Arab Banking Company’s common stock has a present market price per share of $29. A 6-month call option has been written on the stock with an exercise price of $31.5. Presently the option has a market value of $3. At the end of 6 months, you estimate the market price of the stock to be $25 per share with a probability of 0.2, $29 with a probability of 0.3, $34 with a probability of 0.3, and $37 with a probability of 0.2. d. Is the above call option example is a zero sum game? Explain e. Define put option? why they use it?

Arab Banking Company’s common stock has a present market price per share of $29. A 6-month call option has been written on the stock with an exercise price of $31.5. Presently the option has a market value of $3. At the end of 6 months, you estimate the market price of the stock to be $25 per share with a probability of 0.2, $29 with a probability of 0.3, $34 with a probability of 0.3, and $37 with a probability of 0.2. d. Is the above call option example is a zero sum game? Explain e. Define put option? why they use it?

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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Arab Banking Company’s common stock has a present market price per share of $29. A 6-month call option has been written on the stock with an exercise price of $31.5. Presently the option has a market value of $3. At the end of 6 months, you estimate the market price of the stock to be $25 per share with a probability of 0.2, $29 with a probability of 0.3, $34 with a probability of 0.3, and $37 with a probability of 0.2. a. What is the expected value of share price 6 months hence? What is the expiration value of the option if that expected value of share price should ? b. What is the expected value of option price at expiration, assuming that the option is held to this time? c. Based on your answer in part b what is the payoff for call option holder and seller? d. Is the above call option example is a zero sum game? Explain e. Define put option? why they use it?
A.K. Scott’s stock is selling for $37 a share. A 3-month call on this stock with a strike price of $38 is priced at $2. Risk-free assets are currently returning 0.28 percent per month. a) What should be the price of a 3-month put option on this stock with a strike price of $38? b) Which of the two options is currently in the money and does that accord with your conclusions about their relative prices?
The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European put 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 896, and u = 1.1 and d = 0.9. O $2.24 $2.44 $2.64 $2.84
A stock has a current price of $106. An option on this stock that expires in seven months has an exercise price of $105. The stock will pay a dividend of $4.50 in four months. Assume an annualized volatility of 25% and a continuously compounded risk-free rate of 6% per annum. Use the Black-Sholes-Merton model to price this option. (In all your calculations, round the numbers to 4 decimal places.) 1) Suppose the option is a European put. Calculate the value of the put. $ Answer
The current price of a stock is $18. In 1 year, the price will be either $28 or $15. The annual risk-free rate is 3%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. X Open spreadsheet Find the price of a call option on the stock that has a strike price is of $23 and that expires in 1 year. (Hint: Use daily compounding.) Assume 365-day year. Do not round intermediate calculations. Round your answer to the nearest cent. $
A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. The stock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compounded risk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.
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
ABC stock is currently trading at R70 per share. A dividend of R1 is expected after three monthsand another one of R1 after six months. A European call option on ABC stock has a strike priceof R65 and 8 months to maturity. Given that the risk-free rate is 10% and the volatility is 32%,compute the price of the option.
The current price of a stock is $20. In 1 year, the price will be either $28 or $15. The annual risk-free rate is 7%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Find the price of a call option on the stock that has a strike price is of $25 and that expires in 1 year. (Hint: Use daily compounding.) Assume 365-day year. Do not round intermediate calculations. Round your answer to the nearest cent.
Consider a stock in two periods (two years). The stock price goes up by 30% or down by 10%in each period. Current stock price is $100. There is a European put option on the stock withexercise price $110 and time to maturity of two years. The interest rate in each period is 6%. Inthe template, Date 0 denotes today, Date 1 denotes the end of year 1 and Date 2 denotes the endof year 2. Use the two-period binomial tree model and discrete discounting to find the put optionprice on Date 0.
Assume that the current stock price is $50 per share, that call options can be purchased with an exercise price of $60 per share, that bank loans can be obtained for a 10 percent nominal rate, and that at expiration of the option in three months, the stock will either be valued at $30 or $70. Show that it is possible to replicate the stock payoff by borrowing and buying a call option.
The current price of a non-dividend paying stock is $50. Use a two-step tree to value a European put option on the stock with a strike price of $50 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 50%. What is the value of the option according to the two-step binomial model. Please enter your answer rounded to two decimal places (and no dollar sign).