A stock is priced at 120 and 9-month options are written on the stock. An investor purchases a 118-strike European put for 14.08 and sells a 115-strike call for 15.57. If the force of interest is 8%, calculate this investor's total profit after 9 months given that the stock price is 123 at that time.

A stock is priced at 120 and 9-month options are written on the stock. An investor purchases a 118-strike European put for 14.08 and sells a 115-strike call for 15.57. If the force of interest is 8%, calculate this investor's total profit after 9 months given that the stock price is 123 at that time.

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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A stock trades for $45 per share. A call option on that stock has a strike price of $55 and an expiration date twelve months in the future. The volatility of the stock's returns is 44%, and the risk-free rate is 5%. What is the Black and Scholes value of this option? The Black and Scholes value of this call option is $ (Round to the nearest cent.)
You want to price an American Put option that is written on the stock of Shelby Ltd. The price of the stock is £20, the risk-free interest rate is 5%, the annualised volatility of the stock is 42% and the option expires in 5 months. Given that information, calculate the up-multiplier to be used in a nine-step binomial tree. Write your answer in decimal form with up to three decimal points Answer:
The stocks of Cee Mobile Limited is currently trading at $73 each. The call option on the company's stock has an exercise price of $70, with fifty (50) days remaining to expiration. It is assumed that the yield on treasury bills is currently 2%, while the volatility of the stock price is estimated as being 35%. Required: i. Using the Black-Scholes-Merton (BSM) model, calculate the value of the Call option, given the above parameters. Show all relevant workings. ii. Of the value computed, how much is the intrinsic value and the time value of the Call option? iii. Using the BSM model and the information given above, calculate the value of the Put option on the stock, with a similar strike price and days to expiration.
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 stock price of Chocho inc is $125. You expect the stock price a year from now to be either $134 or $86 with equal probabilities. The interest rate at which investors can borrow is 13%. Using the binomial opm, what should be the price (premium) of a call option with an exercise price of $115.00 and an expiration date one year from now?
You sell a call option on Tesla stock with an exercise price of $150.00. The option expires after one month period as soon as the option premium is $12.00. what is the profit on this option is the stock price $180 at expiration?
A stock sells for $125. A call option on the stock has an exercise price of $110 and expires in 3 months. If the interest rate is 0.15 and the standard deviation of the stock’s return is 0.30. What would be the price of a put option on the same stock with an exercise price of $140 and the same time (3 months) until expiration? Show all workings. (See Appendix for the Cumulative Normal Distribution Table) b) Let the spot rate be Yen 100 / $ and the 3-month forward rate be Yen 99/$. Compute the interest rate differential between the U.S. and Japan at which interest rate parity will hold true.
The spot price of a share of XYZ stock is $100. The annual risk-free continuously compounded interest rate is 0.07, and the stock pays no dividends. The annualized standard deviation of the continuously compounded stock return is 0.2. Find the price of a European call option on the stock with strike price $110 and that matures in 4 years.
A stock currently trades at $40, and the volatility of its return is 10%. The continuously compounded rate of interest is 12%. Consider a call option struck at $45, with 75 days to expiration (recall that there are 251 trading days in one year). a) What is the price of the option (rounded to the nearest cent)? Answer = $ . b) What is the option's delta (rounded to four decimal places)? Answer = . c) Use your answer from (b) to estimate the value of the option tomorrow, assuming the stock is trading at $40.95 at that time? Answer = $ . d) What is the exact value of the option tomorrow, assuming the stock is trading at $40.95 at that time? Answer = $ . [Note: Use software to compute the values of the normal CDF, not the table.]
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.
A stock trades for $46 per share. A call option on that stock has a strike price of $53 and an expiration date six months in the future. The volatility of the stock's returns is 45%, and the risk-free rate is 3%. What is the Black and Scholes value of this option? The Black and Scholes value of this call option is (Round to the nearest cent.)
round to nearest dollar

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