, assuming no arbitrage opportunity?
The stock price five months from the expiration of an option is $42, the exercise price of the option is $40, the continuously compounded risk-free interest rate is 11% per annum, and the volatility (o) is 21% per annum. Calculate the price of the option if it is a European call. Calculate the price of the option if it is a European put. 1. а. b.
Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is 6 months. (a) Calculate u, d, and p for a two-step tree. (b) Value the option using a two-step tree.
2. (a) Compute the price of a European call option written on a non-dividend-paying stock. The current stock price is $100 and the volatility of the stock price is 30%. The maturity of the option is in three months and the strike price is $105. The risk free interest rate with continuous compounding is 3% per annum. You should use a three step (period) binomial model to price the option. (b) The option can be replicated by a portfolio consisting of the stock and a risk-free asset. What is the replicating portfolio strategy of the call option? (c) Explain how the delta should change, as the stock price increase and check if this is indeed the case in your tree.
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?

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