Investments
11th Edition
ISBN: 9781259277177
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 21, Problem 39PS
Summary Introduction
To calculate: The Black-Scholes value of the option when the risk-free interest rate is 0.5% p.m. and stock’s volatility = 7% p.m.
Introduction:
Black-Scholes value of the option: It is one of the pricing models which are used to compute the theoretical value of a put or call option. This model considers variables such as volatility, underlying stock price, strike price, risk-free rate and type of option in its calculations.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
XYZ Corp. will pay a $2 per share dividend in two months. Its stock price currently is $60 per share. A call option on XYZ has an exercise price of $55 and 3-month time to expiration. The risk-free interest rate is .5% per month, and the stock’s volatility (standard deviation) = 7% per month. Find the Black-Scholes value of the option. (Hint: Try defining one “period” as a month, rather than as a year, and think about the net-of-dividend value of each share.)
XYZ Corp. will pay a $2 per share dividend in 2 months. Its stock price currently is $72 per share. A call
option on XYZ has an exercise price of $65 and 3-month time to expiration. The risk-free interest rate is
0.3% per month, and the stock's volatility (standard deviation) = 12% per month. Find the pseudo-American
option value. (Hint: Try defining one "period" as a month, rather than as a year.) (Round your answer to 2
decimal places. Omit the "$" sign in your response.)
Pseudo-American option value
XYZ Corporation will pay a $2 per share dividend in two months. Its stock price currently is $80 per share. A European call option on
XYZ has an exercise price of $75 and 3-month time to expiration. The risk-free interest rate is 0.95% per month, and the stock's
volatility (standard deviation) - 18 % per month. Find the Black-Scholes value of the option. (Hint: Try defining one "period" as a month,
rather than as a year, and think about the net-of-dividend value of each share.)
Note: Round your answer to 2 decimal places.
Black-Scholes value of the option
Chapter 21 Solutions
Investments
Ch. 21 - Prob. 1PSCh. 21 - Prob. 2PSCh. 21 - Prob. 3PSCh. 21 - Prob. 4PSCh. 21 - Prob. 5PSCh. 21 - Prob. 6PSCh. 21 - Prob. 7PSCh. 21 - Prob. 8PSCh. 21 - Prob. 9PSCh. 21 - Prob. 10PS
Ch. 21 - Prob. 11PSCh. 21 - Prob. 12PSCh. 21 - Prob. 13PSCh. 21 - Prob. 14PSCh. 21 - Prob. 15PSCh. 21 - Prob. 16PSCh. 21 - Prob. 17PSCh. 21 - Prob. 18PSCh. 21 - Prob. 19PSCh. 21 - Prob. 20PSCh. 21 - Prob. 21PSCh. 21 - Prob. 22PSCh. 21 - Prob. 23PSCh. 21 - Prob. 24PSCh. 21 - Prob. 25PSCh. 21 - Prob. 26PSCh. 21 - Prob. 27PSCh. 21 - Prob. 28PSCh. 21 - Prob. 29PSCh. 21 - Prob. 30PSCh. 21 - Prob. 31PSCh. 21 - Prob. 32PSCh. 21 - Prob. 33PSCh. 21 - Prob. 34PSCh. 21 - Prob. 35PSCh. 21 - Prob. 36PSCh. 21 - Prob. 37PSCh. 21 - Prob. 38PSCh. 21 - Prob. 39PSCh. 21 - Prob. 40PSCh. 21 - Prob. 41PSCh. 21 - Prob. 42PSCh. 21 - Prob. 43PSCh. 21 - Prob. 44PSCh. 21 - Prob. 45PSCh. 21 - Prob. 46PSCh. 21 - Prob. 47PSCh. 21 - Prob. 48PSCh. 21 - Prob. 49PSCh. 21 - Prob. 50PSCh. 21 - Prob. 51PSCh. 21 - Prob. 52PSCh. 21 - Prob. 53PSCh. 21 - Prob. 1CPCh. 21 - Prob. 2CPCh. 21 - Prob. 3CPCh. 21 - Prob. 4CPCh. 21 - Prob. 5CP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Similar questions
- Mansukharrow_forwardABC 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.arrow_forwardThe current price of a stock is $15. In 6 months, the price will be either $18or $13. The annual risk-free rate is 6%. Find the price of a call option on thestock that has a strike price of $14 and that expires in 6 months. (Hint: Usedaily compounding.)arrow_forward
- The Moon company currently sells for 100 $. The annual stock price volatility is %10 and risk- free interest rate %8, the price of a call on a company’s stock with strike price 200 $ and time period 2 months. Find the stock option price with Black and Scholes Model. If option market value 320 $ what is the option strategy?arrow_forwardXYZ stock is currently traded at $40. Consider a put option on XYZ with $38 exercise price expiring in 6 months. Estimate the price of the option using two-period BOPM. Assume the stock price can go up by 10% and down by 15% each period (i.e., (6 months) / (2 periods) = 3 months). The annual risk-free interest rate is 6%. please use excel and show formulas. thanks!arrow_forwardA 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.arrow_forward
- 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. $1.28arrow_forwardA 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.arrow_forwardConsider a 4-month forward contract for which the underlying asset is a stock index with value of 3, 825.97 and a continuous dividend yield of 0.5% Assume the continuous risk-free annual interest rate is 4.5%, a. Determine the no arbitrage forward price. $ Round your answer to the nearest cent b. Calculate the value of a long position if 2 month(s) later the index changes to 3, 825.97 and the risk-free rate is still 4.5% $ Round your answer to the nearest centarrow_forward
- The stock price of BellsNWhistles is currently trading at $120. Over each of the next two six-month periods it is expected to go up by 15% or down by 15%. The risk-free rate is 5% per annum with continuous compounding. There are no dividends due over the life of the option. Use the binomial model of option pricing to compute: (i) the price of a European call option with a strike price of €125. (ii) the price of an American call option with a strike price of €125. (iii) the price of a European put option with a strike price of €125. (iv) the price of an American put option with a strike price of €125.arrow_forwardThe current price of a stock is $20, and at the end of one year its price will be either $22 or $18. The annual risk-free rate is 2.0% (use daily compounding with 365 days/year), based on daily compounding. A 1-year call option on the stock, with an exercise price of $19, is available. Based on the binominal model, what is the option's value?(Please Show Work)arrow_forwardA call option is currently selling for $4.2. It has a strike price of $85 and three months to maturity. The current stock price is $87, and the risk-free rate is 5.7 percent. The stock will pay a dividend of $1.3 in two months. What is the price of a put option with the same exercise price?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
EBK CONTEMPORARY FINANCIAL MANAGEMENTFinanceISBN:9781337514835Author:MOYERPublisher:CENGAGE LEARNING - CONSIGNMENT
EBK CONTEMPORARY FINANCIAL MANAGEMENT
Finance
ISBN:9781337514835
Author:MOYER
Publisher:CENGAGE LEARNING - CONSIGNMENT
Accounting for Derivatives Comprehensive Guide; Author: WallStreetMojo;https://www.youtube.com/watch?v=9D-0LoM4dy4;License: Standard YouTube License, CC-BY
Option Trading Basics-Simplest Explanation; Author: Sky View Trading;https://www.youtube.com/watch?v=joJ8mbwuYW8;License: Standard YouTube License, CC-BY